Two-scale damage modeling of brittle composites

This paper is aimed at developing a non-local theory for obtaining a numerical approximation to a boundary-value problem describing damage phenomena in a ceramic composite material. The mathematical homogenization method based on double-scale asymptotic expansion is generalized to account for damage effects in heterogeneous media. A closed-form expression relating local fields to the overall strain and damage is derived. Non-local damage theory is developed by introducing the concept of non-local phase fields (stress, strain, free energy density, damage release rate, etc.). Numerical results of our model were found to be in good agreement with experimental data from 4-point bend tests conducted on composite beams made of Blackglas™/Nextel 5-harness satin weave.