Damage-based fracture with electro-magnetic coupling

Abstract

Acoupled elastic and electro-magnetic analysis is proposed including finite displacements and damage-based fracture. Piezo-electric terms are considered and resulting partial differential equations include a non-classical wave equation due to the specific constitutive law. The resulting wave equation is constrained and, in contrast with the traditional solutions of the decoupled classical electromagnetic wave equations, the constraint is directly included in the analysis. The absence of free current density allows the expression of the magnetic field rate as a function of the electric field and therefore, under specific circumstances, removal of the corresponding magnetic degrees-offreedom. A Lagrange multiplier field is introduced to exactly enforce the divergence constraint, forming a three-field variational formulation (required to include thewave constraint). No vector-potential is required or mentioned, eliminating the need for gauges. The classical boundary conditions of electromagnetism are specialized and a boundary condition involving the electric field is obtained. The spatial discretization makes use of mixed bubble-based (of the MINI type) finite elementswith displacement, electric field and Lagrange multiplier degrees-of-freedom. Three verification examples are presented with very good qualitative conclusions and mesh-independence.