Implicit Stress Integration in Elastoplasticity of n-Phase Fiber-Reinforced Composites

Abstract

Stress integration schemes for elastoplastic constitutive relations for homogeneous materials have been extensively proposed by several researchers during the last two decades. In this paper, a set of micromechanics equations are formulated based on the Transformation Field Analysis (TFA) method. When integrating the constitutive relation of fibrous composites, an implicit integration scheme, namely the Governing Parameter Method (GPM) is employed to provide the overall elastoplastic stress-strain relations for n-phase fiber-reinforced composites using the J 2-plasticity with strain hardening. This integration scheme is employed instead of the conventional explicit stress integration scheme because it only needs to solve a nonlinear algebraic equation instead of a 6 × (n + 1) system of differential-algebraic equations. The proposed integration scheme can accommodate other complex plasticity models as well. More importantly, the combined TFA and GPM approach can also be used as a constitutive model for use in nonlinear finite element method to analyze structural response.