A bond-based peridynamic model and implicit solution for thermo-elastoplastic fracture analysis

Well-developed thermo-elastoplastic continuum mechanics plays a significant role in various traditional and emerging industry fields; however, it encounters difficulties in addressing thermo-elastoplastic fractures, for which peridynamics has demonstrated significant advantages. Although peridynamics has been widely applied to multiphysics modeling, especially thermomechanical coupling problems, it still has deficiencies in thermo-elastoplastic fracture analysis. Particularly, in the bond-based peridynamics (BB PD), the plastic deformation is difficult to characterize, and the thermo-elastoplastic constitutive relationship has seldom been reported. Therefore, this study establishes a thermal-elastoplastic BB PD model and a corresponding implicit numerical solution. The following achievements have been obtained: Firstly, an incremental bond force density, an isotropic hardening yield function, an associated flow rule, and a bond breakage criterion are rigorously constructed at the bond level, establishing an equivalent mapping relationship with the classical continuum plasticity. Secondly, an implicit Newton-Raphson iteration method with the return-mapping algorithm is developed, enabling a stable and efficient solution of the nonlocal elastoplastic response. Thirdly, several benchmarks are well simulated, including the elastoplastic response of a one-dimensional rod, ductile fracture of a two-dimensional central pre-cracked plate, brittle and ductile cracking of a two-dimensional plate with multiple cracks, and thermo-elastoplastic deformation of a three-dimensional cylinder of a pressure vessel with pre-cracks. These simulations confirm that the bond-level constitutive modeling can seamlessly integrate plasticity accumulation and ductile fracture behavior of metallic materials. Moreover, the research results indicate that the proposed BB PD combines the completeness of the plasticity theory with the effectiveness of simultaneous multiple cracking, thereby offering a robust analysis tool for the coupled thermo-elastoplastic failure of significant structures under complex thermal–mechanical conditions.