An electro-thermo-mechanical peridynamic model for dielectric breakdown simulation

Abstract

Dielectric breakdown in solids is governed by tightly coupled electro-thermo-mechanical (E-T-M) processes. Existing peridynamic (PD) formulations treat only mechanics in PD while discretizing the electrical and thermal fields with FEM/FDM, which can yield inconsistent electric force evaluations across discretizations. To address this limitation, we present a unified PD framework that solves the electro-quasi-static, thermal, and mechanical subproblems entirely within PD. New PD gradient and divergence operators recover electric fields from potentials and evaluate Lorentz and Kelvin body forces consistently with PD kinematics. The coupled system is advanced by a staggered E-T-M solution scheme. Four numerical studies demonstrate the capabilities and verification of the framework. (i) Deformation of a dielectric bar with a hole and (ii) dynamic crack propagation in a notched plate verify accuracy, show convergence, and quantify discretization effects and crack evolution. (iii) Breakdown of a dielectric polymer under electro-mechanical coupling validates the model, reproducing stochastic breakdown paths and strong field-failure feedback. (iv) High-voltage breakdown under full E-T-M coupling reveals tree-like breakdown patterns and rich multiphysics interactions. By computing electric forces natively in PD and eliminating cross-discretization inconsistencies, the framework closes a key consistency gap and enables predictive simulation of coupled E-T-M failure in dielectric materials.