Homogenized mechanical behavior of composite micro-structures including micro-cracking and contact evolution

The aim of this paper is to study the effects of micro-cracking on the homogenized constitutive properties of elastic composite materials. To this end a novel micro-mechanical approach based on homogenization techniques and fracture mechanics concepts, is proposed and an original J-integral formulation is established for composite micro-structures. Accurate non-linear macroscopic constitutive laws are developed for a uniaxial and a shear macro-strain path by taking into account changes in micro-structural configuration owing to crack growth and crack face contact. Numerical results, carried out by coupling a finite element formulation and an interface model, are applied to a porous composite with edge cracks and a debonded short fiber-reinforced composite. The composite micro-structure is controlled by the macroscopic strain and the micro-to-macro transition, settled in a variational formulation, is obtained for three types of boundary conditions, i.e. linear displacements, uniform tractions and periodic fluctuations and anti-periodic tractions. The accuracy of the determined macroscopic constitutive properties to represent the failure characteristics of locally periodic defected composites is also investigated in terms of energy release rate predictions, by comparisons between a direct analysis and homogenization approaches. Results highlight the dependence of the macroscopic constitutive law for a micro-structure with evolving defects on both the macro-strain path and the type of boundary conditions and the capability of the proposed model to provide a failure model for a composite material undergoing micro-cracking and contact.