Homogenization of elasto-plastic composites coupled with a nonlinear finite element analysis of the equivalent inclusion problem

International Journal of Solids and Structures

Volumn 47, Issue 5, 2010, Pages 716-729

  Brassart, L ^a   Doghri, I ^a   Delannay, L ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Composite materials; Elasto plasticity; Finite element; Homogenization; Incremental; Isolated inclusion; Mean field; Mori Tanaka

Indexed keywords

APPROXIMATE EXPRESSIONS; COMPOSITE SYSTEMS; COST-EFFECTIVE SOLUTIONS; ELASTO-PLASTIC; ELLIPSOIDAL PARTICLES; EQUIVALENT INCLUSION; ESHELBY'S TENSOR; FE ANALYSIS; FE-SIMULATION; FINITE ELEMENT; FINITE ELEMENTS; FULL-FIELD; FULLY-COUPLED; HOMOGENIZATION SCHEME; INCLUSION MODELS; ISOLATED INCLUSION; LINEAR ELASTICITY; MEAN-FIELD; MICRO-MECHANICAL MODELING; MONOTONIC LOADING; MORI-TANAKA; NON-LINEAR FE; NON-LINEAR FINITE-ELEMENT ANALYSIS; NON-LINEAR REGIMES; PARTICLE REINFORCED; PLANE STRAINS; STRAIN CONCENTRATION; T-MODEL;

COMPOSITE MATERIALS; COMPOSITE MICROMECHANICS; COUPLED CIRCUITS; ELASTOPLASTICITY; FORECASTING; INDUSTRIAL MANAGEMENT; LOADING; PLASTICITY; PLASTICS; POLYMER MATRIX COMPOSITES; REINFORCEMENT; SIMULATORS; TENSORS; TITRATION;

FINITE ELEMENT METHOD;

EID: 72449195872     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2009.11.013     Document Type: Article

References (36)

1. ABAQUS, 2007. General-Purpose Finite Element Software. ABAQUS Inc., Pawtucket, RI, USA.
2. Benveniste Y. A new approach to the application of Mori-Tanaka's theory in composite materials. Mech. Mater. 6 (1987) 147-157
3. Benveniste Y., Dvorak G.J., and Chen T. On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media. J. Mech. Phys. Solids 39 (1991) 927-946
4. Berveiller M., and Zaoui A. An extension of the self-consistent scheme to plastically-flowing polycrystals. J. Mech. Phys. Solids 26 (1979) 325-344
5. Bornert, M., Bretheu, T., Gilormini, P., 2001. Homogénéisation en mécanique des matériaux. Hermes Science, Paris.
6. Brassart L., Inglis H.M., Delannay L., Doghri I., and Geubelle P.H. An extended Mori-Tanaka homogenization scheme for finite strain modeling of debonding in particle-reinforced elastomers. Comp. Mater. Sci. 45 (2009) 611-616
7. Chaboche J.L., Kanouté P., and Roos A. On the capabilities of mean-field approaches for the description of plasticity in metal matrix composites. Int. J. Plasticity 21 (2005) 1409-1434
8. Corbin S., Wilkinson D., and Embury J. The bauschinger effect in a particulate reinforced Al alloy. Mater. Sci. Eng. A 207 (1996) 1-11
9. Delannay L., Doghri I., and Pierard O. Prediction of tension-compression cycles in multiphase steel using a modified incremental mean-field model. Int. J. Solids Struct. 44 (2007) 7291-7306
10. Delannay L., Pierman A.-P., and Jacques P. Assessment of a micro-macro modeling of the bending and unbending of multiphase steel sheets. Adv. Eng. Mater. 11 (2009) 148-152
11. Doghri I., and Ouaar A. Homogenization of two-phase elasto-plastic composite materials and structures: study of tangent operators, cyclic plasticity and numerical algorithms. Int. J. Solids Struct. 40 (2003) 1681-1712
12. Eshelby J.D. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. London A 241 (1957) 376-396
13. Gilormini P. Insuffisance de l'extension classique du modéle auto-cohérent au comportement non linéaire. C.R. Acad. Sci. Paris 320 Série IIb (1995) 115-122
14. Guillemer-Neel C., Bobet V., and Clavel M. Cyclic deformation behaviour and bauschinger effect in ductile cast iron. Mater. Sci. Eng. A 272 (1999) 431-442
15. Han W., Eckschlager A., and Böhm H.J. The effects of three-dimensional multi-particle arrangements on the mechanical behavior and damage initiation of particle-reinforced MMCs. Compos. Sci. Technol. 61 (2001) 1581-1590
16. Hazanov S., and Huet C. Order relationships for boundary condition effects in heterogeneous bodies smaller than the representative volume. J. Mech. Phys. Solids 42 (1994) 1995-2011
17. Hershey A.V. The elasticity of an isotropic aggregate of anisotropic cubic crystals. J. Appl. Mech. 21 (1954) 236-240
18. Hill R. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids 13 (1965) 89-101
19. Kröner E. Berechnung der elastischen konstanten des vielkristalls aus den konstanten des einkristalls. Z. Physik 151 (1958) 504-518
20. LLorca J., and Segurado J. Three-dimensional multiparticle cell simulations of deformation and damage in sphere-reinforced composites. Mater. Sci. Eng. A 365 (2004) 267-274
21. Masson R., and Zaoui A. Self-consistent estimates for the rate-dependent elastoplastic behaviour of polycrystalline materials. J. Mech. Phys. Solids 47 (1999) 1543-1568
22. Mori T., and Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21 (1973) 571-574
23. NETGEN, 2004. Automatic Mesh Generator, Version 4.4. Available from . J. Schöberl, University of Linz, Austria.
24. Pierard O., and Doghri I. An enhanced affine formulation and the corresponding numerical algorithms for the mean-field homogenization of elasto-viscoplastic composites. Int. J. Plasticity 22 (2006) 131-157
25. Pierard O., and Doghri I. Study of various estimates of the macroscopic tangent operator in the incremental homogenization of elastoplastic composites. Int. J. Multiscale Comp. Eng. 4 (2006) 521-543
26. Pierard O., Gonzalez C., Segurado J., LLorca J., and Doghri I. Micromechanics of elasto-plastic materials reinforced with ellipsoidal inclusions. Int. J. Solids Struct. 44 (2007) 6945-6962
27. Ponte Castañeda P. Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. J. Mech. Phys. Solids 44 (1996) 827-862
28. Ponte Castañeda P. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I-theory. J. Mech. Phys. Solids 50 (2002) 737-757
29. Qiu Y.P., and Weng G.J. On the application of Mori-Tanaka's theory involving transversely isotropic spheroidal inclusions. Int. J. Eng. Sci. 28 (1990) 1121-1137
30. Rekik A., Auslender F., Bornert M., and Zaoui A. Objective evaluation of linearization procedures in nonlinear homogenization: a methodology and some implications on the accuracy of micromechanical schemes. Int. J. Solids Struct. 44 (2007) 3468-3496
31. Segurado J., and LLorca J. Computational micromechanics of composites: the effect of particle spatial distribution. Mech. Mater. 38 (2006) 873-883
32. Segurado J., LLorca J., and González C. On the accuracy of mean-field approaches to simulate the plastic deformation of composites. Scripta Mater. 46 (2002) 525-529
33. Suquet P. Overall properties of nonlinear composites: a modified secant moduli theory and its link with Ponte Castañeda's nonlinear variational procedure. C.R. Acad. Sci. Paris 320 Série IIb (1995) 563-571
34. Tandon G.P., and Weng G.J. A theory of particle-reinforced plasticity. J. Appl. Mech. 55 (1988) 126-135
35. Walpole L.J. Elastic behavior of composite materials: theoretical foundations. Adv. Appl. Mech. 21 (1981) 169-242
36. Weissenbek E., Böhm H., and Rammerstorfer F. Micromechanical investigations of arrangement effects in particle reinforced metal matrix composites. Comp. Mater. Sci. 3 (1994) 263-278