The main goal of the present paper is to demonstrate the value of design optimization beyond its use for structural shape determination in the realm of the constitutive characterization of anisotropic material systems such as polymer matrix composites with or without damage. The approaches discussed are based on the availability of massive experimental data representing the excitation and response behavior of specimens tested by automated mechatronic material testing systems capable of applying multiaxial loading. Material constitutive characterization is achieved by minimizing the difference between experimentally measured and analytically computed system responses as described by surface strain and strain energy density fields. Small and large strain formulations based on additive strain energy density decompositions are introduced and utilized for constructing the necessary objective functions and their subsequent minimization. Numerical examples based on both synthetic (for one-dimensional systems) and actual data (for realistic 3D material systems) demonstrate the successful application of design optimization for constitutive characterization.

References

References
1.
Kaczmar
,
J.
,
Pietrzak
,
K.
, and
Wlosinski
,
W.
, 2000, “
The Production and Application of Metal Matrix Composite Materials
,”
J. Mater. Process. Technol.
,
106
(
1–3
), pp.
58
67
.
2.
Baker
,
A.
,
Dutton
,
S.
, and
Kelly
,
D.
, 2004, “
Composite Materials for Aircraft Structures
,”
2nd ed.
,
AIAA
,
Reston, VA
.
3.
Daniel
,
I.
, and
Ishai
,
O.
, 1994,
Engineering Mechanics of Composite Materials
,
Oxford University Press
,
New York
.
4.
Carlsson
,
L.
, and
Pipes
,
R.
, 1997,
Experimental Characterization of Advanced Composite Materials
,
CRC Press
,
FL
.
5.
Mast
,
P.
,
Beaubien
,
L.
,
Clifford
,
M.
,
Mulville
,
D.
,
Sutton
,
S.
,
Thomas
,
R.
,
Tirosh
,
J.
, and
Wolock
,
I.
, 1983, “
A Semi-Automated In-Plane Loader for Materials Testing
,”
Exp. Mech.
,
23
(
2
), pp.
236
241
.
6.
Mast
,
P.
,
Nash
,
G.
,
Michopoulos
,
J.
,
Thomas
,
R.
,
Badaliance
,
R.
, and
Wolock
,
I.
, 1992, “
Experimental De-Termination of Dissipated Energy Density as a Measure of Strain-Induced Damage in Composites
,”
Technical Report Tec. Rpt. NRL/FR/6383–92–9369
,
Naval Research Laboratory
,
Washington, DC, USA
.
7.
Mast
,
P.
,
Nash
,
G.
,
Michopoulos
,
J.
,
Thomas
,
R.
,
Badaliance
,
R.
, and
Wolock
,
I.
, 1995, “
Characterization of Strain-Induced Damage in Composites Based on the Dissipated Energy Density Part I. Basic Scheme and Formulation
,”
Theor. Appl. Fract. Mech.
,
22
(
2
), pp.
71
96
.
8.
Michopoulos
,
J.
, 2003,
Computational and Mechatronic Automation of Multiphysics Research for Structural and Material Systems
, Recent Advances in Composite Materials: In Honor of S. A. Paipetis,
Kluwer Academic Press
, pp.
9
21
.
9.
Michopoulos
,
J.
, 2004, “
Mechatronically Automated Characterization of Material Constitutive Response
,”
Proceedings of the 6th World Congress on Computational Mechanics (WCCM-VI)
,
Tsinghua University Press and Springer
,
Beijing China
, pp.
486
491
.
10.
Michopoulos
,
J.
,
Hermanson
,
J.
, and
Furukawa
,
T.
, 2008, “
Towards the Robotic Characterization of the Constitutive Response of Composite Materials
,”
Compos. Struct.
,
86
(
1–3
), pp.
154
164
.
11.
Michopoulos
,
J. G.
,
Hermanson
,
J. C.
, and
Iliopoulos
,
A. P.
, 2010, “
Towards a Recursive Hexapod for the Multidimensional Mechanical Testing Of Composites
,”
2010 ASME International Design Engineering Technical Conferences & Computers and Information In Engineering Conference
, August 15–18, 2010,
Montreal, Quebec, Canada
, Paper No. DETC2010/CIE–28699.
12.
Pierron
,
F.
,
Vert
,
G.
,
Burguete
,
R.
,
Avril
,
S.
,
Rotinat
,
R.
, and
Wisnom
,
M.
, 2007, “
Identification of the Orthotropic Elastic Stiffnesses of Composites With the Virtual Fields Method: Sensitivity Study and Experimental Validation
,”
Strain
,
43
(
3
), pp.
250
259
.
13.
Cooreman
,
S.
,
Lecompte
,
D.
,
Sol
,
H.
,
Vantomme
,
J.
, and
Debruyne
,
D.
, 2007, “
Elasto-Plastic Material Parameter Identification by Inverse Methods: Calculation of the Sensitivity Matrix
,”
Int. J. Solids Struct.
,
44
(
13
), pp.
4329
4341
.
14.
Furukawa
,
T.
, and
Michopoulos
,
J.
, 2008, “
Computational Design of Multiaxial Tests for Anisotropic Material Characterization
,”
Int. J. Numer. Methods Eng.
,
74
(
12
), pp.
1872
.
15.
Michopoulos
,
J.
,
Iliopoulos
,
A.
, and
Furukawa
,
T.
, 2009, “
Accuracy of Inverse Composite Laminate Characterization Via the Mesh Free Random Grid Method
,”
Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2009
,
ASME
(ed.), Paper No. DETC2009/CIE–87096.
16.
Bruno
,
L.
,
Furgiuele
,
F.
,
Pagnotta
,
L.
, and
Poggialini
,
A.
, 2002, “
A Full-Field Approach for the Elastic Characterization of Anisotropic Materials
,”
Opt. Lasers Eng.
,
37
(
4
), pp.
417
431
.
17.
Schmidt
,
T.
,
Tyson
,
J.
, and
Galanulis
,
K.
, 2003, “
Full-Field Dynamic Displacement and Strain Measurement Using Advanced 3D Image Correlation Photogrammetry: Part 1
,”
Exp. Tech.
,
27
(
3
), pp.
47
50
.
18.
Kajberg
,
J.
, and
Lindkvist
,
G.
, 2004, “
Characterisation of Materials Subjected to Large Strains by Inverse Modelling Based on In-Plane Displacement Fields
,”
Int. J. Solids Struct.
,
41
(
13
), pp.
3439
3459
.
19.
Meuwissen
,
M.
,
Oomens
,
C.
,
Baaijens
,
F.
,
Petterson
,
R.
, and
Janssen
,
J.
, 1998, “
Determination of the Elastoplastic Properties of Aluminium Using a Mixed Numerical-Experimental Method
,”
J. Mater. Process. Technol.
,
75
(
1
), pp.
204
211
.
20.
Molimard
,
J.
,
Le Riche
,
R.
,
Vautrin
,
A.
, and
Lee
,
J.
, 2005, “
Identification of the Four Orthotropic Plate Stiffnesses Using a Single Open-Hole Tensile Test
,”
Exp. Mech.
,
45
(
5
), pp.
404
411
.
21.
Grediac
,
M.
,
Toussaint
,
E.
, and
Pierron
,
F.
, 2002, “
Special Virtual Fields for the Direct Determination of Material Parameters With the Virtual Fields Method. 1-Principle and definition
,”
Int. J. Solids Struct.
,
39
(
10
), pp.
2691
2705
.
22.
Grediac
,
M.
, and
Pierron
,
F.
, 2006, “
Applying the Virtual Fields Method to the Identification of Elasto-Plastic Constitutive Parameters
,”
Int. J. Plast.
,
22
(
4
), pp.
602
627
.
23.
Chalal
,
H.
,
Avril
,
S.
,
Pierron
,
F.
, and
Meraghni
,
F.
, 2006, “
Experimental Identification of a Nonlinear Model for Composites Using the Grid Technique Coupled to the Virtual Fields Method
,”
Composites Part A
,
37
(
2
), pp.
315
325
.
24.
Michopoulos
,
J.
, and
Iliopoulos
,
A.
, 2009, “
A Computational Workbench for Remote Full Field 2D Displacement and Strain Measurements
,”
Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2009
,
ASME
(ed.), Paper No. DETC2009/CIE–86900.
25.
Andrianopoulos
,
N.
, and
Iliopoulos
,
A.
, 2006, “
Displacements Measurement in Irregularly Bounded Plates Using Mesh Free Methods
,”
Fracture of Nano and Engineering Materials and Structures
,
E.
Gdoutos
, ed.,
Springer
,
Dordrecht
, pp.
587
588
.
26.
Iliopoulos
,
A.
,
Michopoulos
,
J.
, and
Andrianopoulos
,
N.
, 2009, “
Performance Sensitivity Analysis of the Mesh-Free Random Grid Method for Whole Field Strain Measurements
,”
Proceedings of the ASME 2008 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2008
,
Brooklyn, New York
, pp.
545
555
.
27.
Iliopoulos
,
A.
, and
Michopoulos
,
J.
, 2009, “
Sensitivity Analysis of the Mesh-Free Random Grid Method for Measuring Deformation Fields on Composites
,”
Proceedings of the 17th International Conference on Composite Materials, ICCM–17: 27 Jul 2009–31 Jul 2009
,
The British Composites Society: Edinburgh International Convention Centre (EICC)
,
Edinburgh, UK
.
28.
Iliopoulos
,
A.
, and
Michopoulos
,
J.
, 2009, “
Effects of Anisotropy on the Performance Sensitivity of the Mesh Free Random Grid Method for Whole Field Strain Measurement
,”
Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2009
,
ASME
(ed.), Paper No. DETC2009/CIE–86962.
29.
Michopoulos
,
J.
, and
Furukawa
,
T.
, 2007, “
Multi-Level Coupling of Dynamic Data-Driven Experimentation With Material Identification
,”
Lect. Notes Comput. Sci.
,
4487
, pp.
1180
.
30.
Furukawa
,
T.
,
Michopoulos
,
J.
, and
Kelly
,
D.
, 2008, “
Elastic Characterization of Laminated Composites Based on Multiaxial Tests
,”
Compos. Struct.
,
86
(
1–3
), pp.
269
278
.
31.
Furukawa
,
T.
, and
Michopoulos
,
J.
, 2008, “
Online Planning of Multiaxial Loading Paths for Elastic Material Identification
,”
Comput. Methods Appl. Mech. Eng.
,
197
, pp.
885
901
.
32.
Man
,
H.
,
Furukawa
,
T.
, and
Kellermann
,
D.
, 2008, “
Implicit Constitutive Modeling Based on the Energy Principle
,”
Proceedings of XXII ICTAM, 25–59 August 2008
,
Adelaide
, Paper No: 11427.
33.
Michopoulos
,
J.
,
Furukawa
,
T.
, and
Lambrakos
S.
, 2009, “
Data-Driven Characterization of Composites Based on Virtual Deterministic and Noisy Multiaxial Data
,”
2008 ASME International Design Engineering Technical Conferences and omputers and Information in Engineering Conference, DETC 2008
, Vol.
3
,
New York City, NY
, pp.
1095
1106
.
34.
Furukawa
,
T.
, and
Pan
,
J.
, 2009, “
Stochastic Identification of Elastic Constants for Anisotropic Materials
,”
Int. J. Numer. Methods Eng.
,
81
(
4
), pp.
429
452
.
35.
Samarasinghe
,
S.
, 2006, “
Neural Networks for Applied Sciences and Engineering
,”
From Fundamentals to Complex Pattern Recognition
,
1st ed.
,
Auerbach Publications
,
Boston, MA
.
36.
Michopoulos
,
J.
, 1992, “
Constitutive Characterization of Composites Via Artificial Neural Nets
,”
Code 6383 Internal Report
,
NRL
April 1992.
37.
Leighton
,
R.
, 1994, “
AspirinMIGRAINES
,”
release v7.0
.
38.
Yagawa
,
G.
,
Yoshimura
,
S.
,
Okuda
,
H.
, and
Furukawa
,
T.
, 1996, “
Innovative Approaches for Modelling of Inelastic Material Behaviors
,” (Applications of Neural Networks and Evolutionary Algorithms), Localized Damage IV: Computer-Aided Assessment and Control, pp.
169
184
.
39.
Furukawa
,
T.
, and
Yagawa
,
G.
, 1998, “
Implicit Constitutive Modelling for Viscoplasticity Using Neural Networks
,”
Int. J. Numer. Methods Eng.
,
43
, pp.
195
219
.
40.
Furukawa
,
T.
, and
Hoffman
,
M.
, 2004, “
Accurate Cyclic Plastic Analysis Using a Neural Network Material Model
,”
Eng. Anal. Boundary Elem.
,
28
(
3
), pp.
195
204
.
41.
Man
,
H.
,
Furukawa
,
T.
,
Hoffman
,
M.
,
Imlao
,
S.
, and
Lou
,
Z. H.
, 2007, “
An Indirect Implicit Model for Frequency Dependent Hystereses of Piezoelectric Ceramics
,”
J. Aust. Ceram. Soc.
,
43
(
2
), pp.
169
174
. See http://www.austceram.com/_data/docs/journal/jacs2007-2/jacs_2007_43_2_man%2815%29.pdfhttp://www.austceram.com/_data/docs/journal/jacs2007-2/jacs_2007_43_2_man%2815%29.pdf.
42.
Man
,
H.
,
Furukawa
,
T.
,
Hoffman
,
M.
, and
Imlao
,
S.
, 2008, “
An Indirect Implicit Technique for Modelling Piezoelectric Ceramics
,”
Comput. Mater. Sci.
,
43
(
4
), pp.
629
640
.
43.
Ghaboussi
,
J.
, and
Sidarta
,
D.
, 1998, “
New Nested Adaptive Neural Networks (NANN) for Constitutive Modeling
,”
Comput. Geotech.
,
22
(
1
), pp.
29
52
.
44.
Shin
,
H.
, and
Pande
,
G.
, 2003, “
Identification of Elastic Constants for Orthotropic Materials From a Structural Test
,”
Comput. Geotech.
,
30
(
7
), pp.
571
577
.
45.
Jung
,
S.
, and
Ghaboussi
,
J.
, 2006, “
Neural Network Constitutive Model for Rate-Dependent Materials
,”
Comput. Struct.
,
84
(
15–16
), pp.
955
963
.
46.
Haj-Ali
,
R.
, and
Kim
,
H.
, 2007, “
Nonlinear Constitutive Models for FRP Composites Using Artificial Neural Networks
,”
Mech. Mater.
,
39
(
12
), pp.
1035
1042
.
47.
Man
,
H.
,
Furukawa
,
T.
,
Herszberg
,
I.
, and
Prusty
,
G.
, 2009, “
Implicit Modeling of Damage Behavior for Composite Materials Using an Energy-Based Method
,”
SAMPE ’09 Spring Symposium Conference Proceedings
, 18–21 May 2009,
Baltimore, MD
, pp.
54
, Paper No. 5704.
48.
van Rietbergen
,
B.
,
Odgaard
,
A.
,
Kabel
,
J.
, and
Huiskes
,
H. W. J.
, 1996, “
Direct Mechanics Assessment of Elastic Symmetries and Properties of Trabecular Bone Architecture
,”
J. Biomech.
,
29
, pp.
1653
1657
.
49.
Neidinger
,
R. D.
, 1995, “
Computing Multivariable Taylor Series to Arbitrary Order
,”
APL95 Conference Proceedings, APL Quote Quad
,
25
(
4
), pp.
134
144
.
50.
Lawson
,
C. L.
, and
Hanson
,
R. J.
, 1996,
Solving Least Squares Problems
,
Prentice-Hall
,
Englewood Cliffs, NJ
, 1974, Reprinted 1996 by SIAM Publications, Philadelphia, PA.
51.
Wolfram Research, Inc., 2008, Mathematica, Version 7.0, Champaign.
52.
Haupt
,
P.
, 2000, Continuum
Mechanics and Theory of Materials
,
Springer-Verlag
,
Berlin Heidelberg
.
53.
Matzenmiller
,
A.
,
Lubliner
,
J.
, and
Taylor
,
R. L.
, 1995, “
A Constitutive Model for Anisotropic Damage in Fiber—Composites
,”
Mech. Mater.
,
20
, pp.
125
152
.
54.
Van Der Meer
,
F. P.
,
Sluys
,
L. J.
, 2009, “
Continuum Models for the Analysis of Progressive Failure in Composite Laminates
,”
J. Compos. Mater.
,
43
(
20
), pp.
2131
2156
.
55.
Voyiadjis
,
G. Z.
,
Ju
,
J. W.
, and
Chaboche
,
J.-L.
, 1998,
Damage Mechanics in Engineering Materials
,
Elsevier Science
,
Amsterdam
.
56.
Kaliske
,
M.
, 2000, “
A Formulation of Elasticity and Viscoelasticiy for Fibre Reinforced Material at Small and Finite Strains
,”
Comput. Methods Appl. Mech. Eng.
,
85
, pp.
225
243
.
57.
Ryan
,
K. F.
, 1990, “
Dynamic Response of Graphite/Epoxy Plates Subjected to Impact Loading
,”
MSc thesis
,
MIT
,
Cambridge, MA
.
58.
Wegner
,
P. M.
, and
Adams
,
D. F.
, 2000, “
Verification of the Combined Load Compression (CLC) Test Method
,” DOT/FAA Technical Report DOT/FAA/AR–00/26.
59.
Vaidya
,
R. S.
, and
Sun
,
C. T.
, 1997, “
Fracture Criterion for Notched Thin Composite Laminates
,”
AIAA J.
,
35
(
2
), pp.
311
314
.
60.
Minguet
,
P. J.
,
Dugundji
,
J.
, and
Lagace
,
P. A.
, 1989, “
Postbuckling Behavior of Laminated Plates Using a Direct Energy-Minimization Technique
,”
AIAA J.
,
27
(
12
), pp.
1785
1792
.
61.
Lessard
,
L. B.
,
Eilers
,
O. P.
, and
Shokrieh
,
M. M.
, 1995, “
Testing of In-plane Shear Properties Under Fatigue Loading
,”
J. Compos. Reinf. Plast.
,
14
(
9
), pp.
965
987
.
62.
Esp
,
B.
,
Chan
,
W. S.
, 2008, “
Two Parameter Approximation to the Orthotropic Stress Concentration Factor
,”
SAMPE 2008
Long Beach, CA
, May 18–22.
63.
Jones
,
D. R.
,
Perttunen
,
C. D.
,
Stuckman
,
B. E.
, 1993, “
Lipschitzian Optimization Without the Lipschitz Constant
,”
J. Optim. Theory Appl.
,
79
, pp.
157
.
64.
65.
Spall
,
J. C.
, 2003,
Introduction to Stochastic Search and Optimization
,
Wiley
,
NJ
.
66.
ANSYS, Inc., 2009, ANSYS® Mechanical, Release 11.0.
This content is only available via PDF.
You do not currently have access to this content.