A dynamic phase-field model for rock fracture under impact loading: Drucker–Prager energy decomposition with micro-inertia effects

The phase-field method is an effective tool for simulating dynamic fracture. Its application to rock under impact loading, however, requires a pressure-sensitive description of strength together with a physically based account of loading-rate effects. This study develops a dynamic fracture phase-field model for rock that combines a Drucker–Prager-consistent decomposition of the strain energy density with a micro-inertia term in the damage evolution equation. The decomposition characterizes the asymmetric tensile–compressive failure of rock under complex stress states, while the micro-inertia coefficient follows in closed form from the critical energy release rate, the length scale parameter, and the longitudinal wave velocity, so that no additional calibration is required. The coupled equations are solved by an explicit staggered algorithm implemented as a user-defined element (VUEL) in ABAQUS/Explicit. The model is validated against split Hopkinson pressure bar (SHPB) tests on limestone under varying impact velocities and repeated impacts, against dynamic fracture benchmarks, and against semi-circular bend (SCB) impact tests on sandstone with different flaw inclinations. Comparisons of predictions with and without the micro-inertia term, quantified through extracted crack-tip velocities, delineate the loading regimes in which the term becomes significant. Sensitivity analysis based on an orthogonal experimental design identifies Young's modulus, the length scale parameter, and the critical energy release rate as the dominant parameters; these same parameters jointly govern the micro-inertia coefficient, endowing the dynamic formulation with an intrinsic time scale absent from quasi-static phase-field models. This study provides a theoretical basis for rock dynamic fracture simulation under impact loading and for parameter calibration in impact-resistant design.