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.

近年来，在其他智能和多功能材料中，磁电软材料有望开辟新的视野，其中包括无线能量收集，自旋电子和非易失性存储器，磁电随机存取存储器等众多潜在应用。磁电耦合可以定义为材料在施加磁场时发生电极化的能力，反之，在施加电场时发生磁化的能力。与传统的多铁性硬质材料相比，磁电软质材料在电场和磁场以及机械变形在有限的应力下错综复杂地耦合的情况下具有很大的变形能力。在这项贡献中，我们将强调为有限变形的磁电软材料建立广义的数学框架。在阐述了基本方程和控制方程之后，研究了在磁电耦合载荷下的一些齐次和非齐次经典边值问题。