IBVP for electromagneto-elastic materials: Variational approach

This paper aims to establish a variational framework for materials having coupling interactions between electromagnetic and mechanical fields. Based on coupled constitutive equations and the alternative field equations, a general variational form, imposing no restriction on the fields involved, is given. Subsequently, the result is derived for the case when satisfaction of the strain-displacement equation is presumed as a restriction. Next, the variational forms for kinematically admissible processes and, in turn, for kinematically admissible displacementpotential processes are found. Finally, the principles characterizing the stress field instead of the displacement field are formulated. The results of the present work provide a framework in which the satisfaction of initial boundary conditions is inherently considered. The proposed framework furnishes an alternative path for the implementation of numerical approaches for PDEs governing the motion of electromagneto-elastic materials.