A Simple 3D Damage-Plasticity Model with Energy-Based Regularisation in SPH for Modelling Fractured Quasi-brittle Rocks

Abstract This study presents a new 3D coupled damage-plasticity model with energy-based regularisation in Smoothed Particle Hydrodynamics (SPH) for modelling fractured quasi-brittle rocks. The model accounts for energy dissipation in both the tensile and compressive regimes by distinctly separating damage evolution in tension and compression. A semi-analytical solution is introduced to derive damage evolution parameters linked to energy dissipation, facilitating straightforward model calibration and numerical assessment. Additionally, the model integrates the scalar damage variable into a yield surface, unifying the material’s initial state and failure criteria within a single function. This single-loading function approach, which governs both plasticity and damage evolution, simplifies model calibration and numerical implementation for solving boundary value problems (BVPs). To control volumetric behaviour, the model incorporates the dilation angle and its evolution, ensuring no volumetric change at the critical state (CS). The model’s performance, evaluated at both the material point and structural levels, demonstrates effective mesh independence and accurately captures tensile failures, mixed-mode tensile/compression-shear failures, and volumetric responses under various loading conditions.