Strength of Stochastic Brittle Solids under High-Rate Compressive Loading

Most brittle solids of engineering and scientific interest have stochastic microstructures—comprised of a polycrystalline matrix randomly interspersed with micro-scale defects such as cracks, second-phases, precipitates, grain boundaries, and pores. These defects are often initiators of micro-cracking which results in damage-induced softening and non-linearity in stress-strain response. The random nature of the heterogeneities also plays a significant role in the spatial stochasticity of microcracking. Traditionally, representative volume elements have been used to model the constitutive response of two (or more) phase, composite-like, materials. However, without heeding to the variability in the microstructure, a volume average-based modelling approach remains limited in its predictive capability. Since the peak stress achieved in high-rate compression of brittle solids is the result of the competition between softening due to damage and the rate-effect, estimates of the dynamic compressive strength can also be impacted. To improve modelling of materials with evolving microstructures with progression of damage, its critical to model the “mesoscale” evolution i.e. the evolution of a collection of stochastic micro-structural features. Further, spatial variability introduced by this evolution needs to be handled in an ensemble-averaged sense. Towards this end have developed a mechanism-based, non-local model for brittle solids for appropriate scaling of key statistical information from micro- through meso- to macroscopic-scales. Using this framework, we predict an uncorrelated volume element for accurate strength prediction of a brittle microcracking solid under dynamic loading.