Effective Properties for Non-linear Composite Materials: Computational Aspects

Abstract

This paper considers some aspects of the computational evaluation of effective properties of composite materials. The computational models used assume that the composite materials can be represented by the periodic repetition of a microstructure. Based on this assumption and using asymptotic expansions (homogenization theory) the effective properties for linear composite materials can be derived, as is well known [1–6]. The characterization of effective properties for nonlinear composite materials is a more involved issue and had been studied by researchers in different fields [6–16]. The computational models for the nonlinear case consider the same kind of approach, asymptotic expansions, and are restricted to the quasi static loading conditions, i.e., neglecting inertia effects. Two different kind of models are introduced. One based on incremental formulation, and another based on Newton’s general iterative scheme for nonlinear equations. The incremental model is particularized for large deformation of elasto-plasticity of composites. Assumptions with respect to the components constitutive relations are: rate independent plasticity, additive decomposition of velocity gradient, isotropic and kinematic hardening, and normal flow rule. The Newton’s model is introduced for both the general case or the hyperelastic case. Any of the presented models is able to characterize the effective tangent modulli of the composite, however, since these depend on the microstructure stress distribution, overall global properties are, in general, difficult to characterize. The numerical examples presented for the nonlinear case consider only the incremental model. For these examples, the components of the composite microstructure are assumed to have constitutive relations based on J2 flow plasticity theory with isotropic hardening. Determination of “equivalent” plasticity properties for the composite and convergence issues are addressed.