A two-scale damage model for dynamic rock behavior

Modeling the dynamic damage response of rocks requires taking into account the mechanics of micro-cracks and their overall response to applied loading. This paper presents a new micro-mechanical damage model accounting for inertial effects. The two-scale damage model is fully deduced from small-scale descriptions of dynamic microcrack propagation, without macroscopic assumptions. The passage from the micro-scale to the macro-scale is done through an asymptotic homogenization approach. An appropriate micromechanical energy analysis is proposed leading to a dynamic damage evolution law. Numerical simulations are presented in order to illustrate the ability of the model to describe known behaviors upon high strain rate, like size dependency of the structural response or strain-rate sensitivity.