Crack propagation analysis using a hybrid 2D finite element–peridynamics framework with a residual-based quasi-static solver

Abstract This paper presents a hybrid finite element–peridynamics (FE–PD) framework for two-dimensional fracture simulation. The framework embeds a peridynamic fracture zone within surrounding finite element domains through a modified volume-based (VL) coupling scheme, enabling accurate representation of crack initiation and propagation while retaining the computational efficiency of finite element analysis in the elastic far field. A major contribution of this work is the development of a residual-based dynamic relaxation solver (RBDR) for quasi-static analyses of hybrid FE–PD coupled systems. Unlike adaptive dynamic relaxation (ADR) methods, which rely on artificial damping and fictitious mass to suppress oscillations, the proposed solver is entirely damping-free and achieves equilibrium by directly minimizing the residual force field through a Richardson-type pseudo-time iteration. The solver is matrix-free, reaches higher accuracy, and 23 times faster in wall-clock time than the standard Adaptive Dynamic Relaxation method. The framework is validated against the classical Kirsch stress concentration problem, where the ABAQUS FE model recovers the analytical SCF of 3.0 and the hybrid FE–PD model reproduces the correct quantitative distribution, except at the hole surface. The hybrid method with both RBDR and ADR is then applied to crack propagation problems under Mode I tensile loading, reproducing the crack morphology and global kinetic energy evolution of a reference PD-only model with high accuracy. For the crack propagation case under quasi-static loading at four times the dynamic load level solved through the hybrid method with RBDR, crack branching does not occur, consistent with classical fracture mechanics theory that inertia is the driven factor for dynamic instability.