Mean-field homogenization of elasto-viscoplastic composites based on a new map**-tangent linearization approach

Abstract

In this work, a new homogenization method of elasto-viscoplastic composites is developed. Using the fully implicit backward Euler’s integration algorithm, the nonlinear ordinary differential equations in the constitutive laws of the matrix and inclusion phases are discretized. Three classical incremental linearization approaches, i.e., direct, secant and tangent ones are adopted and an affine relationship between the stress and strain increments is deduced. In order to reduce the interaction between the inclusion and matrix phases, a second-ordered map** tensor is introduced and a new map**-tangent linearization approach is proposed. Different linearization approaches are implemented by the incremental self-consistent scheme to predict the overall stress-strain response of particle-reinforced composites. It is shown that the predicted stress-strain curves given by the proposed map**-tangent linearization approach are softer than that by other three classical ones, and are much closer to that from a fullfield finite element simulation. Moreover, the linearized elasto-viscoplastic constitutive equation based on the proposed map**- tangent approach has the same mathematical structure as the rate-independent elasto-plastic constitutive law. In this sense, the homogenization problems faced in the elasto-plastic and elasto-viscoplastic heterogeneous materials can be unified.