A multiphysics time-dependent model of dielectric breakdown in solids

A time-dependent model of dielectric breakdown in solids is presented wherein electro-quasi-statics, adiabatic heating, and peridynamics are coupled. First, the time dependent electro-quasi-static approximation is used to solve for the electrostatic potential and a nonlinear, electric-field- and temperature-dependent conductivity is used. The electric field is coupled to both the temperature (through Joule heating) and the mechanical displacement (through the Lorentz and Kelvin forces). Fracture and failure of the material are modeled using peridynamics, a non-local formulation of solid mechanics, and failure of the material may occur due to both high temperatures and high mechanical strain induced by thermal expansion. Results demonstrate several features of dielectric breakdown that are consistent with experiments.