Effects of microfracture and contact induced instabilities on the macroscopic response of finitely deformed elastic composites

An original non-linear analysis of the homogenized response of periodic elastic composites under large deformations, is here carried out by accounting for the coupled effects of micro-cracks in unilateral self-contact and of instabilities and bifurcation microstructural phenomena. The structure and properties of the composite macroscopic response are investigated by obtaining new analytical results able to distinguish the contributions of microstructural heterogeneities, including fractures and voids, crack self-contact and local constitutive behavior. In light of these results the relations between microstructural instability mechanisms and macroscopic instabilities detected by loss of ellipticity or softening behavior of the homogenized tangent moduli tensor related to conjugated stress and strain rate measures, are studied. Novel numerical applications of the theory, developed by means of coupled FE models of a 2D microcracked composite with circular inclusions driven along uniaxial and biaxial macro-deformation paths, are presented pointing out the sequence of bifurcation and instability load factors for different micro-geometries and the relations among the stability domains at both micro and the macro levels.