Universal relations in coupled electro-magneto-elasticity

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 [equation] for a class of an EME material parallel to an equation [equation] 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