A peridynamic model for mixed-mode fracture and compression-shear failure in geomaterials

In this paper, we propose a tension/compression-aware ordinary state-based peridynamic (OSB-PD) formulation for geomaterials that is thermodynamically consistent and friction-capable. The force-density state is split into volumetric and deviatoric parts: the volumetric response is retained in compression and degrades only in tension, while the deviatoric response degrades in both. A Mohr-Coulomb-type friction state activates post-damage under compression to supply residual sliding resistance. An energy split into positive/negative parts with mode-dependent degradation enforces the Clausius-Duhem inequality; frictional work remains non-conservative. Softening is driven by equivalent normal and shear strains reconstructed via peridynamic differential operator method, with thresholds tied to tensile/shear strengths and Mode I/II fracture energies for transparent calibration. Benchmarks and representative problems confirm accuracy and robustness: single-edge-notched plates in tension and pure shear reproduce theoretical initiation angles and peak loads; a long-shear apparatus recovers Palmer-Rice scaling and a uniform-traction slip surface; flawed-gypsum compression captures observed crack coalescence and post-peak softening; and a pseudo-3D slope develops a continuous shear band consistent with FEM strength-reduction analysis. The framework unifies tensile, mixed-mode, and shear-dominated failure within a single, calibratable model.