In this paper, we systematically derive the phase field model for electric breakdown channel propagation. The model includes electric charge, mass, momentum and energy conservation equations as well as Allen–Cahn type equation which governs the phase field evolution. The medium motion is described by the Godunov–Romenski type hyperelastic model. Electromagnetic part of the model consists of Maxwell’s equations in quasi(electro)stationary approximation including electric charge conservation law. Derivation of the model is based on the Coleman–Noll procedure and Gurtin’s microforces and microstress framework.
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