Crack Propagation in Elastoplastic Thin-Walled Structures Using Global–Local XFEM Formulation

Abstract

We present a globally enriched extended finite element method (XFEM) for elastoplastic analysis and fracture of thin-walled beams. The displacement approximation is augmented by (1) global enrichment functions obtained from beam free-vibration modes to capture the dominant bending kinematics on very coarse meshes, and (2) a local Heaviside enrichment to resolve crack surfaces independently of the mesh. Small-strain von Mises plasticity with linear kinematic hardening is integrated by an implicit return–mapping algorithm and assembled with a consistent (algorithmic) tangent. Fracture is assessed through a crack tip opening displacement (CTOD)-based energy-release rate; in propagation studies, a displacement-controlled procedure grows the crack whenever G ≥ G c with adaptive step control. The approach is validated in 2D and 3D against refined standard FEM baselines. In 2D, the globally enriched model reproduces benchmark force-displacement loops and plastic fields on very coarse meshes, achieving order-of-magnitude lower L 2 errors and substantially lower cost than standard FEM. In 3D I-beam tests, a single bending-mode enrichment attains near-benchmark accuracy for the global response and CTOD with only ∼ 20 longitudinal elements, whereas a nonenriched model requires far finer meshes. The results demonstrate that global–local XFEM provides an efficient and accurate framework for the elastoplastic fracture of beamlike thin-walled structures whose response is dominated by global bending modes, enabling substantial degrees-of-freedom (DOF) reduction without sacrificing fidelity for this class of problems.