On Damage Induced Anisotropy for Fiber Composites

A stress-strain relation on the basis of a homogenized continuum is devel oped from a potential energy function for an elastic material with anisotropic damage. It is assumed that the influence of the state of damage can be represented by a vector-valued function, resulting from an array of surface discontinuities with coinciding orientation such as disk-like, parallel cracks. Usually, only low-order polynomial expansions in terms of the damage variable have been considered in the literature, limiting the results to non- interacting microcracks. In this paper, a complete polynomial expansion of the potential function with respect to the damage variable is developed and the general form of the con stitutive tensor for the damaged material is derived. This allows account to be taken of nonlinear dependencies of the effective elastic properties on the damage variable in the case of interacting microcracks.