On boundary conditions in nonlinear magneto- and electroelasticity

The mathematical modelling of magneto- and electro-active elastomers is complicated because of the strong nonlinear coupling of the mechanical and electromagnetic responses. For this reason the development of numerical methods is essential for solving realistic boundary-value problems. To find appropriate variational formulations is an important first step towards solving the governing differential equations using the finite element method. In this paper we provide an overview of different boundary conditions used in nonlinear magneto- and electroelasticity, and we present a modified variational formulation that accounts for mixed mechano-magnetic boundary conditions.