Eulerian Formulation of the Constitutive Relation for an Electro-Magneto-Elastic Material Class

A novel class of electro-magneto-elastic (EME) materials comprises electro-active and magneto-active particles in the polymer matrix that change their elastic behavior with an applied electromagnetic field. The material response for such a material class is usually formulated using Lagrangian strain tensor and Lagrangian electromagnetic field vectors as “push forward” to the current configuration. This article presents a novel formulation of an electro-magnetoelasticity in terms of an Eulerian strain tensor and Eulerian electromagnetic field vectors referring to the current configuration. Such an Eulerian formulation is often favorable from both theoretical and computational standpoints, which avoids the “push forward” operation to get the current configuration. An exercise to deduce the constitutive relation for an EME material class available in the existing literature from the newly proposed relation is also illustrated.