A general phase-field model for electrical degradation and breakdown under electro-thermo-mechanical loading

  • Fuentes, Federico (Pontificia Universidad Catolica de Chile)
  • Mardonez, Joaquin (Pontificia Universidad Catolica de Chile)
  • Basulto, Jose (Pontificia Universidad Catolica de Chile)

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We present a general continuum-based thermodynamically consistent "meta"-model that couples electromagnetic fields via Maxwell's equations along with the usual conservation laws, and includes phase-field variables representing the damage caused by the electromagnetic and thermomechanical fields capable of causing electrical breakdown/failure in solid materials. We show how this metamodel includes as special cases a series of recent models proposed in the literature to attempt to model time-domain phenomena associated with electrical degradation and breakdown in polymers, such as avalanche breakdown and treeing. The resulting models are fundamental in capturing degradation in electrically insulating materials under complex loading conditions and general geometries, such as those found in modern batteries, form-wound stator coils, and electric pulse drilling. Moreover, we elucidate how particular choices of constitutive models result naturally in Allen-Cahn equations describing the evolution of the phase-field variable, and the connection with (static or pseudo-static) Ginzburg-Landau theory that allows this metamodel, when the phase-field is interpreted in a specific way, to represent ferroelectric materials. Lastly we focus on modeling avalanche electrical breakdown between two parallel plates. First, we specify the necessary mathematical requirements of the model to be able to observe the phenomenon, which are more stringent than those typically used to model mechanical fracture. Then, using a finite element staggered method we produce numerical results of the resulting nonlinear model capturing the desired phenomenon.