On finitely strained magnetorheological elastomers

Abstract

Magnetorheological elastomers (MREs) are ferromagnetic particle impregnated rubbers whose mechanical properties are altered by the application of external magnetic fields. Due to their strong magnetoelastic coupling response MREs are finding an increasing number of engineering applications, thus necessitating appropriate theoretical descriptions which is the objective of this work. Two different continuum formulations for MREs are presented: an Eulerian (current configuration) based approach using the second law of thermodynamics plus the conservation laws method of mechanics and a new, Lagrangian (reference configuration) based formulation based on the unconstrained minimization of a potential energy functional. It is shown that both approaches yield the same governing equations and boundary conditions. Following a discussion of general properties of the free energy function of MREs, we use a particular such function to illustrate the magnetoelastic coupling phenomena in a cylinder subjected to traction or torsion under the presence of external magnetic fields.