A neural-operator-accelerated boundary element method for nonlinear isotropic thermo-viscoplastic fracture problems

Abstract A rigorous boundary-integral framework is developed for nonlinear thermo-viscoplastic solids with history-dependent behavior. The approach extends classical thermoelastic BEM by embedding incremental, path-dependent constitutive evolution through the dual reciprocity method (DRM). Inelastic and thermal source terms are transformed into equivalent boundary contributions after approximation on boundary nodes and a sparse set of internal DRM interpolation points. The formulation therefore avoids full volumetric element-mesh generation while retaining the boundary-element reduction in dimensionality. Thermo-viscoplasticity is handled incrementally through a bounded recurrent constitutive operator without changing the fundamental boundary integral kernels. Numerical benchmarks under coupled thermal and mechanical loading demonstrate smooth field recovery, near-quadratic convergence under boundary refinement, and close agreement with reference finite-element viscoplastic solutions for temperature and stress. The formulation is validated against the classical Kirsch analytical solution and further verified against FE-VPSC simulations. Computational comparisons show substantial reductions in degrees of freedom, wall-clock time, and memory relative to the reference finite-element models. The proposed framework thus provides a mesh-reduced DRM-BEM alternative for nonlinear thermo-mechanical analysis while explicitly retaining the sparse internal interpolation points required by the dual reciprocity approximation.