The purpose of this article is to develop a class of universal relations for an incompressible isotropic electro-magneto-elastic (hereafter EME) material in order to generalize the continuum concept to electro-magneto-elasticity. In line with that, we adopt an electro-magneto-elasticity theory following the second law of thermodynamics-based approach. More precisely, we first extend a thermodynamically consistent deformation of a continua to a coupled EME interaction through a new amended energy function (hereafter AEF). This AEF succeeds the physical insight of the Maxwell stress tensor (hereafter MST) under large deformations. Next, we introduce a new inequality \(\mathbf{Tb} -\mathbf{bT} \ne 0\) for a class of an EME material parallel to an equation \(\mathbf{Tb} -\mathbf{bT} = 0\) for a class of an elastic material existing in the literature. At last, the formulated universal relations are applied to some homogeneous and non-homogeneous deformations to exemplify the consequences of an electromagnetic field on the mechanical deformation. Additionally, the validity of the proposed universal relations in electro-magneto-elasticity is also checked by obtaining an existing universal relation in nonlinear elasticity in the absence of an applied electromagnetic field.

中文翻译：

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非线性电磁弹性的通用关系

本文的目的是为不可压缩的各向同性电磁弹性（以下称为EME）材料开发一类通用关系，以便将连续统概念推广到电磁弹性。与此相应，我们遵循基于热力学方法的第二定律采用电磁弹性理论。更准确地说，我们首先通过新的修正能量函数（以下称为AEF）将连续体的热力学一致变形扩展到耦合的EME相互作用。该AEF继承了大变形下麦克斯韦应力张量（以下称MST）的物理原理。接下来，我们为与等式\（\ mathbf {Tb}-\ mathbf {bT} =平行的一类EME材料引入新的不等式\（\ mathbf {Tb}-\ mathbf {bT} \ ne 0 \）0 \）用于文献中存在的一类弹性材料。最后，将公式化的通用关系应用于某些均质和非均质变形，以举例说明电磁场对机械变形的影响。另外，通过在不存在电磁场的情况下获得现有的非线性弹性通用关系，也可以检验所提出的电磁弹性通用关系的有效性。