Simulated Micromechanical Models Using Artificial Neural Networks
Publication: Journal of Engineering Mechanics
Volume 127, Issue 7
Abstract
A new method, termed simulated micromechanical models using artificial neural networks (MMANN), is proposed to generate micromechanical material models for nonlinear and damage behavior of heterogeneous materials. Artificial neural networks (ANN) are trained with results from detailed nonlinear finite-element (FE) analyses of a repeating unit cell (UC), with and without induced damage, e.g., voids or cracks between the fiber and matrix phases. The FE simulations are used to form the effective stress-strain response for a unit cell with different geometry and damage parameters. The FE analyses are performed for a relatively small number of applied strain paths and damage parameters. It is shown that MMANN material models of this type exhibit many interesting features, including different tension and compression response, that are usually difficult to model by conventional micromechanical approaches. MMANN material models can be easily applied in a displacement-based FE for nonlinear analysis of composite structures. Application examples are shown where micromodels are generated to represent the homogenized nonlinear multiaxial response of a unidirectional composite with and without damage. In the case of analysis with damage growth, thermodynamics with irreversible processes (TIP) is used to derive the response of an equivalent homogenized damage medium with evolution equations for damage. The proposed damage formulation incorporates the generalizations generated by the MMANN method for stresses and other possible responses from analysis results of unit cells with fixed levels of damage.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
ABAQUS user's manual; version 5.8. ( 1998). Hibbitt, Karlsson and Sorensen, 1998.
2.
Aboudi, J. ( 1982). “A continuum theory for fiber-reinforced elastic-viscoplastic composites,” Int. J. Eng. Sci., 20, 605–622.
3.
Aboudi, J. ( 1991). Mechanics of composite materials—A unified micromechanical approach, Elsevier, Science, New York.
4.
Adams, D. F. ( 1970). “Inelastic analysis of a unidirectional composite subjected to transverse normal loading.” J. Comp. Mat., 4, 310–328.
5.
Bahei-El-Din, Y. A., Dvorak, G. J. ( 1989). “A review of plasticity theory of fibrous composite materials.” Metal matrix composites—testing, analysis and failure, W. S. Johnson, ed., STP-1032, ASTM.
6.
Benveniste, Y. ( 1987). “Mori-Tanaka,” Mech. of Mat., 6, 147.
7.
Christensen, R. M. ( 1990). “A critical evaluation for a class of micromechanics models.” J. Mech. Phys. Solids, 38(3), 379–404.
8.
Caiazzo, A. A., and Costanzo, F. ( 2000a). “On the constitutive behavior of layered composites with evolving cracks.” Int. J. Solids Struct., 38, 3469–3485.
9.
Caiazzo, A. A., and Costanzo, F. ( 2000b). “On the effective elastic properties of composites with evolving microcracking.” J. Reinforced Plastics Comp., 19, 152–163.
10.
Costanzo, F., Boyd, J. G., and Allen, D. H. ( 1996). “Micromechanics and homogenization of inelastic composite materials with growing cracks.” J. Mech. Phys. Solids, 44(3), 333–370.
11.
Dvorak, G. J. ( 1991). “Plasticity theories for fibrous composite materials.” Metal-matrix composites, Vol. 2, R. K. Everett and R. J. Arsenault, eds., Academic, San Diego, 1–77.
12.
Ellis, G., Yao, C., Zhao, R., and Penumadu, D. (1995). “Stress-strain modeling of sands using artificial neural network.”J. Geotech. Engrg., ASCE, 121(5), 429–435.
13.
Feyel, F., and Chaboche, J.-L. ( 2000). “FE2 multiscale approach for modeling the elastoviscoplastic behavior of long SiC/Ti composite materials.” Comput. Methods Appl. Mech., 183, 309–330.
14.
Foye, R. L. ( 1973). “Theoretical post-yielding behavior of composite laminates Part I—Inelastic micromechanics.” J. Comp. Mat., 7, 178–193.
15.
Gavazzi, A. C., and Lagoudas, D. C. ( 1990). “On the numerical evaluation of Eshelby's tensor and its application to elastoplastic fibrous composites.” Computational Mech., 7, 13–19.
16.
Ghaboussi, J., Garrett, J. H., and Wu, X. (1991). “Knowledge-based modeling of material behavior with neural networks.”J. Engrg. Mech., ASCE, 117(1), 132–153.
17.
Ghaboussi, J., Lade, P. V., and Sidarta, D. E. ( 1994). “Neural network based modeling in geomechanics.” Proc., Int. Conf. on Numerical Methods and Advances in Geomechanics.
18.
Ghaboussi, J., Pecknold, D. A., Zhang, M., and Haj-Ali, R. M. ( 1996). “Neural network constitutive models determined from structural tests.” Proc. of the 11th Conf. of Engineering Mechanics, Vol. 2, ASCE, New York, 701–704.
19.
Ghaboussi, J., Pecknold, D. A., Zhang, M.-F., and Haj-Ali, R. M. ( 1998). “Autoprogressive training of neural network constitutive models,” Int. J. Numer. Methods in Engrg., 42, 105–126.
20.
Haj-Ali, R. M., Kurtis, K. E., and Sthapit, A. R. ( 2001). “Neural network modeling of concrete expansion during long-term sulfate exposure.” ACI Mat. J., 98(1), 36–43.
21.
Haj-Ali, R. M., and Pecknold, D. A. ( 1996). “Hierarchical material models with microstructure for nonlinear analysis of progressive damage in laminated composite structures.” Structural research series No. 611, UILU-ENG-96-2007, Dept. of Civ. Engrg., University of Illinois at Urbana-Champaign.
22.
Haj-Ali, R. M., Pecknold, D. A., and Ghaboussi, J. ( 1998). “Micromechanics-based constitutive damage models for composite materials using artificial neural-networks.” Modeling and simulation based engineering, S. N. Atluri and P. E. O'Donoghue, eds., Proc. of Int. Conf. Computational Engrg. Sci., ICES98, Atlanta, Ga., 551–557.
23.
Haj-Ali, R. M., Pecknold, D. A., and Ghaboussi, J. ( 1999). “Micromechanical damage models using artificial neural-networks.” Proc., 13th ASCE Engrg. Mech. Div. Conf., June 13–16, Baltimore, Md.
24.
Hertz, J., Krogh, A., and Palmer, R. G. ( 1991). Introduction to the theory of neural computations, Addison-Wesley, Reading, Mass.
25.
Lagoudas, D. C., Gavazzi, A. C., and Nigam, H. ( 1991). “Elastoplastic behavior of metal matrix composites based on incremental plasticity and the Mori-Tanaka averaging scheme.” Computational Mech., 8, 193–203.
26.
Lemaitre, J. ( 1992). A course on damage mechanics, Springer, New York.
27.
Lissenden, C. J., and Herakovich, C. T. ( 1992). “Comparison of micromechanical models for elastic properties.” Space '92, Proc. 3rd Int. Conf., W. Z. Sadeh, S. Sture, and R. J. Miller, eds., ASCE, New York, 1309–1322.
28.
Maugin, G. A. ( 2000). The thermomechanics of nonlinear irreversible behaviors, Series A, Vol. 27, World Scientific, River Edge, N.J.
29.
Mori, T., and Tanaka, K. ( 1973). “Average stress in matrix and average elastic energy of materials with misfitting inclusions.” Acta Metall., 21, 571–574.
30.
Noor, A. K., and Shah, R. S. ( 1993). “Effective thermoelastic and thermal properties of unidirectional fiber-reinforced composites and their sensitivity coefficients.” Comp. and Struct., 26, 7–23.
31.
Paley, M., and Aboudi, J. ( 1992). “Micromechanical analysis of composites by the generalized cells model.” Mech. of Mat., 14, 127–139.
32.
Pecknold, D. A., and Haj-Ali, R. M. ( 1993). “Integrated micromechanical/structural analysis of laminated composites.” Mechanics of Composite Materials—Nonlinear Effects, M. W. Hyer, ed., SES/ASME/ASCE joint meeting, Charlottesville, Va., Vol. 159, 197–206.
33.
Pidaparti, R., and Palakal, M. ( 1993). “Material model for composites using neural networks.” AIAA J., 31, 1533–1535.
34.
Ritter, H., Martinez, T., and Schulten, K. ( 1991). Neural computation and self-organizing maps: An introduction, Addison-Wesley, Reading, Mass.
35.
Suresh, S., and Brockenbrough, J. R. ( 1994). “Continuum models for deformation: Metals reinforced with continuous fibers.” Fundamentals of Metal-Matrix composites, S. Suresh, A. Mortensen, and A. Needleman, eds., Butterworth-Heinemann, Stoneham, Mass.
36.
Tsai, S. W., Adams, D. F., and Doner, D. R. ( 1966a). “Effect of constituent material properties on the strength of fiber-reinforced composite materials.” Air Force Research Lab. CR, AFML-TR-66-190.
37.
Tsai, S. W., Adams, D. F., and Doner, D. R. ( 1966b). “Analysis of composite structures.” NASA CR-620.
38.
Voyiadjis, G. Z., and Kattan, P. I. ( 1999). Advances in damage mechanics: Metals and metal matrix composites, Elsevier, Science, New York.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 127 • Issue 7 • July 2001
Pages: 730 - 738
History
Received: Apr 16, 2001
Published online: Jul 1, 2001
Published in print: Jul 2001
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.