A Mechanism-Based Constitutive Model for Competent Rocks Subjected to Impact Loading

Abstract

The dynamic behavior of rocks under dynamic loading conditions is important in a wide range of processes, including meteorite impact, planetary defense, earthquakes, and mining. Phenomenological constitutive models have been extensively developed to capture rock behavior but have difficulty describing response under such extreme conditions. In this study, we present a mechanism-based model to describe the behavior of rocks under high-velocity impact and related dynamic loading conditions. The model captures elasticity, the equation of state, micro-cracking induced fracture, crystal plasticity, granular flow, and porosity evolution of granular material within a thermodynamically consistent finite-deformation framework. We select sandstone as the model material and determine the material parameters based on independent experimental data. We then conduct high-velocity ($\sim 2$ km/s) impact tests on sandstone samples, and use the experimental data to validate the calibrated model. The results show that our model captures the competition and evolution of the failure mechanisms within sandstone during high velocity impact, and provides good agreement with experiments in terms of in situ impact processes and post-mortem crater dimensions. Our results also highlight the critical role of the cap component in the granular flow mechanism submodel for capturing the dynamic response of sandstone under high velocity impact, while demonstrating the relative insensitivity to the choice of non-associative and associative granular flow rules within this particular application. Our model can be applied to other competent rocks (e.g., granite and basalt) and other extreme conditions (e.g., shock and explosion) because of the similarity in deformation and failure mechanisms shared by these geomaterials.