A matrix formulation for the elastoplastic homogenisation of layered materials

Abstract

In this article attention is given to the homogenisation of periodic layered materials. Based on the assumption of a homogeneous state of stress and strain in each layer, a novel matrix formulation capable of representing the elastic behaviour of the composite material is established. The matrix formulation yields a much clearer implementation of linear elastic homogenisation algorithms and a relatively straightforward extension to inelastic behaviour. The theory of plasticity, which is adopted to describe the inelastic behaviour, follows modern concepts, including a unconditionally stable implicit Euler backward return mapping, a local Newton–Raphson method and a consistent tangent stiffness matrix. A comparison between the homogenised continuum and the standard continuum with an exact discretisa tion of the geometry of the composite shows excellent agreement, both in the presence of elastic and inelastic material behaviour.