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

ABSTRACT: 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