Abstract
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
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.
The Mathworks, “
Matlab
,” http://www.mathworks.comhttp://www.mathworks.com65.
Spall
, J. C.
, 2003, Introduction to Stochastic Search and Optimization
, Wiley
, NJ
.66.
ANSYS, Inc., 2009, ANSYS® Mechanical, Release 11.0.
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