An improved bond-associated peridynamics for modelling elastoplastic deformation and progressive fracture in geomaterials

Geomaterials are pressure-dependent and exhibit non-linear elastoplastic deformation and failure behaviours, including strain localisation and complex cracking. To study these phenomena, this paper develops an improved non-ordinary state-based peridynamic (NOSB-PD) framework for simulating the elastoplastic response and progressive failure of geomaterials. A bond-associated (BA) stabilisation approach is incorporated to eliminate zero-energy deformation modes, while a divergence-form peridynamic differential operator (PDDO) is employed to remove residual stresses near boundaries. Using the principle of virtual work, a new equation of motion is derived that naturally incorporates both zero and non-zero traction boundary conditions. Furthermore, a modified staggered algorithm is introduced to mitigate spurious plastic yielding arising from surface effects and inaccuracies in stress history. The improved BA-NOSB-PD framework enables direct implementation of elastoplastic constitutive laws and mixed-mode failure criteria. Model accuracy and convergence performance are verified against analytical solutions. The numerical simulations confirm the model’s capability to capture elastoplastic behaviour, including stress redistribution, shear band development, and plasticity-induced crack propagation. Moreover, the mixed-mode fracture mechanisms arising from different pre-existing fissure configurations are thoroughly analysed. The results demonstrate that the proposed model accurately captures shear band formation and fracture coalescence, exhibiting good numerical stability and convergence. The improved PD model provides a robust and feasible framework for investigating elastoplastic behaviour and the underlying failure mechanisms in geomaterials.