A simplified approach to continuous damage of composite materials and micromechanical analysis

A comprehensive approach to the continuous damage of materials is formulated within the framework of thermodynamic reasoning. Particular emphasis is put on the application to composites. The starting point lies in the assumption that damage evolution can be described at the macroscopic scale by means of a tensor variable. The thermodynamic force associated with the evolution of the damage tensor is deduced from the expression of the intrinsic dissipation. A phenomenological criterion for damage yielding is then proposed and a hardening law associated with the damage process is identified from available experiment results. For completeness, the rate-type constitutive equations are derived. This damage model is therefore implemented within a finite element procedure. The numerical tool is then applied to analyze the damage induced by mechanical loading in several examples of composite materials. The numerical predictions are compared to available closed-form solutions or experimental results. The last part of the paper is dedicated to a micromechanical analysis of damage in the composite material. A simplified macro-to-micro framework is formulated for the evaluation of damage and stress concentrations within the constituents of the composite from the knowledge of the composite morphology and from the stress and damage at the macroscopic scale.