Abstract:
Fatigue and catastrophic loads can induce crack initiation and propagation in engineering structures, leading to fracture damage that threatens structural safety. However, the nonlinear and microscale nature of fracture problems often results in low computational efficiency. This study integrates the Inelasticity-Separated Finite Element Method (IS-FEM) and the Extended Finite Element Method (XFEM) to propose an Inelasticity-Separated Extended Finite Element Method (IS-XFEM). First, a fracture-zone element model is established based on XFEM principles, incorporating generalized compatibility conditions, degree-of-freedom condensation, and matrix generalized inverse to convert shared enrichment degrees of freedom (DOFs) into internal element DOFs. This avoids dimension changes in the global stiffness matrix typical of conventional XFEM. Next, by reformulating the stiffness of fracture-zone elements as a perturbation of undamaged element stiffness, the localized nature of fracture damage is captured. The isolated nonlinear governing equations for fracture-damaged structures are derived, eliminating time-varying terms in the global stiffness matrix. Instead, fracture effects are described via low-rank perturbations of the initial undamaged stiffness. The Woodbury formula is employed for equation solving, updating only small-scale matrices representing localized damage at each step, ensuring accuracy while significantly improving efficiency. Numerical examples demonstrate that the proposed method maintains crack prediction accuracy while drastically reducing computational costs.