A continuum model with microstructure for materials with flaws and inclusions

A continuum endowed with affine microstructure is adopted for the macroscop ic description of fiber composite materials. The microstructure is made of a rigid and of a deformable local structure. The former represents the fibe rs of the composite, perceived as rigid inclusions. The latter accounts for the presence of distributed flaws, considered as slit microcracks. In the framework of a degree one theory, a formula for the mechanical power is der ived from a discrete microscopic model using an integral procedure of equiv alence. Constitutive elastic stress-strain relationships, accounting for th e geometry of the internal phases, are identified. The balance equations fo r both the continuum macro and micro-actions are derived from the axiom of vanishing power and of invariance of power under change of observer. It is also shown that the material symmetries are preserved in the transition fro m fine to grass description.