A Damage Law for Dynamic Failure in Brittle Solids with Penny-Shaped Microcracks

A damage model for dynamic tensile failure of nominally brittle solids is constructed using a two-scale approach. The asymptotic homogenization method is applied to microstructures with penny-shaped microcracks evolving dynamically in order to obtain the new damage law. A microstructural length is present in the deduced evolution equation for which a strain-rate dependent fragment-size type expression is proposed. The ability of the new approach to predict the rate sensitivity of the tensile strength observed in experiments is illustrated for concrete and ceramic materials.