smart-structures-and-materials-2017

198 S. Storm and J. Kirn

Fig. 10.2 Actuator force during deployment (cruise position 0°- droop position 17°, simulation)

each spanwise kinematic station, consequently all main levers show the same axis
of rotation and uniform kinematic connection to the drive actuator. Hence, the
overall system fulfills the requirement of a simple actuation system by firstly cre-
ating and secondly exploiting the advantage of synergies.

Regarding a single spanwise kinematic station, the main lever is in fact an
interconnection of several levers (r1, r2 and r3) to a single structural component. The
main lever is linked on one side to the overall drive chain DC by using the strut l3,
whereas the spherical bearings of this strut allow an out of plane rotational
movement. One huge benefit of this drive mechanism is that the necessary actuator
forces are remarkably minimized by supporting the introduced loads by means of
the inner structure. This is the result of the varying gearing factor, determined by
the angle between the cross link and the drive-chain. At drooped position a right
angle between the cross link and drive chain is designed, which reduces the actuator
forces theoretical to zero, see Fig. 10.2. On the other side the main lever is linked to
the skin by using the struts l1 and l2, which are attached inside of the stringers at the
skin brackets. The measure of locating the load introduction points LIP1 and LIP2
inside of the stringers increases the limited design space and, therefore, enables a
better kinematic design [13].

10.3 Computational Modeling

10.3.1 Numerical Optimization

For optimization purposes the kinematic system is simplified to a reduced sub-
system that consists of a single load introduction point K linked by a lever kine-
matics l and r with the actuation system DC. A crucial factor is the main lever,
which ensures same rotational angle for all kinematic subsystems. Independent of
its actuation the rotatory movement of the main lever is responsible for simulta-
neous and uniform deformation of the skin, which is predefined by the trajectories

10 Towards the Industrial Application of Morphing Aircraft … 199

of the load introduction point (provided by project partner DLR). The mathematical

formulation of the optimization problem uses discrete-time positions of

LIP-trajectories as input parameter, the kinematic points K and M as independent
variable and the rotational angle α as dependent output variable, as shown in
Fig. 10.3. As the structural conditions limit the position of the axis of rotation M to
a small area and a large rotational angle α is desirable to achieve low bending
moment, the position M and the angle α are given manually apriori. By this means,
the inner optimization loop is considered to apply the quadratic deviation of the
calculated rotational angle from the target rotational angle (αcalculated − αtarget)2 as
the optimization function is merely dependent on the position of the kinematic point
K. A helpful secondary condition, to fulfill the requirement of simultaneous and
uniform deformation of the skin, is given by the variances of all rotational angles at

the same time step. The sum of the variances is added to the optimization function

Fig. 10.3 Simplification of the kinematic station by a crank mechanism with an eccentrically
mounted shaft

200 S. Storm and J. Kirn

by a weighting factor under the assumption that at each position the variance is
equally important. Depending on the weighting factor the result of the optimization
can be focused on achieving small deviations between the different lever kinematics
either at a special droop angle and/or at a certain range of droop angles [14]. If the
result of the inner optimization loop leads to undesirable results like length of struts
too short, crossing struts or angle between skin and struts out of range (70°–110°),
then the target rotational angle has to be adapted or even the axis of rotation M has
to be changed.

In the literature this kind of lever kinematics is described as a crank mechanism
with an eccentrically mounted shaft [15]. The difference to the presented problem is
that the offset q between the rotational axis M and motion direction p is so large that
no complete rotation of the lever r is possible. Actually, only a pivoting motion is
necessary to move the load introduction point from cruise position Xc to droop
position Xd. The distance from the top dead center OB to a random load intro-
duction point B is described by the equation

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð10:1Þ
x = ðl + rÞ2 − q2 − l ⋅ cos β + r ⋅ cos φ.

Although the notation of this Eq. (10.1) is fairly simple, it is hardly possible to

transform it in an appropriate form to solve the optimization problem. The reason

for this is that further dependencies would have to be taken into account. Firstly the
rotational angle α is the result from the difference of φ associated to Kc and Kd.
Further the angles β (also associated to Kc and Kd) depend on the parameters q, r, l
and α. And finally, although the distance between the positions Xc and Xd remains
constant the value x for these positions is changing depending on the position OB
(which in turn is depending on the parameter r and l). Taking into consideration all

mentioned dependencies the core equation becomes exceptionally complex and

would not be the best way to solve this problem.

A novel approach has to be taken for the numerical optimization. An applicable

equation for the numerical optimization is established based on the law of cosines
for arbitrary triangles. The equation calculates the rotational angle α by using the
distance formula in the Cartesian coordinate system, it is described with

α = σ − ε, o r
r2 + b2 − l2 r2 + b2 − w2
α = arccos 2⋅r⋅b − arccos 2⋅r⋅b , with ð10:2Þ

r = KcM = r′, l = KcXc = l′, b = XdM, and w = KcXd

The improvement of this approach is, that the rotational angle α is directly

derived from the kinematic points Kc and M for the given load introduction points
at cruise position Xc and droop position Xd, as illustrated in Fig. 10.4.

The drawback of the presented numerical approaches is, that the kinematic point
Kc could not be derived for a given rotational angle α and axis M. Especially the
dependency of the rotational angle α would be very helpful, because in most cases
the uniformity of motion can be verified by selecting three different points of the

10 Towards the Industrial Application of Morphing Aircraft … 201

Fig. 10.4 Geometrical description to the equation applied for the numerical optimization

trajectories, e.g. cruise, drooped position and an intermediate position. Furthermore
the information of possible kinematic points Kc can immediately show, if generally
a solution is possible and which measures are necessary to achieve a good solution.

10.3.2 Geometrical Construction Method

In contrast to the numerical approach, the geometrical construction method allows
to visualize all valid kinematic points Kc, which result from inputs given by two
load introduction points (e.g. at cruise position Xc and droop position Xd), rota-
tional angle α and rotational axis M. This methodology enables not only to find a
very precise kinematic solution in a convenient way, but shows the impact of
parameter variation. This helps to identify potential measures for improvement.
Likewise here, a reduced subsystem consisting of a single lever kinematics is used,
that will be assembled to an overall system at the final stage. Geometrically the
possible kinematic points Kc lie along a straight line. If the rotational axis M is
fixed, this line is exclusively depending on the rotational angle α. As curves with
equal angle dependency are also described as isogonic lines, this naming will be
utilized for the line of possible kinematic points Kc.

One simple method to generate the isogonic line is illustrated in Fig. 10.5 for the
case, that the movement of all kinematic points is in-plane. The procedure is as
follows, the end point of the trajectory Xd is rotated around the rotational axis M by
the rotational angle −α to create the new point Xd’. The line segment bisector
generated from the two points, namely the starting point of the trajectory Xc and the
new defined point Xd’ characterizes the isogonic line Iso for the starting position of
all possible kinematic points Kc. The rotation of the line Iso around the rotational
axis M by the rotational angle α leads to the isogonic line Iso’ characterizing the

202 S. Storm and J. Kirn

α = α1 = α2 = α3

Fig. 10.5 Graphical illustration of the design procedure for the isogonic lines in case of 2D
movement

end position of all possible kinematic points Kd. The idea behind this construction
method is that basically the line segment bisector represents the set of all possible
points with equal distances to both reference points. Therefore, the distance
between the point Xc and the point Kc on the isogonic line Iso is identical to the
distance between the point Xd and the point Kd, which is the resulting point after
rotating the point Kc around the axis M by the angle α. The condition of a consistent
distance is mandatory for this lever kinematics to insert the strut l.

The isogonic line provides the information that inaccuracies in production along
the isogonic line have no effect on reaching the end position by a given rotational
angle α, but could lead to unequal deformation of the skin. On the other hand,
orthographic deviations from the isogonic line have huge impact on reaching the
end position, depending how close together the isogonic lines of different rotational
angles α are lying.

Even though the isogonic line represents all valid kinematic points Kc to move
the load introduction point from start position Xc to end position Xd of the tra-
jectory, the way of movement between these positions is not constantly progressing
and, in fact, is dependent from the location of kinematic point Kc on the isogonic
line. That’s why for synchronization of all different lever kinematics it is favorable
not to generate only a single isogonic line but also taking at least another position of
the trajectory in-between. At a defined time step the corresponding position on the
trajectory can be taken as a temporary end position together with an adapted target

10 Towards the Industrial Application of Morphing Aircraft … 203

rotational angle to generate the associated isogonic line. Crossing these isogonic
lines indicates the optimum for the kinematic point Kc.

For deformation of the flexible skin of the SARISTU project there are 14
different-sized lever kinematics required; seven kinematic stations with two lever
kinematics each. Its interconnection is achieved by same rotational angle of each
main lever. With Fig. 10.6 the cross-section of an airfoil with all projected lever
kinematics is shown. The characteristic of nearly same slopes of isogonic lines are a
sign for an overall good solution, regarding the upper and lower kinematic stations
separately. The selected hinge points Kc are the result of crossing the isogonic lines
with intersection lines. These intersectional lines are selected due to the fact, that
they represent in average the best solution for simultaneous and uniform defor-
mation. In addition it simplifies the construction of the kinematic. The result of a
subsequently numerical optimization process with Eq. (10.2) was deliberately not
utilized in order not to lose the benefits of clearly-structured kinematic points, since
the calculated misalignment of the skin lies within the required tolerances.

Finally, the main levers are linked to the overall drive chain DC using a similar
lever kinematics, consisting of a main lever r and a strut l as described above. But
the crucial difference is that the movement of the strut connected to the drive chain
goes out-of-plane. Due to the fact that all main levers are synchronized by means of

Fig. 10.6 Cross-section of airfoil with all projected lever kinematics together with the overlay of
isogonic and intersection lines

204 S. Storm and J. Kirn

the same rotational axis and rotational angle, only one single design of cross link is
required.

For an arbitrary arrangement of rotational movement and linked trajectories in a
three-dimensional space it is still possible to construct an isogonic line. As shown in
Fig. 10.7, the linear motion of the drive-chain from Xc to Xd is parallel to the rotation
axis of the main lever. For simplification purposes a coordinate transformation is
carried out, whereby the rotational axis through M is equivalent to the z-coordinate
axis. The methodology to generate the isogonic line is similar to the previous
description for the two-dimensional case. Instead of the line segment bisector the
bisecting plane is utilized. Afterwards, the intersection of the rotational plane, here
the xy plane, with the bisecting plane results in the depicted isogonic line. Especially
for the design of this lever kinematics, connecting the main lever with the drive
chain, the isogonic line is helpful. Appropriate kinematic points can be found, which
are located within the limited design space and require only low actuator forces.

The presented geometrical construction method can also be easily transferred to
other application scenarios. The usage of this geometrical construction method is
not only considerable for the development of actuation kinematics of a droop nose
in future aircraft, but also for automotive, watercraft or even for wind power plants,
whenever flexible, fluid-dynamic acting surfaces are employed [16].

Fig. 10.7 Graphical illustration for the usage of the isogonic lines to design a drive chain, general
3D construction method

10 Towards the Industrial Application of Morphing Aircraft … 205

10.4 Weight Estimation of the Mechanical Actuation
System

Based on the developed tools presented in this paper the mechanical system was
designed based on representative air-loads (complete flight envelope with 2 g gust
case) and included in a multitude of different demonstrators over the course of the
SARISTU project. The most relevant of these demonstrators for the kinematics was
the full-scale endurance ground test demonstrator, an outboard section of the droop
nose with a span length of 4 m. This demonstrator incorporated the full function-
ality including de-icing, lightning protection etc., except the bird-strike protection
system. The latter was proven to be feasible in a different test, which also incor-
porated the full functionality but in a shorter version. For more detailed information
on the results from the test-campaign see [17, 18].

The droop nose design in SARISTU is based on a short-range single aisle
passenger transport aircraft with a wingspan of 16 m. The droop nose system acts
as the leading-edge part of the high-lift system and is used over the whole span with
a cut-out for the engine and fuselage-cowling. As a detailed design was only
performed for the seven most outboard stations, an overall weight assessment of the
system can only be approximated and only for the stations outboard of the kink
(inboard of the kink no structural data on the center wing-box was available).
Figure 10.8 shows the position of the different stations along the front of the wing
(outboard of the kink).

The weight of each station can be seen in Table 10.1 below, the weight herein
contains only the structural mass of each station, exclusive the weight of the skin or
the actuator.

If a weight of 2.5 kg per station is added for the drive chain and three differently
sized actuators are considered with a total weight of 50 kg an estimated weight of
roughly 12 kg/m for the actuation system can be estimated. Not directly comparable
(as the wing-planform is bigger and the system is different) but useful as per-
spective; the actuation system for the slat on an A320 weights 18.6 kg/m [19].

Fig. 10.8 Kinematic stations on the wing (outboard of the kink)

206 S. Storm and J. Kirn

Table 10.1 Weight of the different stations (without driveshaft and actuators)

Position RIB1 RIB2 RIB3 RIB4 RIB5 RIB6 RIB7 RIB8 RIB9
Weight [kg] 4,000 3,816 3,629 3,442 3,255 3,068 2,881 2,694 2,507
Length [m] 0,635 0,577 0,525 0,477 0,434 0,394 0,358 0,326 0,296
Estimated values
Position RIB10 RIB11 RIB12 RIB13 RIB14 RIB15 RIB16
Weight [kg] 2,320 2,147 2,053 1,963 1,847 1,716 1,620
Length [m] 0,267 0,239 0,217 0,205 0,192 0,177 0,163
Measured values

10.5 Conclusions

The developed tool aims for minimal deviation from an optimal kinematical tra-
jectory and a simultaneous and uniform deflection of all kinematic stations. Due to
the 3D free-formed surface each kinematic station has to be sized differently but it is
optimized collectively with the other stations. The methodology is split into a
geometrical construction tool whose results go in a subsequent second numerical
optimization tool. Design variables are hinge points and angles of the kinematics.

A droop nose suitable for a single aisle passenger aircraft was presented. At the
end of the project a full-scale demonstrator of the enhanced adaptive droop nose

Fig. 10.9 Operation of the developed droop nose (4 m span) at the static test in the facilities of
VZLÚ, Prague

10 Towards the Industrial Application of Morphing Aircraft … 207

was tested in a wind tunnel under realistic flow conditions. Bird strike and life-cycle
ground tests were also part of the project and were successfully validated with
different demonstrators, as shown in Fig. 10.9.

In this contribution we have taken a further step towards the industrial appli-
cation of morphing wings in future aircraft.

Acknowledgements We would like to thank all participating partners from the FP7 project-
consortium SARISTU for the good teamwork and the support during the development of the
described kinematic system. Special thanks go to our partners DLR, INVENT GmbH and VZLÚ.

This work received funding from the European Union’s Seventh Framework Program for
research, technological development and demonstration under grant agreement no 284562.

References

1. SARISTU, FP7 project-consortium. http://www.saristu.eu
2. Wright O, Wright W (1903) Flying-machine. Patent No. US821393 A, Mar 1903
3. Pendleton E, Griffin K, Kehoe M, Perry B (1996) A flight research program for active

aeroelastic wing technology. AIAA, pp 96–1574, Apr 1996
4. ACARE, Vision 2020, European Commission. http://www.acare4europe.org/documents/

vision-2020
5. ACARE, Flightpath 2050, European Commission, http://www.acare4europe.org/sria/

flightpath-2050-goals
6. SARISTU 1st Periodic Report Publishable Summary, SARISTU Consortium. http://www.

saristu.eu/downloads/documents/
7. Monner HP, Kintscher M, Lorkowski T, Storm S (2009) Design of a smart droop nose as

leading edge high lift system for transportation aircraft. AIAA, May 2009
8. Zimmer H (1979) Quertriebskörper mit veränderbarer Profilierung, insbesondere

Flugzeug-flügel. Patent No. DE 2907912-A1, Mar 1979
9. SADE Newsletter, 2012, SADE Consortium. http://www.sade-project.eu/publications.html
10. Lorkowski T (2010) Aktuatorsystem für “Morphing Devices” In: Hochauftriebs-

konfigurationen, Invited Lecture, DLR Wissenschaftstag, Braunschweig, Sept 2010
11. Kintscher M, Wiedemann M, Monner HP, Heintze O, Kuehn T (2011) Design of a smart

leading edge device for low speed wind tunnel tests in the European project SADE. Int J
Struct Int 2(4) (2011). ISSN: 1757-9864
12. Monner HP, Riemenschneider J, Kintscher M (2012) Groundtest of a composite smart droop
nose. AIAA/ASMR/ASCE/AHS/ASC 2012, Honolulu, Hawaii, Apr 2012
13. Kirn J, Storm S (2013) Deformable leading edge structure. Patent No. EP 2883786, Dec 2013
14. Kirn J, Storm S (2014) Kinematic solution for a highly adaptive droop nose, ICAST2014. The
Hague, The Netherlands, Oct 2014
15. Grote K-H, Feldhusen J (2011) Dubbel, Taschenbuch für den Maschinenbau. Springer 23.
Auflage, 2011
16. Wolfgang K (2014) http://www.ingenieur.de/Fachbereiche/Windenergie/Rotoren-Windraedern-
passen-Form-blitzschnell-Wind-an. Accessed Sept 2014
17. Kintscher M, Kirn J, Storm S, Peter F (2016) Assessment of the SARISTU enhanced adaptive
droop nose. In: SARISTU Proceedings final project conference. Springer (2016)
18. Kintscher M, Kirn J, Monner HP (2016) Ground Test of an enhanced adaptive droop nose
device. In: ECCOMAS congress 2016
19. Becker H (2000) CFK-Tragflügel-Verifikation eines CFK- Demonstrator- Flügelkastens durch
statische/dynamische Versuche. DaimlerChrysler Aerospace Airbus GmbH, Hamburg

Chapter 11

Artificial Muscles Design Methodology
Applied to Robotic Fingers

J.L. Ramírez, A. Rubiano, N. Jouandeau, L. Gallimard and O. Polit

Abstract In the domain of prosthetic robots, main challenges are related to the flex-
ibility and adaptability of devices allowing people to achieve daily tasks. Particularly
for robotic hand prosthesis, these challenges can be addressed from two approaches:
the soft robotic and the utilization of smart materials. In this paper we propose a
methodology to design artificial muscles for robotic fingers, showing the implemen-
tation feasibility of smart materials for precision grasping tasks. This work is part of
the ProMain project that concerns the modeling and the design of a soft robotic hand
prosthesis, actuated by artificial muscles and controlled with surface Electromyog-
raphy (EMG) signals. In a first stage, we designed a robotic finger based on the
equivalent mechanical model of the human finger. The model considers three pha-
langeal joints to perform flexion and extension movements. The robotic finger has
three Degrees of Freedom (DoF), is under-actuated and is driven by tendons. i.e.
only one actuator activates the whole finger, and the motor is coupled to the finger
mechanism through two flexible wires. Then we carry out two experiments: the first
experiment measures the pinch force of the human finger and the second measures
kinematics and force of our robotic finger. We enhance experimental results with the
mathematical model of the finger, to identify and quantify the main parameters of
the artificial muscle. An approach to design an shape memory alloy based artificial
muscle is introduced and justified.

J.L. Ramírez (✉) ⋅ A. Rubiano ⋅ L. Gallimard ⋅ O. Polit 209

LEME, Université Paris Ouest Nanterre le Défense, 50 rue de Sèvres,
92410 Ville d’Avray, France
e-mail: [email protected]

A. Rubiano
e-mail: [email protected]

A. Rubiano
Universidad Militar Nueva Granada, Cr 11 101-80, Bogotá, Colombia

N. Jouandeau
LIASD, Université Paris 8, 2, Rue de la Liberté, 93526 Saint-Denis, France
e-mail: [email protected]

© Springer International Publishing Switzerland 2017
A.L. Araujo and C.A. Mota Soares (eds.), Smart Structures and Materials,
Computational Methods in Applied Sciences 43,
DOI 10.1007/978-3-319-44507-6_11

210 J.L. Ramírez et al.

11.1 Introduction

In the domain of robotic prostheses, the main challenge is the design of well sized
mechatronic limbs and smart controllers that should help people to achieve desired
movements. Concerning the hand prostheses, several robotic hands have been de-
signed to accomplish dexterous manipulation tasks, imitating the behavior of the
human hand, some examples are:

1. KH Hand [1]: is anthropomorphic, uses DC motors and has five fingers and 15
Degrees of Freedom (DoF).

2. Shadow Hand [2]: has five fingers and 20 DoF, and uses pneumatic actuators.
3. HIRO III hand [3] has 15 DoF and is actuated by DC motors, and has an interest-

ing application because it was designed to be a haptic device with force feedback
in the fingertips.

Nevertheless, despite their potential, the hands present in the state of the art have
drawbacks that hinder them to be used as a hand prostheses. The main disadvan-
tages are associated to the rigid behavior and the actuation limits, which restricts
adaptability and flexibility. The necessity of adaptability and flexibility in robotic
has increase the interest in smart and soft materials, which in turn has led to the
development of new adaptive devices (known as soft robots [4]) for physical reha-
bilitation and improvement of human skills.

Concerning the soft materials for robotic hands, some works have been con-
ducted, the UB Hand [5] and the Pisa/IIT hand [6] are good examples of the achieved
developments. Even the DLR Hand II [7] can be considered to has a soft behavior
due to its driving mechanism that is based on tendons.

However, regarding the smart materials for artificial muscles, technologies are
considered to be far from implementation in anthropomorphic robotic hands [8].
This is why, in the context of ProMain project1 we propose a methodology to design
artificial muscles for robotic fingers, showing the implementation feasibility of smart
materials for precision grasping tasks. The methodology is based on four steps:

1. Application requirements modeling,
2. Experimental parameter identification,
3. Parameters quantification, and
4. Material choosing.

The artificial muscle’s requirements are closely related to the robot’s features as
the used mechanism, the desired level of softness, and the task to be performed.
Therefore, it is necessary to develop a mathematical model to describe the robot
and the task, allowing the analysis in a more general way. The mathematical mod-
els for robotic hands are based on the kinematic and dynamic analysis of articulated

1ProMain project concerns the development of a soft robotic hand prosthesis, with artificial muscles
and a control system based on surface EMG signals.

11 Artificial Muscles Design Methodology Applied to Robotic Fingers 211

chains. Consequently, in this paper, we adopt a kinematic model based on the mod-
ified Denavit-Hartemberg (D-H) parameters [9–11] and a dynamic model that uses
the principle of virtual displacements and virtual work [12].

Artificial muscle’s requirements are linked with the robot mechanism, so we use
the finger of the ProMain-I [10] hand as the prototype. This finger is the result of
a morphological optimization process [12] and consists of three phalangeal joints
with flexion—extension, (i.e. 3 DoF). The finger is designed to be under-actuated
and driven by tendons, so, only one servo motor actuates the whole finger, and the
motor is coupled to the mechanism through flexible wires.

Two experiments are presented to identify the actuation characteristics, the first
measures the human force. The second evaluates the required amount of input torque
and angle, needed to flex the finger until it touches an object applying a force in the
same range of human pinch.

Experimental data are analyzed using the kinematic and dynamic models to de-
fine the characteristics of the artificial muscle. The obtained results indicate that
smart materials can fulfill the force, speed and displacement requirements of a ro-
botic hand prosthesis during precision grasping. These results are encouraging and
permit to follow new directions in the research of smart materials for artificial mus-
cles in robotic hands.

Furthermore, the layout of this paper is as follows. First in Sect. 11.2, we intro-
duce our design methodology and the particularization to apply it in a robotic fin-
ger. Subsequently, in Sect. 11.3, we introduce our finger prototype and its modeling.
Then, Sect. 11.4 shows the experimental set-up and the measures. Finally, Sect. 11.5
exposes the identification quantification of the artificial muscle main parameters
through the analysis of experimental data using kinematic and dynamic models. As
a result, an approach to design an shape memory alloy based artificial muscle is
introduced and justified.

11.2 Artificial Muscle Design Methodology

We propose a general methodology which aims at designing smart material based
actuators for particular applications. This methodology is based on the following
four stages:

1. Application requirements modeling: In this phase the main parameters and the
relationships between them are modeled, allowing to establish the operating con-
ditions of the actuators.

2. Experimental parameter identification: Once the key parameters and their re-
lationships have been modeled, it is necessary to carry out an experiment. The
experimental protocol is designed in agreement with proposed models, to mea-
sure the required parameters.

3. Parameters quantification: Experimental data must be analyzed using the de-
fined models to characterize the artificial muscle and quantify operational limits
of the actuator.

212 J.L. Ramírez et al.

4. Material selection: Finally, the retrieved information is used to approximate the
actuator dynamic behavior, allowing the selection of a smart material that fits the
application requirements.

11.2.1 Particularized Methodology for Robotic Fingers

In our case we are focused in artificial muscles that can be considered as smart mate-
rials based actuators with operational similarity to biological muscles. Consequently,
it is important to take into account the human hand muscles capabilities and the ro-
botic finger mechanisms that also impact the actuator requirements.

Application requirements modeling: Considering that the artificial muscle will
drive a robotic hand, the operational conditions and actuator parameters are observed
from kinematics and dynamics of a robot. Main parameters of our artificial muscle
are active strain , force fa, and frequency n.

Parameters and fa are obtained regarding the amount of rotation 1 and torque
1 needed to move the finger and apply a force fR on an object. Likewise, frequency
n is obtained based on the dynamic behavior of the mechanism. Consequently, in
Sect. 11.3 we propose two models (kinematic and dynamic) to identify relationships
between parameters regarding the mechanism.

Experimental parameter identification: Considering that the target is to mimic hu-
man precision grasping, we carry out an experiment to measure maximal an minimal
values of human pinch force (pinch force should corresponds to fR). To measure pa-
rameters 1 and 1 (needed to identify , fa, and n) we perform an experiment with
the robotic finger using a test platform. Both experiments are addressed in Sect. 11.4.

Parameters quantification: Experiments provide dynamic and steady-state values
of 1 and fR, these experimental data are combined with the kinematic and dynamic
models allowing the quantification of , fa, and n. The quantification procedure is
detailed in Sect. 11.5.

Material selection: The retrieved data allows the proposition of a dynamic behavior
permitting the selection of the smart material that best fits the application require-
ments. the selection is explained in Sect. 11.5.

11.3 Under Actuated Robotic Finger ProMain-I

Our prototype is a bio-inspired tendon-driven finger [12] composed of three joints:
the metacarpophalangeal (MP), the proximal interphalangeal (PIP) and the distal
interphalangeal (DIP). All the joints have one DoF to perform flexion and extension.
The finger is controlled by only one actuator, and the drive mechanism uses two
tendons for transmitting motion, one for the flexion and one for the extension, as

11 Artificial Muscles Design Methodology Applied to Robotic Fingers 213

Fig. 11.1 Finger
mechanism

Joint 1 Joint 2 Joint 3
Extension (MP) (PIP) (DIP)
tendon

Flexion
tendon

shown in Fig. 11.1. Considering that the tendons are fastened to the motor pulley

and the fingertip, the clockwise rotation of the actuator produces the flexion, and the

counterclockwise rotation produces the extension.

Due to the under actuation, the rotation angle of the PIP and DIP joints are linked

with the rotation angle of the MP joint. The relation between the angles is approx-
imated with 2 = 0.23 1 and 3 = 0.72 1, where 1 is the MP joint angle, 2 is the
PIP joint angle and 3 is the DIP joint angle. Furthermore, the parameters l1, l2 and
l3 are the lengths of the proximal, medial and distal phalanges, as shown in Fig. 11.1.
The kinematic and the dynamic models are presented in the following subsections.

11.3.1 Kinematic Model of the ProMain-I Finger

The modified D-H convention [11], allows the representation of open-loop and close-

loop kinematic chains, and presents a convenient definition of the axes zi, which
corresponds to the rotation axis of the ith joint. The angle of rotation around zi is
denoted by i, and is applied using the transformation matrix that is described in Eq.
(11.1). The matrix i−1Ti results of the application of: (1) a rotation i around xi−1, (2)
a translation ai along of xi−1, (3) a rotation i around zi and (4) a translation di along
of zi. The parameters i, ai, i and di, are known as the modified D-H parameters, a
graphical representation of the parameters is shown in Fig. 11.2.

⎡ cos i − sin i 0 ai ⎤

i−1Ti = ⎢sin i cos i cos i cos i − sin i − sin idi ⎥ (11.1)
⎢ i sin i cos i sin i cos i cos idi ⎥
⎣⎢ sin ⎦⎥
0 0 0 1

Consequently, the kinematic of a robot composed of n joints is the matrix 0Tn,
which is a composition of the orientation 0Rn, and the position vector [0Pxn,0 Pny ,0 Pzn],

as shown in the following expression:

214 J.L. Ramírez et al.
Fig. 11.2 Graphical
representation of modified
D-H parameters [10, 11]

Fig. 11.3 Kinematic model
of the robotic finger

0Tn = ∏n = ⎡ 0Rn 00PPnynx ⎤ (11.2)
i−1Ti ⎢ 0 0Pnz ⎥
⎢ ⎥
i=1 ⎢⎣ 0 ⎥
0 1⎦

The equivalent kinematic model of the finger is shown in Fig. 11.3. The frame
(x1, y1, z1) and the hypersphere S13 are associated to the joint 1 (MP). The frame
(x2, y2, z2) and the hypersphere S23 are associated to the joint 2 (PIP). And the frame
(x3, y3, z3) and the hypersphere S33 are associated to the joint 3 (DIP). The frame
(xf , yf , zf ) corresponds to the fingertip position. Table 11.1 shows the DH parame-
ters of the ProMain-I finger.

11 Artificial Muscles Design Methodology Applied to Robotic Fingers 215

Table 11.1 DH parameters of the ProMain-I Finger d
i a 0
0 1
100 0 2
2 0 l1 0 3
3 0 l2 0
f 0 l3

Fig. 11.4 Dynamic model
of the robotic finger

11.3.2 Dynamic Model of the ProMain-I Finger

The equivalent dynamic model of the finger is shown in Fig. 11.4. w1, w2 and w3 are
respectively the weights of the proximal, medial and distal phalanges, and are placed
at the centroid coordinates (x1′ , y1′ ), (x2′ , y′2) and (x3′ , y′3) that are used to simplify the
mass matrix M. fR is the applied force that is equivalent to the reaction force.

The proposed dynamic model uses the principle of the virtual displacements and

virtual works [12]. The virtual work W is calculated for the external forces (e.g.

weight, applied force and input torque) in Eq. (11.3) and the inertial forces (e.g.

centrifugal forces) in Eq. (11.4).

We = QeT re (11.3)

where QeT is the external forces vector and re is the virtual displacement vector of
the forces application points.

W = Mq̈ T r (11.4)

where M is the diagonal mass matrix composed with the masses mi and inertias Ji.
The index i is used to denote the ith joint, and the index (i.e. without dot) is used
to notice the independent coordinates. q̈ T is the second derivate with respect to the

time of the q vector shown in Eq. (11.5), and represents the acceleration vector. And

r is the virtual displacement vector of the inertial frameworks.

q = [x1′ , y1′ , 1, x2′ , y2′ , 2, x2′ , y2′ , 1] (11.5)

216 J.L. Ramírez et al.

The dynamic equilibrium is given by qT [Mq̈ − Qe] = 0 when substituting Eqs.
(11.3) and (11.4) in We = W . In order to solve the equilibrium equation, consider-
ing the movements restrictions, it is necessary to separate dependent and independent

coordinates. The separation is performed using the transformation proposed in Eq.

(11.6), as result we have the equilibrium defined by Eq. (11.7), which is separable.

[ −Cq−d1Cq ]
I
q = B qi , B = (11.6)

where Cqd is the jacobian of dependent coordinates, Cq is the Jacobian of indepen-
dent coordinates and I is the identity matrix.

qTi BT [Mq̈ − Qe] = 0 (11.7)

Solving Eq. (11.7), we obtain the dynamic function which gives the input torque

1 as function of the force fR and the kinematic q, q̇ , q̈ . The resulting expression is
shown in Eq. (11.8), where we use the abbreviations Ci ∶= cos( i) and Si ∶= sin( i).

1(fR, q, q̇ , q̈ ) = H1 − 4l1H10 + H11(l2S2 − 4) (11.8)
8l2S2 − 32

whereHHHHH2354 ====1 =(l−(2(mx(m2̈221l2l12m+2l ̈22 C31Sy3̈(2222l l̈2 1̈2 +(2Cm+∕1m22 ̈2 31+gl3+)mCml13222) ̈ S̈+ 322(+(m−2m 2̈ 42+2my+̈112)gm−C)3m26)∕Cm3222+2+))∕Sm24121mg3−l3S23fR ̈ )3l2S2 ̈ 2

H6 = (( ̈ −m2l612g(+m−32 m6+ẍ212∕)m2m)32l∕12+ 3̈ 1)(CC−2124∕+ẍ422−m34lg3)Cm33 ̈ 3+∕38fR − 4m1g + 2J2
H7 =

H8 =

H9 = 4m3ÿ2∕3 + 2m2ÿ1

H10 = (H2 + H3 + H4 + H5 + H6 )+S1J1 ̈ 1)
H11 = 8(H7 + 3l1(H8 + H9)C1∕8

11.4 Experimental Set-Up

With the aim of defining the actuator characteristics, we held two experiments. The
first measures the human pinch force, that is compared with the force achieved by the
robotic finger mechanism through a second test. In the following subsections, both
experiments are described.

11 Artificial Muscles Design Methodology Applied to Robotic Fingers 217

11.4.1 First Experiment: Measure of the Human Hand
Pinch Force

The pinch force can be considered as the force applied by two fingers of the hand,
usually the index and the thumb fingers. The applied force must be adapted to the ob-
ject’s weight, acceleration, surface texture, contour and structure [13]. Consequently,
the measure of the pinch force have to be customized to each problem [14], and that
is why in this study we carried out an experiment suited to precision grasping re-
quirements.

The force is measured in a group of five healthy subjects between 24 and 32 years
old, all of them are males. The sensor is a hand dynamometer Vernier™ D-BTA,
suitable to measure the pinch force, whose characteristics are: (1) accuracy of 0.6 N,
(2) resolution of 0.2141 N and (3) operational range from 0 to 600 N. The data is
collected using a digital oscilloscope connected to a computer. Figure 11.5 shows
the scheme of the experiment. Each subject is asked to apply the maximal pinch
force during a period of 15 s. To avoid fatigue each subject perform only three trials.
Results presented in Table 11.2 correspond to the mean value of the pinch force per-
formed by each subject, and the corresponding standard deviation of each measure.

Dynamometric Single signal Mean signal analysis
Measures capture

Fig. 11.5 Experimental set-up to measure the human pinch force

Table 11.2 The mean value of the human pinch force

Subject Mean pinch force (N) Standard deviation (N)
0.95
1 6.74 0.08
0.21
2 6.45 0.71
0.33
3 4.97

4 6.71

5 4.80

218 J.L. Ramírez et al.

11.4.2 Second Experiment: Measure of the Robotic Finger
Pinch Force

With the objective of establishing the actuation requirements to mimic the human
precision grasping with a robotic hand, we design a test platform. The platform con-
sist of two fingers placed against them, and is used to measure kinematic and pinch
force applied by the robotic fingers. The CAD model of the test platform is shown
in Fig. 11.6. Considering that the target is to measure the amount of rotation and
torque, required by the robotic hand mechanism, during grasping, the experiment
can be carried out with any kind of actuator. Therefore, for the sake of simplicity, we
use a standard servo motor HS-422 with maximal torque = 0.324 Nm.

Considering that the finger performs flexion and extension in 2D, the kinematic is
measured using a high-performance CCD camera Prosilica GE-2040, which tracks
black markers placed on the finger joints and the fingertip. To measure the force, we
used a resistive-based force sensor FlexiforceⓇ, that measures up to 5 N. The sensor
is calibrated in the range of 0.6–4.8 N and is placed on the trajectory of the fingertip.
Figure 11.7 shows the scheme of the experiment.

The test are conducted for four different distances between fingers (50, 55, 60
and 65 mm). For each distance the test is carried out five times. Table 11.3 shows
the measured grip force. The experimental data is correlated with the kinematic and
the dynamic model to identify the torque and displacement requirements of artificial
muscles. Kinematic results are presented and analyzed in the next section.

Fig. 11.6 CAD model of Force Sensor
the platform

DIP Joint
PIP Joint

MP Joint

Adjustable
height

Adjustable separation

11 Artificial Muscles Design Methodology Applied to Robotic Fingers 219

Kinematic
tracking

Force
measuring

Interface for controlling the platform

Fig. 11.7 Experimental set-up to track the kinematic and measure applied force of the robotic
finger

Table 11.3 Mean pinch force (two-finger platform)

Distance (mm) Mean pinch force (N) Standard deviation (N)
0.02
50 4.02 0.08
0.05
55 4.62 0.06

60 4.70

65 3.54

11.5 Requirements and Characterization of the Artificial
Muscle

The main features of an actuator are the force fa, active strain and frequency n.
Thus, we need to define these characteristics for the artificial muscle. Considering
that our goal is to design a robotic hand that will be able to mimic human precision
grasping movement, the actuator features can be established from measures of the
human hand pinch. However, it is important to take into account that the robotic
finger mechanism can modify the actuator requirements. Consequently, the proposed
approach, to identify the artificial muscle requirements, is defined by three kind of
measures: (1) the human pinch force, (2) the settling time of the human force and (3)
the kinematic and dynamic behavior of the robotic finger ProMain-I.

220 J.L. Ramírez et al.

11.5.1 Parameters Quantification

Pinch force requirements: To define a reference value of the human pinch force,
we have collected multiple samples from all subject and computed a mean force
value for each one, as shown in Table 11.2, Sect. 11.4. Thus, the pinch force is in the
interval [4.80 N, 6.74 N], and the mean value is 5.94 N. Furthermore, we measured
the settling time of the force for each subject, and we obtained a mean value of 0.244 s
with a standard deviation of 0.06 s.

Kinematic tracking and resulting force of the ProMain-I finger: As result of
[0Px1,0 P1y, 0] for the
the test, we get the position vectors of the joints, i.e. the vector Likewise the vector

[jo0Pinxft,10,P[0fyP, 0x2],0cPoy2r,re0s]pfoonr dthsetojotihnet2 and [0P3x,0 P3y, 0] for the joint3. that the movement
fingertip position. Considering

is performed in the plan, 0Piz is always zero. Figure 11.8 shows the results of the
measured kinematic using the HS-422 servo motor.

The standard deviation of the measures of the MP joint (whose position is always

zero) is 0.4733 mm. Likewise, the standard deviation of the measures of the joints

PIP and DIP are 0.1848 mm and 0.5598 mm respectively. The standard deviation of

the measures of the fingertip is 1.6069 mm.

Concerning the pinch force, the lower difference (with respect the human force

interval) takes place when the distance between the fingers is 60 mm, in that case,

Fig. 11.8 Results of the position tracking using the HS-422 servo motor

11 Artificial Muscles Design Methodology Applied to Robotic Fingers 221

Experiment Measured Kinematic
Force data

Applied force Joints and fingertip Positions

Kinematic Inverse Calculated
model computing input angle

Joint angles

Dynamic Torque Calculated
model computing input torque

Fig. 11.9 Parameter quantification workflow

the pinch force is 4.70 N. Thus, the force applied by the mechanism is 0.1 N below
the human range.

Analysis of results: Summarizing the obtained results, we can state that if we attempt
to reproduce the human precision grasping, the actuator must fulfill the following
features:

1. the force fR applied by the robotic finger must be inside the human pinch force
interval [4.80 N, 6.74 N]. Thus, the torque should be enough to produce at least a

fingertip force fR = 4.80 N.
2. Settling time must be 0.244 s.

3. The actuator should be suitable to produce a rotation of ∕2 rad.

To calculate the required torque 1 to apply a force of fR = 4.80 N2 using the
proposed dynamic model, it is necessary to know the vector q, which corresponds to

the dependent and independent coordinates of the robot and is composed as shown in

Eq. (11.5). Taking into account that the orientation of (xi, yi) is the same of (xi′, y′i ), we
use the relations xi′ = xi + li cos i∕2 and y′i = yi + li sin i∕2 to calculate the vector

q. The values xi and yi correspond to the measured kinematic information, the angle

i is calculated based on the experimental data and the kinematic model. Workflow is

shown in Fig. 11.9. As a result, we found out the torque 1(fR, q, q̇ , q̈ ) = 124.6 Nmm
and the input angle i = pi∕2 rad. Finally, regarding the human settling time,3 we

can state that the actuator frequency is required to be n = 4∕0.244 s = 16.39 Hz.

2Torque is calculated in transient and steady state.
3Settling time is four times the time constant when 2 % settlement criterion is used.

222 Cooling J.L. Ramírez et al.
100 Heating 345
Fig. 11.10 Temperature
versus strain for NiTi SMAs 50

00 1 2

Fig. 11.11 Schema of the
SMA-based actuator

NiTi SMA Wire

11.5.2 Material Selection

According to the performed analysis, the actuator must provide a rotation of ∕2 rad
and a torque of 124.6 Nmm. There are different kind of smart materials e.g. ionic
polymer metal composites (IPMC), hydrogels, conductive polymers (CP), piezoelec-
tric ceramics (PC), electronic electroactive polymers (electronic EAP), and shape
memory alloys (SMAs). Regarding the main characteristic of our application, the
material that best fits the requirements is SMAs. In the following we justify that
selection.

Shape memory alloys (SMAs): SMAs are a kind of materials that can recover a
shape. The shape recovery effect is the result of a change in the internal material
structure, i.e. the crystalline structure is transformed from martensite phase to austen-
ite phase when the temperature increases. Considering that the Young’s modulus is
lower in the martensite phase, during the austenite phase, the material can recover
strain produced by external loads. The required temperature for changing phase is
known as austenite start temperature.

Martensitic and austenitic transformations are reversible, and thus, the mater-
ial deformation can be controlled by an external stimulus. Strain-temperature re-
lation is different during heating (martensite-austenite transformation) and cooling
(austenite-martensite transformation), this hysteresis is shown in Fig. 11.10, for a
nickel-titanium (NiTi) based SMA.

For our application, the actuator will be composed by a NiTi SMA wire fastened
to a pulley, see Fig. 11.11. Therefore the active strain must rotate the pulley ∕2 rad,
applying a torque of 124.6 Nmm. Considering the maximal active strain = 5 %,4
we can calculate the wire length variation l needed to produce a rotation of ∕2 rad.

4Typical maximal strain of the NiTi SMA.

11 Artificial Muscles Design Methodology Applied to Robotic Fingers 223

Then using l, we can calculate the pulley radius r = 2 l∕ . Likewise the required

force fa is obtained as fa = ∕r.
Considering a wire length l = 200 mm, length variation l = 0.05l = 10 mm. The

pulley radius r = 2 l∕ = 6.35 mm. The force fa is calculated using the required in-
put torque 1 = 124.6 Nmm, as a result fa = 124.6 Nmm∕r = 19.6 N. Summarizing
we need a NiTi SMA wire with the following conditions: (1) length l = 200 mm, (2)

active strain = 5 %, and (3) force fa = 19.6 N. These conditions are fulfilled by a
NiTi SMA wire with a diameter of 0.38 mm.

For the selected wire, the austenite start temperature of 90 ◦C is produced by an

electric current i = 2.25 A applied to the SMA wire. Considering the electric resis-

tance of the material R = 1.66 , we need apply a voltage u = 3.72 V. Furthermore,

and taking into account the behavior of the NiTi SMAs, the active strain can be mod-

eled with respect to the electrical current through a second order transfer function

as:

n(s) = s2 + 2n + n2 (11.9)
in(s) 2 ns

where n = ∕ max is the normalized active strain, is the damping coefficient, n
is the frequency, and in = i∕2.25 A is the normalized electric current.

With the objective of identifying the SMA wire transfer function, we carried out

an experimental observation, measuring the active strain produced during the exci-

tation with an applied step of electric current. The obtained results, see Fig. 11.12,

show that overshoot is zero and consequently the damping coefficient is = 1. The
frequency n, can be calculated as the inverse of the time constant 1∕ , which for
a critically damped response is considered the time to reach 26.42 % of the steady
state value, thus, from the measured time constant n = 13.02 Hz. As a result the
SMA wire transfer function is:

1
0.8
0.6
0.4
0.2

0
-0.2

0 0.5 1 1.5 2 2.5

Fig. 11.12 Identified transfer function of the normalized strain (based on the strain of NiTi SMA
wire in response to a current step input)

224 J.L. Ramírez et al.

Table 11.4 Comparison of ProMain-I hand requirements and actuator characteristics

Parameter ProMain-I hand requirements SMA-based actuator
(rad) ∕2 r = 6.5 mm,
Fa = 19.65 N and l = 200 mm

∕2

(Nmm) 124.6 124.8

(Hz) 16.36 13.02

n(s) = s2 + 169.5 (11.10)
26.04s + 169.5

Comparing the SMA-based actuator characteristics with the actuation require-

ments of the ProMain-I hand, see Table 11.4, we can see that the rotation and torque
fulfill the requirements of the robotic hand. The frequency n is the 80 % of the
required, even so, it is enough to achieve human-like grasping movements.

11.6 Conclusions

We have presented a methodology to design artificial muscles based on four steps: (1)
Application requirements modeling, (2) Experimental parameter identification, (3)
Parameters quantification, and (4) Material selection. The methodology was applied
to design an artificial muscle for a robotic finger.

The finger is anthropomorphic, under-actuated, and driven by flexible wires to
produce more adaptive grasping movements. The proposed kinematic and dynamic
models allow us to calculate the torque requirement to mimic human finger force.
Experiments allow us to identify and quantify the main actuator parameters. Ac-
cording to the obtained results and the performed analysis, we identify that shape
memory alloys (SMAs) can fulfill the requirements of artificial muscles for robotic
finger. Furthermore, our results are encouraging to continue developing smart ma-
terials technologies to be applied in robotics for example IPMC. Consequently, we
envisage the implementation of artificial muscles, based on smart materials, in the
next prototype of our robotic finger.

Acknowledgements Through this acknowledgment, we express our sincere gratitude to the Uni-
versité Paris Lumières UPL for the financial support through the project PROMAIN. This work
has been partly supported by Université Paris Lumières UPL and by a Short Term Scientific Mis-
sion funding from LEME-UPO-EA4416/LIASD-UP8-EA4383. We also acknowledge Colciencias
- Colombia and the Universidad Militar Nueva Granada for the financial support of the PhD stu-
dents.

11 Artificial Muscles Design Methodology Applied to Robotic Fingers 225

References

1. Mouri T, Kawasaki H, Umebayashi K (2005) Developments of new anthropomorphic robot
hand and its master slave system. In: Proceedings of IEEE/RSJ international conference on
intelligent robots and systems (IROS), Alberta, Canada, Aug 2005. IEEE, pp 3225–3230

2. Röthling F, Haschke R, Steil JJ, Ritter H (2007) Platform portable anthropomorphic grasping
with the bielefeld 20-dof shadow and 9-dof tum hand. In: Proceedings of IEEE/RSJ interna-
tional conference on intelligent robots and systems (IROS), San Diego, CA, USA, Nov 2007.
IEEE, pp 2951–2956

3. Endo T, Kawasaki H, Mouri T, Ishigure Y, Shimomura H, Matsumura M, Koketsu K (2011)
Five-fingered haptic interface robot: Hiro iii. IEEE Trans Haptics 4(1):14–27

4. Nurzaman SG, Iida F, Laschi C, Ishiguro A, Wood R (2013) Soft robotics [tc spotlight]. IEEE
Robot Autom Mag 20(3):24–95

5. Ficuciello F, Palli G, Melchiorri C, Siciliano B (2011) Experimental evaluation of the UB Hand
IV postural synergies. In: Proceedings of IEEE/RSJ international conference on intelligent
robots and systems (IROS), San Francisco, CA, USA, September 2011, pp 1775–1780

6. Catalano MG, Grioli G, Farnioli E, Serio A, Piazza C, Bicchi A (2014) Adaptive synergies for
the design and control of the Pisa/IIT SoftHand. Int J Robot Res 33(5):768–782

7. Reinecke J, Dietrich A, Schmidt F, Chalon M (2014) Experimental comparison of slip detection
strategies by tactile sensing with the biotac on the dlr hand arm system. In: Proceedings of
IEEE international conference on robotics and automation (ICRA), Hong Kong, China. IEEE,
pp 2742–2748

8. Melchiorri C, Palli G, Berselli G, Vassura G (2013) Development of the UB Hand IV: overview
of design solutions and enabling technologies. IEEE Robot Autom Mag 20(3):72–81

9. Denavit J, Hartenberg R (1955) A kinematic notation for lower-pair mechanisms based on
matrices. Trans ASME J Appl Mech 77:215–221

10. Ramirez J, Rubiano A, Jouandeau N, El Korso MN, Gallimard L, Polit O (2015) Hybrid kine-
matic model applied to the under-actuated robotic hand prosthesis promain-i and experimental
evaluation. In: Proceedings of14th IEEE/RAS-EMBS international conference in rehabilita-
tion robotics (ICORR), Singapore, Aug 2015. IEEE

11. Khalil W, Kleinfinger J (1986) A new geometric notation for open and closed-loop robots. In:
Proceedings of IEEE international conference on robotics and automation. Proceedings, vol 3,
pp 1174–1179

12. Ramirez J, Rubiano A, Jouandeau N, Gallimard L, Polit O (2016) New Trends in Medical
and Service Robots, chapter Morphological optimization of prosthesis’ finger for precision
grasping. Springer, Nantes, France, pp 1–15

13. Ramsay JO, Wang X, Flanagan R (1995) A functional data analysis of the pinch force of human
fingers. Appl Stat 44:17–30

14. Schreuders TA, Roebroeck ME, Goumans J, van Nieuwenhuijzen JF, Stijnen TH, Stam HJ
(2003) Measurement error in grip and pinch force measurements in patients with hand injuries.
Phys Therapy 83(9):806–815

Chapter 12

Methods for Assessment of Composite
Aerospace Structures

T. Wandowski, P. Malinowski, M. Radzienski, S. Opoka
and W. Ostachowicz

Abstract In this paper results of detection and localization of artificially initiated
delaminations in small carbon fibre reinforced polymer (CFRP) and glass fibre
reinforced polymers (GFRP) samples were presented. The first method was elec-
tromechanical impedance method (EMI). In the research real part of electrical
impedance (resistance) was measured. Delamination in CFRP sample caused fre-
quency shift of certain resonance frequencies visible in resistance characteristic.
The second method was based on scanning laser vibrometry. It is a noncontact
technique that allows to measure vibration of structure excited by piezoelectric
transducer. During research standing waves (vibration–based method) and propa-
gating waves (guided waves–based method) were registered for CFRP sample. In
the vibration–based method, the frequency shifts of certain resonance frequencies
were analyzed. In guided waves-based technique, the interaction of elastic waves
with delamination can be seen in the RMS energy map. The third method is based
on terahertz spectroscopy. Equipment utilizes an electromagnetic radiation in the
terahertz range (0.1–3 THz). During research time signals as well as sets of time
signals creating B–scans and C–scans were analysed. The obtained results showed
that the THz spectroscopy technique can detect and visualize delamination between
the GFRP layers.

⋅ ⋅Keywords Electromechanical impedance EMI Laser vibrometry Guided
⋅ ⋅waves Terahertz spectroscopy Composite materials

T. Wandowski (✉) ⋅ P. Malinowski ⋅ M. Radzienski ⋅ S. Opoka ⋅ W. Ostachowicz 227

Polish Academy of Sciences, Institute of Fluid–Flow Machinery, 14 Fiszera St.,
80–231 Gdansk, Poland
e-mail: [email protected]

W. Ostachowicz
Faculty of Automotive and Construction Machinery, Warsaw University of Technology,
84 Narbutta St., 02–524 Warsaw, Poland

© Springer International Publishing Switzerland 2017
A.L. Araujo and C.A. Mota Soares (eds.), Smart Structures and Materials,
Computational Methods in Applied Sciences 43,
DOI 10.1007/978-3-319-44507-6_12

228 T. Wandowski et al.

12.1 Introduction

Nowadays carbon fiber reinforced polymers (CFRPs) and glass fiber reinforced
polymers (GFRPs) are more and more utilized in many industrial manufacturing
branches. These materials are widely used in various aerospace structures (e.g.:
passenger airplanes like Airbus A380, A350 or Boeing 787, military aircrafts and
helicopters, small planes and gliders). Composite materials are also utilized in
automotive and maritime industry (car chassis, yacht, boats). Moreover these
materials are widely used in renewable energy industry for wind turbine blades.

The main feature that makes CFRP and GFRP so attractive in the manufacturing
of structural parts is their strength to weight ratio. These materials are light and
simultaneously their strength is very high. On the other hand these materials are
very sensitive to impacts which are sources of delaminations between composite
layers. A source of delamination can be for example a fall of tools utilized by
airplane maintenance crew or bird strike at the fuselage skin. As a consequence of
such impact delamination can initiate in composite part. Very often, this delami-
nation is not visible during the conventional visual inspection. Such delamination
can further grow till it reaches critical size that is dangerous for structural integrity.
Because of this, nondestructive testing (NDT) techniques need to be used in order
to check structural state of composite elements.

Application of conventional NDT techniques is related to exclusion of structure
from its normal exploitation, moreover in many cases additional preparation of
structure is needed. Personnel that performs NDT inspection must be highly
qualified. In aerospace, reduction of time for NDT inspection can generate huge
money savings.

In order to reduce the maintenance costs for composite aerospace structures
approach called structural health monitoring (SHM) was developed [1, 2]. This is
an approach that aims at continuous assessment of the structure. Instead of periodic
NDT inspection, SHM system can continuously (in–real time) asses the structure
even during its normal exploitation. Moreover highly qualified personnel is no
longer needed.

Very promising SHM techniques are based on piezoelectric transducers. Such
transducers are very light, thin and can be used as sensors and actuators due to
direct and inverse piezoelectric effect. Piezoelectric sensors can be used to generate
and receive elastic waves or can be utilized for electromechanical impedance
(EMI) measurements, [1]. The development of SHM systems is still in early stage
so NDT techniques are still in use.

Besides conventional damage, like delaminations or fiber cracking composite
materials in aerospace structures are exposed to thermal degradation (exhausting
gases from jet engine, lightning strike), chemical degradation (Skydrol, Kerosene,
deicing agents) or moisture uptake, [3]. Therefore novel extended NDT method
(E–NDT) need to be developed.

In this paper results of application of extended NDT and SHM techniques for
detection of delamination in CFRP and GFRP samples are presented. Investigations

12 Methods for Assessment of Composite Aerospace Structures 229

were conducted for such methods like: electromechanical impedance, laser
vibrometry and terahertz spectroscopy.

The aim of the conducted research was to compare different diagnostic methods
that can be utilized for assessment of composite structures. Authors compared EMI
method that can be utilized as SHM technique and NDT methods based on laser
vibrometry and terahertz spectroscopy. Authors have shown that there is no ideal
technique that gives information about damage existence, size and shape.

12.2 Composite Samples

During the research two composite samples were used. First one was small plate
with dimensions 100 mm × 100 mm × 3.5 mm, manufactured of carbon fiber
reinforced polymer CFRP pre–pregs GG204P IMP503 42 (Fig. 12.1a). The second
one was also plate with dimensions: 100 mm × 100 mm × 3.3 mm made out of
glass fiber reinforced polymer GFRP (12 plies with stacking [0/90/0/90/0/90]s,
glass S fibers with Araldite LY1564 epoxy)—Fig. 12.1b.

First sample was prepared in autoclave while the second one by infusion
method. Carbon pre–pregs are mainly utilized in aerospace structures (passenger
airplanes, helicopters) while composite made out by infusion methods are utilized
very often in yacht and boat industries. CFRP sample was instrumented with
piezoelectric transducer (Fig. 12.1a) and was tested using following methods:
electromechanical impedance EMI and scanning laser vibrometry (vibration–based
method and guided wave based method). Transducer was in the form of disc with
diameter 10 mm and thickness 0.5 mm manufactured of NOLIAC NCE51 piezo-
electric material.

Fig. 12.1 Composite samples investigated during research: a CFRP instrumented with
piezoelectric transducer, b GFRP

230 T. Wandowski et al.

Three structural states of CFRP sample were investigated: referential, with small
delamination Dam 1 and with large delamination Dam 2 (extended size of Dam 1).
Damage was initiated on the right hand side edge of the sample (according to
Fig. 12.1a. Delamination was made between layers of composite material using
chisel. Approximated sizes of the delaminations Dam 1 and Dam 2 will be visible
in results for vibration based method. Moreover size of delamination Dam 2 will be
clearly visible for results obtained with laser vibrometry.

GFRP sample was tested only by terahertz spectroscopy technique. This
approach is not suitable for carbon based composite sample because conducting
fibers will reflect or absorb the incoming signal either immediately at the surface or
within a few sample layers, depending on the polarization of the incoming terahertz
waves, [4]. In GFRP sample two delaminations were initiated. Location and size
will be discussed in the section with terahertz spectroscopy.

12.3 Electromechanical Impedance Method (EMI)

This method is based on measurements of electrical parameters of piezoelectric
transducer attached to the investigated structure. These measurements are per-
formed in frequency domain. Due to electromechanical coupling of piezoelectric
transducer and the host structure, mechanical resonances of structure can be
observed in electrical characteristics of piezoelectric transducer. In this method such
a electrical parameters like impedance, admittance, its real parts (respectively
resistance and conductance) and its imaginary parts (reactance and susceptance) can
be registered and analyzed.

Imaginary part of electrical parameters is used for monitoring of bonding layer
between transducer and structure or transducer itself, [5] when real part of electrical
parameters is utilized for monitoring of the structure. For example, in [6] the
imaginary part of impedance (reactance) was utilized as a parameter that allows to
detect transducer debonding, while as real part of impedance (resistance) was used
for assessment of the structure. However, in [7] resistance and susceptance mea-
surements were used to detect sensor faults. It should be underlined that in this case
measurements were focused on regions with resonant frequencies.

Generally this method is very sensitive to small damage and is very often
utilized in structural health monitoring SHM [5, 8–10]. However this method is also
very sensitive to ambient temperature change what is a main drawback of this
method. Increasing temperature causes leftward shift of peaks in real part of electric
impedance (resistance) characteristics of piezoelectric transducer attached to the
structure [10, 11].

In order to distinguish the damage state from the referential state of the structure,
different damage indexes can be utilized. Most popular are the root mean square
deviation (RMSD) and cross correlation distance (CCD) that are defined as fol-
lows, [10]:

12 Methods for Assessment of Composite Aerospace Structures 231

RMSD = n tvuuffiÀffiffiRffiffiffieffiffiðffiffiZffiffiffiðffiffiiffiRÞffiffiÞffieffiDffiðffiffiZ−ffiffiffiðffiRffiiffiÞffieffiÞffiðffiR2ffiZffiffiffiðffiffiiffiÞffiffiÞffiffiRffiffiÁffiffi2ffiffiffi,ffiffi ð12:1Þ
ð12:2Þ
∑

i=1

 Ã Ã
n ReðZðiÞÞR − ReðZÞR ReðZðiÞÞD − ReðZÞD ,

CCD = 1 − ∑
i=1 σRσD

where: ReðZðiÞÞR—i–th sample of real part of electrical impedance of piezoelectric
transducer for referential (undamaged) state, ReðZðiÞÞD—i–th sample of real part of
electrical impedance of piezoelectric transducer for damaged state, ReðZÞR,
ReðZÞD—averaged values for referential and damaged state respectively and σR,
σD—are the standard deviations for referential and damaged state. Value of damage
index close to zero means that structure is still in referential state. Growing damage
causes increasing damage index value.

In order to calculate these indexes signals from two states of the structure need to
be used. It should be mentioned that these indexes not only indicate the damage of
the structure but also the change of the temperature of structural element with
piezoelectric transducer.

In order to evaluate the state of the composite CFRP sample measurements at
four states were taken. In the first (initial) state sample was intact, which means that
there was no damage inside the sample. The ambient temperature was equal 22 °C
in this case. In the second case the ambient temperature was equal to 24 °C and
sample was still in the intact state. In the third and fourth case delamination with
different extent was introduced to the sample.

In these last two cases ambient temperature was the same like in initial case—
22 °C. Temperature equal 22 °C was maintained in the laboratory by air condi-
tioning system. Without this system temperature fluctuated up to 24 °C during the
period when the measurements took place. The aim of selecting those two very
similar temperatures was to show that even such a small temperature difference has
influence on damage index values. Parameter analyzed in this research was real part
of electrical impedance (resistance) of piezoelectric transducer bonded to the CFRP
sample. Location of piezoelectric transducer can be seen in Fig. 12.1a. During the
research different boundary conditions were investigated however authors selected
case of the sample supported by bubble foil (Fig. 12.1a). This approach allow to
achieve the best repeatability of measurements after the manipulations with the
sample (delamination initiation). Due to utilized low frequency range (up to
50 kHz) EMI measurements are very sensitive to even slight changes of boundary
conditions. Authors of paper [12] investigated the problem of different boundary
conditions on EMI measurement for metallic plates.

In the Fig. 12.2a characteristics of resistance for referential case in temperature
22 °C (Ref) and at temperature 24 °C (Temp) are compared. Small horizontal shift
in frequency and vertical shift in values (for frequencies below 5 kHz) can be
noticed. In Fig. 12.2b comparison of signal for referential sample state at 22 °C
(Ref) is compared with case with introduced smaller delamination (Dam 1). Here

232 T. Wandowski et al.

Fig. 12.2 Resistance plots for comparison of referential CFRP sample state with other
investiagted states: a temperature change, b damage–delamination 1, c damage–delamination 2

frequency shift of few characteristic peaks (not all) can be noticed. Moreover
change of its amplitudes are also visible. For the case of much larger delamination
Dam 2 (Fig. 12.2c) this frequency shifts and amplitude changes are much larger.

In next step values of proposed indexes (1) and (2) were computed for inves-
tigated cases. In the Fig. 12.3 values of the both indexes for three states of structure
were presented. In all cases first initial state (at temperature 22 °C) was utilized as
referential one. Analysing the results for RMSD damage index (Fig. 12.3a) it can
be noticed that for temperature change value of index is relatively large in com-
parison to the first and second case with delamination. It means that RMSD index is
very sensitive to changing temperature. RMSD index is generally sensitive to

12 Methods for Assessment of Composite Aerospace Structures 233

Fig. 12.3 Damage indexes for different sample states: a RMSD, b CCD

vertical and horizontal signal shift as well for small signal fluctuations. Source of
such fluctuations can be related to measurements instability like mentioned tem-
perature but also due to equipment sensitivity, measurement errors or electromag-
netic interferences. Large RMSD index value for the case of changing temperature
is mainly caused by vertical shift of resistance curve for frequencies bellow 5 kHz
(Fig. 12.2a). The RMSD index value for smaller delamination is larger than for the
temperature influence however the size of this delamination is relatively large in
comparison to the whole sample area. Moreover temperature changed only a little
(2 °C). In the case of smaller damage than investigated it can be hard to distinguish
damage case from the temperature–influenced case. Sometimes temperature influ-
ence can be even larger than influence of the damage. This will cause false alarm of
SHM system.

Analysing the results for CCD index presented in Fig. 12.3b, it can be noticed
that, index value for temperature change achieves much smaller value than for the
case of smaller and larger delamination. Moreover extent of delamination can be
simply distinguished by comparing CCD index values. Small value of CCD index
due to temperature is because this index is sensitive only to horizontal signal shift.
CCD index is not sensitive to vertical shift of signals and small fluctuations
(without horizontal shift). As it was mentioned in this particular research, tem-
perature change is mostly seen as vertical shift of resistance characteristic and as
very small horizontal shift. In this case temperature change was very small but for
much higher temperature change, large horizontal shift of the resistance charac-
teristics can be observed [10, 11]. In such cases this temperature shift must be
compensated.

EMI method allows only to detect the delamination but not to determine its
shape or location. The main advantage of this method is the possibility of its
application in a SHM system. However sensitivity of this method to changing
temperature need to be taken into account and appropriate compensation method for
this influence must be used in order to reduce the false alarm probability. Range of
the method (distance from the transducer at which damage can be still detected) in
composites strongly depends on its damping properties. This must be also con-
sidered during SHM system development.

234 T. Wandowski et al.

12.4 Laser Doppler Vibrometry

Laser Doppler Vibrometry LDV is a noncontact measurement technique that allows
to measure velocities or displacements of vibration in structural parts. This tech-
nique can be utilized for measurements of standing waves as well as guided wave
propagating in the structure. This technique is very often called SLDV when
Scanning Laser Doppler Vibrometer is utilized. In experimental research authors
utilized Polytec 3D Scanning Laser Doppler Vibrometer PSV400 that is able to
measure 3D components of vibrations velocity (out–of–plane and in–plane com-
ponents). However during the research all measurements were performed only in
1D scanning mode which allow to measure only out–of–plane vibration velocity
component. Measurements were related to standing waves as well as guided waves
propagating in the CFRP sample. In both cases piezoelectric transducer was used
for vibrations and guided waves excitation.

12.4.1 Vibration-Based Method

In the vibration–based method with using scanning laser vibrometry the structure is
excited using for example piezoelectric transducer or electromechanical exciter.
Next, laser vibrometer registers velocities of structural vibration of the sample.
These measurements are performed at a dense mesh of points that cover the sample
surface. As result frequency response function can be created for chosen point or its
average value for all measured points. Moreover mode shapes can be simply
extracted and visualized. Frequency Response Function (FRF) presents distribution
of the resonant frequencies of the sample. Such analysis is very often called modal
analysis.

During research for CFRP sample its vibration velocities were measured for
excitation produced by piezoelectric transducer. Excitation signal was in the form
of chirp signal. The sample was support in the same way like during the mea-
surements for EMI method.

Averaged frequency response function was measured by laser vibrometer. Next
this function was compared with electromechanical impedance measurements. In
the case of the EMI method real part of electrical impedance was taken into account
for this comparison.

In the Fig. 12.4 averaged frequency response function for vibration velocities
extracted from laser vibrometer measurements was compared with real part of
electrical impedance (resistance) of piezoelectric transducer placed on CFRP
sample. These measurements were performed for initial referential case (in both
cases temperature was constant at 22 °C).

It should be mentioned that both characteristics were scaled for easier comparison
in one figure. Analyzing results presented in Fig. 12.4 it can be easily noticed that
both characteristics are very similar, only small differences in the peak amplitudes

12 Methods for Assessment of Composite Aerospace Structures 235

Fig. 12.4 Comparison of frequency response for impedance analyzer (resistance) and laser
vibrometer (vibration veloctiy)

can be noticed. The comparison of both characteristics is a little bit difficult due to
noticeable trend of the resistance characteristic. It should be mentioned that such a
agreement of laser vibrometry and impedance analyzer not always occurs. In this
research only out–of–plane velocities were measured. Piezoelectric transducer
measures directly strains that are converted to charge/voltage.

These comparisons have shown that electromechanical impedance method is
very similar to the conventional modal analysis. However, in the EMI method very
often much higher frequencies are analysed (especially for the metallic structures—
due to much lower damping). These frequencies can go up to hundreds of kilohertz,
[6] or even up to megahertz, [13]. In the work [13] composite materials with high
damping were investigated. However, only local change very close to the piezo-
electric transducer was detected. In the present research measurements were per-
formed till 50 kHz. However, narrow clear resonance peaks can be noticed only for
frequency range lower than 20 kHz (Figs. 12.2, 12.4). Large damping of composite
material reduces the size of area at which damage can be detected by piezoelectric
sensor.

In the Fig. 12.5 frequency response functions for vibration velocities register by
laser vibrometry for different CFRP sample are presented. In Fig. 12.5a comparison
of FRF for initial–referential state and for the state with smaller extent of delami-
nation (Dam 1) is presented. Natural frequency shift can be simply noticed in this
figure. In the Fig. 12.5b FRFs for referential state and state with larger delamination
(Dam 2) are compared. Here the frequency shift is much larger however size of
delamination is also much larger than in previous case.

In next step, mode shapes for CFRP sample vibrations for three investigated
states were extracted. In Fig. 12.6 chosen mode shapes were presented for: refer-
ential state, Dam 1 (small delamination) and Dam 2 (large delamination). Location
of the piezoelectric can be noticed for mode shape (Dam 2, f = 3.52 kHz) on the
left in the respect to the sample middle. Delamination is located near the edge on
the right hand side. Introduction of delamination causes frequency shift of natural
vibrations as well as mode shape change. These changes are very large for the

236 T. Wandowski et al.

Fig. 12.5 Comparison on frequency responses for different CFRP states: a referential–delami-
nation 1, b referential–delamiantion 2

larger size of delamination (Dam 2). All these mode shapes are related to frequency
peaks visible in Fig. 12.5.

In the next step simple algorithm that creating RMS energy map for vibration
velocity was used. Such a map indicates the region with concentration of energy
related to structural vibration of composite sample. Such a energy concentration can
be noticed mostly in the place where the wave excitation was applied, near the
sample boundary and in the all places where different discontinuities are located
(for example damage). RMS index for chosen scanning point j can be created based
on the following formula:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

RMSj = 1 N S2j, k, ð12:3Þ
N
∑

k=1

where, Sj, k—signal gathered in the point j, N—length of the signal. Comput-
ing RMS index values for full mesh of scanning points allows to create RMS
energy map. Such a maps for the energy of vibration for the referential state, state
with small delamination and with large delamination are presented respectively in
Fig. 12.7a–c. Here full frequency band of registered vibration was utilized. In all
cases location of piezoelectric transducer can be simply noticed.

12 Methods for Assessment of Composite Aerospace Structures 237

Reference Dam 1 Dam 2

f=3.74 kHz f=3.71 kHz f=3.52 kHz

f=5.46 kHz f=5.37 kHz f=4.96 kHz

f=6.62 kHz f=6.45 kHz f=6.17 kHz

f=10.01 kHz f=9.72 kHz f=8.90 KHz

Fig. 12.6 Comparisons of mode shapes for few choosen frequencies and different CFRP sample
states

238 T. Wandowski et al.

Fig. 12.7 RMS maps for different CFRP sample states: a referential, b smaller delamination—
Dam 1, c larger delamination—Dam 2

In Fig. 12.7a some energy distribution in the place where smaller delamination
is existing can be noticed. It allow to notice the approximate shape and size of
delamination. Shape and size of delamination is much better visible in the case of
larger delamination (Fig. 12.7c).

12.4.2 Guided Waves-Based Method

Measurements taken by scanning laser vibrometer performed for surface of CFRP
sample also allowed to visualize guided wave propagation. This measurement
approach is called full wavefield approach. For this purpose dense mesh of mea-
surement points was spanned over the sample surface.

In the frame of research measurements were performed on the surface without
piezoelectric transducer. In this case only the damage case was investigated, where
delamination with larger size (Dam 2) was located in the sample. Excitation signal
was in the form of tone burst with five cycles. Three values of signal carrier
frequencies were investigated: 16.5, 100 and 150 kHz.

It should be mentioned that guided wave–based method is more sensitive to
much smaller damage that vibration based method due to utilization of higher
frequencies. In guided wave–based method frequencies up to few hundreds of
kilohertz are utilized while for the vibration–based method till tens of kilohertz.
That means that for the excitation frequency equal 16.5 kHz sensitivity of method
will be very poor due low frequency and large wavelength.

In next step of research all gathered signals have been processed using simple
method based on RMS energy map calculated for propagating elastic waves. In the
Fig. 12.8 such a RMS energy maps calculated for different excitation frequency
were presented. These maps are presented in the logarithmic scale (map amplitude).
For the case of excitation frequency equal 16.5 kHz (Fig. 12.8a) the space reso-
lution and sensitivity is very low due to relative large wave length, what was
mentioned above. However some energy concentration around the sample edges

12 Methods for Assessment of Composite Aerospace Structures 239

Fig. 12.8 RMS energy maps for guided waves propagation for Dam 2, excitation frequency:
a 16.5 kHz, b 100 kHz, c 150 kHz

and on the right side where the delamination is located can be simply noticed. In the
case of frequency 100 kHz (Fig. 12.8b) wave energy is concentrated mainly in the
place where piezoelectric transducer is located and generates guided waves.
However further energy concentration can be simply noticed in the delaminated
region. Moreover shape and location of delamination can be here clearly distin-
guished. For the highest excitation frequency 150 kHz (Fig. 12.8c) the image is
very similar to previous one.

Guided wave–based method can be simply utilized in SHM system when
piezoelectric transducers are used for guided wave excitation and sensing. This is
the main advantages of this method apart from its high sensitivity to very small
damage in early stage of growth. However in the case of this method large damping
related to reinforced composite material need to be taken into account.

This method allows to localize delamination and even to determine its shape.
Laser vibrometry can be useful tool during development and prototyping of SHM
system (actuator/sensor placement, analysis of guided waves in complex structures
[14, 15]) or for non destructive testing purpose.

12.5 Terahertz Spectroscopy

During investigations presented in this section Terahertz spectrometer Ter-
aview TPS Spectra 3000 which generates impulses in frequency range from 0.1 up
to 3 THz was utilized. These impulses are sent repeatedly and interact with the
investigated sample material. This equipment works in time domain and is called
time domains spectroscopy (TDS), [16]. This non–contact measurement system
allows to perform measurements in reflection and transmission modes but the
results presented in this paper were based exclusively on measurements done for the
scanning heads working in reflection mode. Reflection mode is more feasible for
analyzing real structures where access to it is very often limited to only one side.

240 T. Wandowski et al.

Fig. 12.9 GFRP sample with
delaminations and aluminium
strip

The spectrometer is equipped with moving table that allows for XY scanning of
large objects.

As it was already mentioned this technique is not suitable for material like CFRP
that conducting electric current. Therefore in this case GFRP sample was investi-
gated (see Fig. 12.9). Two delaminations were initiated in this sample using chisel.
Larger delamination located on the sample edge is clearly visible, the smaller one is
located in the corner on the right and bottom part of sample. Aluminum strip causes
strong reflection of THz radiation and is used for determination of sample orien-
tation during the measurements.

In the Fig. 12.10, THz signals taken from GFRP sample in referential region and
region with delamination were presented. In the case of signal for referential region
(Fig. 12.10a) two reflections can be distinguished: with larger amplitude (at 10 ps)
—related to top surface reflected THz waves and with smaller amplitude (at 50 ps)—
related to reflection from bottom surface of the sample. In the case of signal taken for
region with delamination additional reflection can be noticed at 30 ps (Fig. 12.10b).

In the Fig. 12.11, B–scans for the referential sample region and for the region
with delamination were presented. In the case of the delaminated sample, damage
can be clearly observed in the B–scan observing region between top and bottom
surface (Fig. 12.11b). Its width and thicknes as well as location can be noticed.

In the last step C–scan was created for the sample with delaminations
(Fig. 12.12). Analysing this C–scan strong wave reflection can be noticed that is
related to aluminum strip on the sample surface (on the right, in the middle of the
sample edge). Moreover artifact on the left can be noticed that is caused by
clamping metal element that is higher than the sample. Terahertz waves reflect from
this element and do not reach sample surface. Both delaminations are also visible
on this C–scan: larger one (in the middle of the bottom edge) and smaller one
(bottom corner on the right side). During creation of C–scan plot of maximal peak
value in signals was plotted.

Results prove that this NDT technique is appropriate for detection of delami-
nation in GFRP composites. Moreover this method can determine the shape of the

12 Methods for Assessment of Composite Aerospace Structures 241

Fig. 12.10 THz signal taken from: a referential region (without delamination), b region with
delamination

Fig. 12.11 B–scan for GFRP sample: a referential region, b region with delamination (see
position –20;0 and delay 25–35 ps)

242 T. Wandowski et al.

Fig. 12.12 C–scan for GFRP sample with delaminations

delamination, its dimensions as well as its location. B-scan shows location of
delamination with respect to the sample thickness while C-scan shows planar
location of delamination.

As it was mentioned earlier this method can not be used for CFRP. A limitation
of this method is also thickness of the sample. Thick composite material will damp
the THz radiation, so the penetration depth is limited. Moreover time length of
signal in this equipment is also limited which also determines maximum allowable
thickness of the investigated sample.

12.6 Conclusions

In this paper result of detection and localization of artificially initiated delamina-
tions in small CFRP and GFRP samples were presented. During research elec-
tromechanical impedance EMI method, laser vibrometry (vibration–based and
guided wave–based method) and terahertz spectroscopy were investigated.

EMI method is very sensitive to small damage but results are also influenced by
changing ambient temperature. These temperature changes need to be compensated
in order to eliminate false damage detection. This method utilizes piezoelectric
transducers that can be permanently installed on interrogated structure and it is
possible to perform real–time structural monitoring (SHM). Range of the method
(distance from the transducer at which damage can be still detected) depends on
damping properties of composite materials as a consequence of thickness, stack
lay–up or geometrical complexity.

12 Methods for Assessment of Composite Aerospace Structures 243

Laser vibrometry technique can be used for vibration–based damage detection.
This is similar to the conventional modal analysis where changes in natural fre-
quencies and mode shapes are investigated. It is also possible to detect damage
based on analysis of distribution of vibration energy (RMS energy map). Method is
also similar to EMI method however in the first one much higher frequencies can be
utilized (depending on damping). It need to be mentioned that laser vibrometry is
NDT technique.

Laser vibrometry can be also utilized in guide–based damage localization
method. By observing of guided wave energy distribution (RMS energy map for
guided waves) it is possible to detect and localize damage. This method can be used
for higher frequencies up to hundreds of kilohertz. It offers high sensitivity to small
damage due to small wavelength for high frequencies. Laser vibrometry can be
used for optimization of sensor placement and guided wave propagation analysis
during SHM systems development which is based on the piezoelectric transducer
and guided waves method.

The last one is terahertz spectroscopy method. This is extended NDT method
that can be used for delamination detection. This method is appropriate for GFRP
and other materials that are not electrically conducting. Method can determine the
shape and location of delamination in GFRP sample.

The aim of this research was to show that there is no ideal technique that allow to
assess the aerospace composite materials. For the SHM purposed EMI method can
be utilized. However this method does not give clear information about damage
localization. Vibration based method and guided wave-based method using laser
vibrometer give information about damage existence, location and approximated
shape. Guided wave based method due to higher frequencies (shorter wavelength)
indicates much better the shape of delamination than vibration based method.
However these methods are NDT methods not suitable for SHM. Terahertz spec-
troscopy is very sensitive technique that gives information about damage shape,
size and location. However, this is also NDT technique that is moreover limited to
electrically not conducting composite materials like GFRP.

Presented NDT techniques are very suitable in the research for comparison of
results obtained by EMI method. It can be useful for calibration of the EMI method
based on real damage size and location given by NDT methods.

Further research will be related to determination of the range of EMI method in
much larger CFRP and GFRP samples.

Acknowledgements This research was supported by the project entitled: Non–invasive Methods
for Assessment of Physicochemical and Mechanical Degradation (PBS1/B6/8/2012) granted by
National Centre for Research and Development in Poland.

The research leading to these results has been partially supported by project funded by Polish
National Science Center under the decision no. DEC–2013/11/D/ST8/03355.

244 T. Wandowski et al.

References

1. Giurgiutiu V, Lin B, Santoni-Bottai G, Cuc A (2011) Space application of piezoelectric wafer
active sensors for structural health monitoring. J Intell Mater Syst Struct 22(8):1359–1370

2. Diamanti K, Soutis C (2010) Structural health monitoring techniques for aircraft composite
structures. Prog Aerosp Sci 46:342–352

3. La Saponara V (2011) Environmental and chemical degradation of carbon/epoxy and
structural adhesive for aerospace applications: Fickian and anomalous diffusion, Arrhenius
kinetics. Compos Struct 93:2180–2195

4. Karpowicz N, Dawes D, Perry MJ, Zhan X–C (2006) Fire damage on carbon fiber materials
characterized by THz waves. In: Proceedings of SPIE, p 6212

5. Park G, Farrar CR, di Scalea FL, Coccia S (2006) Performance assessment and validation of
piezoelectric active-sensors in structural health monitoring. Smart Mater Struct 15(6):1673–
1683

6. Giurgiutiu V (2008) Structural health monitoring with piezoelectric wafer active sensors.
Elsevier, pp 747

7. Buethe I, Moix–Bonet M, Wierach P, Fritzen C–P (2014) Check of piezoelectric transducers
using the electro–mechanical impedance. In: 7th European workshop on structural health
monitoring, Nantes, France

8. An Y–K, Kim MK, Sohn H (2012) Airplane hot spot monitoring using integrated impedance
and guided wave measurements. Struct Control Health Monit 19(7):592–604

9. Na S, Lee KK (2013) A multi–sensing electromechanical impedance method for non–
destructive evaluation of metallic structures. Smart Mater Struct 22:095011 (8pp)

10. Baptista FG, Budoya DE, de Almeida VAD, Ulson JAC (2014) An experimental study on the

effect of temperature on piezoelectric sensors for impedance-based structural health
monitoring. Sensors 14:1208–1227
11. Siebel T, Lilov M (2013) Experimental investigation on improving electromechanical

impedance based damage detection by temperature compensation. In: 10th international
conference on damage assessment of structures, Dublin, Ireland, July 8–10
12. Priyaa CB, Reddy AL, Raob GVR, Gopalakrishnan N, Raoa ARM (2014) Low frequency and
boundary condition effects on impedance based damage identification. Case Stud Nondestr
Test Eval 2:9–13
13. Malinowski PH, Wandowski T, Ostachowicz WM (2014) Characterisation of CFRP adhesive
bonds by electromechanical impedance. In: Proceedings of SPIE, p 9064
14. Ruzzene M (2007) Frequency–wavenumber domain filtering for improved damage visual-
ization. Smart Mater Struct 16(6)
15. Wandowski T, Malinowski P, Ostachowicz W (2013) Guided waves–based damage
localization in riveted aircraft panel. In: Proceedings of SPIE, p 8695
16. Palka N, Miedzinska D (2014) Detailed non–destructive evaluation of UHMWPE composites
in the terahertz range. Opt Quant Electron 46(4):515–525

Chapter 13

Design Optimization and Reliability
Analysis of Variable Stiffness Composite
Structures

A. Sohouli, M. Yildiz and A. Suleman

Abstract This paper presents a study on the reliability analysis of variable stiffness
composites to improve the performance of curved fiber composites in the presence
of uncertainties. A comparison to the response of conventional straight fiber
composites is presented while assuming the same material properties. To this end, a
computational design framework for advanced composites has been developed and
implemented and it includes both deterministic and reliability analysis capabilities.
The deterministic design module uses the Discrete Material Optimization
(DMO) technique, and the reliability analysis module uses the Response Surface
Method (RSM) based on the First Order Reliability Method (FORM) and the Monte
Carlo Simulation (MCS). Variable Stiffness Composite Laminates (VSCL) are
achieved by a continuous change in fiber orientation in the plane of the laminate.
The design objective is to tailor and/or maximize the stiffness of the composite
structure, and the design variables are the piecewise patch orientations of the fibers
in the presence of manufacturing constraints. The manufacturing constraints enforce
a bounded change in fiber orientation between adjacent patches in order to ensure
fiber continuity to minimize gaps and overlaps. In the reliability analysis, tip
deflection and first ply failure are considered separately as the limit state function
and the random variables are material properties. The results show that the VSCL
are more reliable even in the presence of a high standard deviation compared to the
straight fiber composites with low standard deviation assuming the same material
properties. It was also observed that the curved fiber composites are more effective
in handling concentrated stresses.

A. Sohouli ⋅ A. Suleman (✉) 245

MIT-Portugal Program, IDMEC-CCTAE, Instituto Superior Técnico,
University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
e-mail: [email protected]

M. Yildiz
Advanced Composites & Polymer Processing Laboratory, Faculty of Engineering
and Natural Sciences, Sabanci University, Orhanli-Tuzla, 34956 Istanbul, Turkey

A. Suleman
Department of Mechanical Engineering, University of Victoria, Victoria, BC, Canada

© Springer International Publishing Switzerland 2017
A.L. Araujo and C.A. Mota Soares (eds.), Smart Structures and Materials,
Computational Methods in Applied Sciences 43,
DOI 10.1007/978-3-319-44507-6_13

246 A. Sohouli et al.

⋅ ⋅Keywords Reliability analysis Variable stiffness composite Discrete mate-
⋅ ⋅rial optimization (DMO) First order reliability method (FORM) Response
⋅surface method (RSM) Monte carlo simulation (MCS)

13.1 Introduction

The application of fiber reinforced composite materials in high performance
structures has been growing in recent years due to their enhanced and tailor able
mechanical properties. A new concept on advanced composite structures is based
on the Variable Stiffness Composite Laminates (VSCL), where the stresses and
strains in the structure can be adapted according to the performance objectives.
VSCL were introduced several decades ago, but only recently researchers are
actively exploring new designs based on the VSCL concept due to the advances in
design optimization and manufacturing capabilities. VSCL can be achieved by
either changing the fiber volume fraction in the laminate [1], by dropping or adding
plies to the laminate [2], or by using curvilinear fibers [3–7]. The design space is
significantly expanded when considering variable stiffness composites compared to
the classical stacking sequence design problem and it results in structural
improvements under the same weight constraints. The work presented here is
focused specifically on curvilinear fibers for the synthesis of VSCL.

There are many methods to optimize the structural performance or any other
stated objective for composite structures [8]. One of the common methods used to
design and optimize composite laminates is the discrete stiffness method [9]. In
discrete approaches [10–16], the fiber orientation of each design space, which could
be an element or a patch, and the stacking sequences are designed independently.
Discrete Material Optimization (DMO) is one of the discrete stiffness method
introduced by Stegman and Lund [12]. DMO can be considered as a generalization
of multi-phase topology optimization problems [13] in that it distributes a set of
discrete candidate materials over a structural domain by means of material inter-
polation techniques.

Also, uncertainties in the composite structures can result from errors in the
simulation and modeling, manufacturing process, material properties and loading.
The effects of such uncertainties on the performance of the structure are not con-
sidered in deterministic optimization, and may result in a under-designed structure.
The reliability analysis of optimized composite structures is important due to the
fact that the performance is highly sensitive to the anisotropic material properties
and the applied loads. Any change in material properties leads to a reduction in the
structural performance and reliability of the structure. Sriramula et al. [17] has
published a classification for uncertainties in composite structures and a summary
of the different stochastic modeling approaches. An extensive review of reliability
in composites has been presented in [18] where the methods of reliability analysis
in the structure, random variables, methodologies and output variables are
reviewed. There are several methods to predict reliability of structures and the

13 Design Optimization and Reliability Analysis … 247

Monte Carlo Simulation (MCS) and the First Order Reliability Method (FORM) are
the two most common methods [19–21].

The Variable Stiffness Composite Laminates can be manufactured using auto-
mate fiber placement techniques. One of the most common manufacturing defects
in curvilinear fiber composites to achieve variable stiffness are the gaps and
overlaps which can cause propagation of cracks and damage to the structural
performance. In this study, the influence of the gaps and overlaps in the structural
performance of VSLC is carried out by varying material properties of the optimized
variable stiffness composites and the results are compared to the optimal classical
straight fiber fiber composites. The reliability analysis is computed using First
Order Reliability Method (FORM) and Monte Carlo Simulation (MCS) and the
Response Surface Method (RSM) is used to quantify the structural performance.

13.2 Discrete Material Optimization (DMO)

The Discrete Material Optimization (DMO) is adopted from structural topology
optimization studies [12–16]. In this method, the distinct number of materials can
be selected for each element instead of a binary selection between solid and a void.

DMO distribute a set of discrete candidate materials over structural domain such

that the objective function is minimized. These candidate materials can be same
material with different orientations or other user defined materials. In the finite
element formulation, the element stiffness matrix, Ke, is computed as follows:

Z ð13:1Þ
Ke = ðBÞT CeBdV

where B is the strain-displacement matrix and Ce is the constitutive matrix over the
element volume. The DMO formulation is a technique whereby the element con-
stitutive matrix, Ce, is interpolated using a set of constitutive matrix, Ci, of can-
didate materials. For each element, this can be expressed as a sum over the number
of candidate materials, nc:

nc ð13:2Þ

Ce = ∑ wiCi, 0 ≤ wi ≤ 1

i=1

where wi are the weights of candidate materials. The objective here is to set to one
for a single weight and to zero for all other weights. The Ci matrix represents the
material properties. Common interpolation functions to calculate wi are given as:

nc ð13:3Þ

Ce = ∑ wiCi = ðxiÞpCi, wi = ðxiÞp, 0 ≤ xi ≤ 1

i=1

248 A. Sohouli et al.

Fig. 13.1 An example of four-patch design; the discrete fiber orientations and the converted
continuous tow paths

This representation is adopted from the Solid Isotropic Material with Penaliza-

tion (SIMP) method [12], where xi is the design variable with a value between zero
and one, and p is the penalization. The weights, wi, can be expressed in the form
given:

nc ð13:4Þ

wiðxÞ = ðxiÞp ∏ ½1 − ðxiÞpŠ

j = 1, j ≠ i

In this study, Eq. (13.4) is used to parameterize the weights of candidate
materials. The total number of design variables for the structure is the number of
elements multiplied by the number of candidate materials. Therefore, the number of
design variables is high and it represents one of the most critical disadvantages of
DMO. The design variables can be reduced by merging several design variables
from different layers and elements into a single variable by using a patch design
variable that spans several elements. The plates in this study are divided solely
along the X-direction and the objective is to minimize the gaps and overlaps
between the neighbors patches. However, this limits the design space when com-
pared to a two-directional patch design. As an illustration of the approach, consider
the optimal design results shown in Fig. 13.1 for a plate divided into four patches
along the x-direction and the associated discrete fiber orientations solution for each
element. The discrete fiber orientations are then converted into continuous tow
paths using the Quadratic Bezier Curve [22].

13.3 Problem Formulation

The objective function consists in minimizing the compliance to solve for the optimal
orientation of the curvilinear fibers. The optimization problem can be stated as:

13 Design Optimization and Reliability Analysis … 249

Objective: min C = UT F ð13:5Þ

Subject to: KU = F

gmðxÞ ≤ 0
nc À Á
gwðxÞ = ∑ wc, p xc, p = 1; ∀ðpÞ

c=1

xc, p ∈ ½0; 1Š; ∀ðc, pÞ

where gmðXÞ and gwðXÞ are the manufacturing aÀnd wÁeight constraints, respectively.
For simplicity, the weights are defined in wc, p xc, p form where c and p are the
candidate material and patch number, respectively.

The optimal designs must comply with the manufacturing adjacency constraint,
such that the optimal orientation in each patch may only change a specified max-
imum angle within the set Ii. This constraint ensures the prevention of large changes
in the ply orientation between adjacent patches [23]. For each layer, this constraint
can be defined as follows:

ÀÁ ÀÁ
gmðxÞ = wc, p xc, p ∑ wc, p + 1 xc, p + 1 − τ ð13:6Þ

pϵIi

where Ii is a set of indices that includes the adjacent design variables that cannot be
used:

Ii = f1, 2, . . . , cg\fi − L, . . . , i + Lg ð13:7Þ

where L is shifting orientation between patches. The values of τ should be zero.
However, values larger than zero are considered due to numerical difficulties when
using a gradient based optimization [23], and these values approach to zero during
in each iteration in the optimization process. The design sensitivities for compliance
as the objective function are given by:

∂C = − UT ∂K U = − UT ∂K ∂w U ð13:8Þ
∂x ∂w ∂w ∂x

The sensitivities of constraints are not mentioned herein due to the simplicity of
calculation.

13.4 Optimization Strategy

In this study, the Sequential Approximate Optimization (SAO) techniques are used
to assure a reasonably fast optimization. The basic concept in SAO techniques is to
construct approximate analytical sub-problems successively at the design point for
the objective function and constraints, and these computationally inexpensive. The
sub-problems can be solved in the sub-region of the total design space by using an
efficient mathematical programing algorithm. The sub-regions are defined by a