A symplectic-analysis-based extended finite element method for bending of bi-material plates with interface cracks

Plate structures with interface cracks suffer from complex bending-fracture behavior due to material discontinuity, making accurate stress intensity factor (SIF) calculation critical for structural safety. This study proposes a symplectic-analysis-based extended finite element method (XFEM) for bending analysis of bi-material plates with interface cracks under Kirchhoff plate theory. Based on the Hamiltonian system, the symplectic analytical solution of plate bending is obtained, and orthogonal symplectic series terms related to stress singularity are constructed into enrichment functions for XFEM. The three-node triangular Discrete Kirchhoff Theory (DKT) element is adopted for discretization, with Heaviside and interface-improvement functions introduced to handle displacement and material property discontinuities, respectively. Furthermore, an interaction integral method tailored for evaluating SIFs in bi-material plate bending problems is developed, wherein the auxiliary fields are rigorously obtained from the symplectic analytical solution. Numerical simulations of square/rectangular plates with central/edge interface cracks under bending moment and uniform transverse load verify the model’s accuracy and convergence. The method reveals that elastic modulus ratio, crack length/inclination, and Poisson’s ratio significantly affect SIFs, providing reliable data for bi-material plate fracture assessment.