A Micromechanics Approach for Constructing Locally Averaged Damage Dependent Constitutive Equations in Inelastic Composites

Homogenization techniques are utilized herein to construct locally aver aged mechanical constitutive equations for composites. Techniques are first reviewed for elastic composites, followed by a review of elastic composites with cracks and inelastic composites without cracks. These reviews are followed by a development of homogenized equations for inelastic composites with cracks. All equations are constructed for the case wherein a representative volume element is subjected to spatially uniform boundary strains. Several examples are presented for a representative SiC/Ti continuous fiber com posite subjected to tensile deformations transverse to the fiber direction. It is demonstrated that as the damage and matrix material model are increased in complexity, the computa tional requirements needed to obtain homogenized properties increase to the point where homogenization techniques may not be computationally tenable when applied recursively in macroscale structural analyses.