Fundamental Solution-Enhanced Peridynamic Differential Operator Modeling for Thermal Conduction

Abstract

Ensuring the integrity and safety of reactor pressure vessels (RPVs) during severe nuclear accidents is critical. Under extreme conditions such as pressurized thermal shock, RPV may undergo complex thermo-mechanical coupled elastoplastic deformation, cracking, and thermal ablation. Peridynamic differential operator (PDDO) is a nonlocal modeling approach that exhibits excellent stability and convergence in numerical analysis, making it widely used for solving mechanical deformation and heat conduction involving nonlocality and discontinuity. Focusing on the thermal effects, the present study proposed a fundamental solution-enhanced PDDO (E-PDDO), which introduced the Fundamental solution of the local heat conduction equation into the construction of peridynamic function, improved computational efficiency and accuracy while retaining advantages of the original PDDO in converting differential into integration. Subsequently, a nonlocal axisymmetric model based on E-PDDO was proposed to evaluate the temperature distribution and ablation behavior of RPV under extreme conditions. Moreover, E-PDDO was used to solve several typical temperature field problems, including (1) the first- and second-order derivative calculations for several one-dimensional temperature distributions, (2) the transient heat conduction in a two-dimensional plate, and (3) the heat conduction in an axisymmetric ring. Comparison with finite element results and original PDDO results confirmed that E-PDDO provides high accuracy in solving transient heat conduction problems, with superior convergence compared to the original PDDO. The RPV's dynamic ablation behavior during coolant leakage was also analyzed, capturing ablation morphology and temperature evolution. Overall, the proposed E-PDDO model lays a solid foundation for future research on the thermal-mechanical coupling damage and fracture behavior of RPVs.

Keywords: Thermal conduction, peridynamic differential operator, thermal ablation, reactor pressure vessel, fundamental solution, nonlocal modeling