A Multiphysics Finite Element and Peridynamics Model of Dielectric Breakdown
Technical Report,01 Jun 2016,01 Jun 2017
US Army Research Laboratory Aberdeen Proving Ground United States
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A method for simulating dielectric breakdown in solid materials is presented that couples electro-quasi-statics, the adiabatic heat equation, and solid mechanics. These equations are coupled in several ways, including a temperature- and electric-field-dependent conductivity model, Joule heating, thermal expansion, Lorentz and Kelvin electrostatic forces, and a damage-dependent permittivity. A finite element approximation is used for the electro-quasi-static problem and peridynamics is used to model fracture in the solid material. Damage to the material may occur either from high temperatures or high strains. The Kelvin force computation used in the method is verified against a 1-D solution and the linearization scheme used to treat the nonlinear conductivity is verified against a fixed-point iteration solution. Finally, several numerical results are presented, including 2-D point plane problems, a 2-D composite capacitor with a conductive flaw, and a 3-D point plane problem. The results show that the method is capable of reproducing both channel-like and tree-like breakdown patterns.
- Electricity and Magnetism