Computational damage mechanics for composite materials based on mathematical homogenization

This paper is aimed at developing a non-local theory for obtaining numerical approximation to a boundary value problem describing damage phenomena in a brittle composite material. The mathematical homogenization method based on double-scale asymptotic expansion is generalized to account for damage e!ects in heterogeneous media. A closed-form expression relating local "elds to the overall strain and damage is derived. Non-local damage theory is developed by introducing the concept of non-local phase "elds (stress, strain, free energy density, damage release rate, etc.) in a manner analogous to that currently practiced in concrete [1, 2], with the only exception being that the weight functions are taken to be C0 continuous over a single phase and zero elsewhere. Numerical results of our model were found to be in good agreement with experimental data of 4-point bend test conducted on composite beam made of BlackglasTM/Nextel 5-harness satin weave.