Abstract In the present work, we develop a class of the coupled universal relations with the possible forms of electro-magneto-elastic (EME) deformation families in smart materials. In line with that, we adopt a classical continuum mechanics-based approach following the second law of thermodynamics. More precisely, we first formulate the deformation of an EME continua through the fundamental laws of physics with an amended form of energy function. This amended energy function successfully resolves the physical interpretation of the Maxwell stress tensor under large deformations. Next, we develop the EME coupling type of universal relations through a new inequality Tb − bT ≠ 0 for a class of an EME material parallel to an equation Tb − bT = 0 for an isotropic elastic material existing in the literature. Wherein, T and b denote the total Cauchy stress tensor and left Cauchy-Green deformation tensor, respectively. Further, we propose the possible forms of EME deformation families in smart materials for some standard experimental arrangements. At last, we also apply the above findings to a magnetostriction phenomenon in order to check the practical feasibility of the same and a good agreement is achieved successfully.

中文翻译：

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耦合电磁弹性的普遍关系

摘要 在目前的工作中，我们开发了一类与智能材料中电磁弹性 (EME) 变形族的可能形式的耦合普遍关系。与此一致，我们遵循热力学第二定律采用基于经典连续介质力学的方法。更准确地说，我们首先通过具有修正形式的能量函数的物理基本定律来制定 EME 连续体的变形。这种修正的能量函数成功地解决了大变形下麦克斯韦应力张量的物理解释。接下来，我们通过新的不等式 Tb − bT ≠ 0 开发 EME 耦合类型的通用关系，用于平行于文献中存在的各向同性弹性材料的方程 Tb − bT = 0 的一类 EME 材料。其中，T 和 b 分别表示总柯西应力张量和左柯西-格林变形张量。此外，我们为一些标准实验安排提出了智能材料中 EME 变形族的可能形式。最后，我们还将上述发现应用于磁致伸缩现象，以验证其实际可行性，并成功实现了良好的一致性。