A continuum model with microstructure for materials with flaws and inclusions

Abstract
A continuum endowed with affine microstructure is adopted for the macroscopic description of fiber composite materials. The microstructure is made of a rigid and of a deformable local structure. The former represents the fibers 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 derived from a discrete microscopic model using an integral procedure of equivalence. Constitutive elastic stress-strain relationships, accounting for the geometry of the internal phases, are identified. The balance equations for 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 from fine to gross description.