Modelling the residually stressed magneto-electrically coupled soft elastic materials

Residual stresses may exist in different finitely deformed soft multifunctional materials such as in electro-active and magneto-active polymers. In order to develop accurate constitutive frameworks of these smart materials experiencing electro-magneto-mechanically coupled loads, the presence of residual stresses needs to be considered on the onset of the model development. In this contribution, a spectral constitutive equation for finite strain magneto-electric soft material bodies with residual stresses is developed using spectral invariants, where each spectral invariant has a clear physical meaning. A prototype total energy function comprising of single-variable functions is proposed; a single-variable function that depends on an invariant with a direct meaning is easily handled and is experimentally attractive. Results of some boundary value problems are given.