Mathematical formulations for elastic magneto-electrically coupled soft materials at finite strains: Time-independent processes

Recently, among other smart and multifunctional materials, magneto-electric soft materials are expected to open a new horizon with myriad of potential applications such as wireless energy harvesting, spintronics and nonvolatile memories, magneto-electric random access memory, to mention a few. Magneto-electric coupling can be defined as the ability of a material to electrically polarize upon the application of a magnetic field and conversely, to magnetize under the application of an electric field. In contrast to traditional multi-ferroic hard materials, magneto-electric soft materials are of largely deformable where electric and magnetic fields and mechanical deformations are intricately coupled at finite strians. In this contribution, we will emphasis to formulate generalised mathematical frameworks of finitely deformed magneto-electric soft materials. After elaborating fundamental and governing equations, some homogeneous and non-homogeneous classical boundary value problems are studied under magneto-electrically coupled loads.