Modified peridynamic time-domain integration methods for generalized thermoelastic problems

Numerical treatment of hyperbolic differential equations frequently induces spurious oscillations near high-gradient zones. This phenomenon, known as the Gibbs phenomenon, can significantly degrade the accuracy of numerical solutions. Peridynamic theory, which accounts for spatial nonlocal effects and discontinuities, has been combined with generalized thermoelasticity theory to analyze thermal and stress wave propagation. However, numerical oscillations still frequently occur in such simulations. Based on bond-based peridynamic theory, the generalized thermoelastic model is reformulated into an integral form. Three time-domain methods (explicit Taylor method, implicit Newmark method and explicit-implicit staggered method) are proposed to replace the original time-domain method (central difference method). Applied to several benchmark thermomechanical problems, these methods produce more accurate results and significantly reduce spurious oscillations compared to traditional approaches. The study further evaluates each method's ability to capture steep wavefront features and their computational efficiency. Researchers can choose the appropriate method based on the characteristics of the problem and computational efficiency requirements. The paper provides a simple and efficient methodological reference for high-precision solutions of Multiphysics hyperbolic equations.