A Woodbury-accelerated consistent ordinary state-based peridynamic framework for brittle fracture and elastoplastic analysis

Ordinary state-based peridynamics (OSPD) provides a flexible nonlocal framework for fracture and nonlinear analysis, but its conventional formulation remains highly sensitive to mesh refinement and horizon size, resulting in reduced accuracy and efficiency. The consistent ordinary state-based peridynamic (C-OSPD) formulation alleviates these limitations by adopting a horizon discretization consistent with the underlying grid, thereby improving numerical consistency and reducing mesh sensitivity and boundary-induced errors. However, current C-OSPD studies have been limited to linear elastic fracture, and its extension to elastoplastic analysis with efficient implicit solution strategies remains insufficient. This study develops an enhanced implicit C-OSPD framework for brittle fracture, elastoplastic deformation, and ductile failure analysis. A Woodbury-formula-based reduced-order Newton strategy is proposed to accelerate nonlinear implicit simulations with localized stiffness changes induced by bond breakage or yielding. Meanwhile, a bond-level return-mapping algorithm based on classical J 2 plasticity with mixed hardening is incorporated to establish an elastoplastic C-OSPD formulation. Numerical examples demonstrate that the proposed framework predicts smoother and more stable crack propagation, markedly reduces boundary-induced errors, and accurately captures local and global nonlinear responses. It also simulates the entire failure process from plasticity to fracture. In addition, the proposed Woodbury-based strategy significantly improves the efficiency of nonlinear implicit analysis. The proposed method offers an accurate, robust, and efficient nonlocal framework for nonlinear failure analysis.