A strain rate enhanced continuum damage model for rocks subjected to dynamic loading

Abstract

Deformation and failure mechanisms of rocks are dependent on the imposed loading rate and its range, like quasi-static and dynamic. This study proposes a continuum damage model (CDM) to predict the rate-dependent deformation response of rocks subjected to dynamic compressive (impact) load. The model formulation considers the coupling of damage and plasticity in the dissipative stress space, while compressive damage alone governs the yielding in the true stress space. Strain rate effects under dynamic conditions are accounted for through a Perzyna-type viscoplastic formulation using an overstressed function of the yield equation of CDM. A fully implicit stress integration scheme is adopted for finite element (FE) implementation of the model as a user-defined material. Further, it is demonstrated that the proposed strain rate enhancement can regularise the model to overcome bifurcation instability and associated mesh sensitivity during numerical simulations. The FE model is validated against the experimental results of three types of rocks (rock-like material, marble and sandstone). The model predicts the impact loading response of rock, especially constitutive response, post-peak structural response, and energy dissipation at varying strain rates in agreement with the experimental results, requiring fewer parameters than similar classes of other existing CDMs. The model response indicates that localised damage evolution is strain rate sensitive, and its intensity and distribution across the sample increase with the increment in strain rates. Further, the analysis shows that the dynamic loading response is highly sensitive to the exponent used for defining the Perzyna overstressed function, while insensitive under quasistatic loading conditions.