Universal relations in nonlinear electro-magneto-elasticity

• Published in: Archive of applied mechanics (1991) 2020-07, Vol.90 (7), p.1643-1657
• Main Authors: Kumar, Deepak, Sarangi, Somnath, Bhattacharyya, Ranjan
• Format: Article
• Language: English
• Subjects: Classical Mechanics; Computational fluid dynamics; Deformation; Elasticity; Electromagnetic fields; Electromagnetism; Engineering; Isotropic material; Magnetoelectroelasticity; Original; Tensors; Theoretical and Applied Mechanics; Thermodynamics
• ISSN: 0939-1533; 1432-0681
• DOI: 10.1007/s00419-020-01688-1

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 Tb - bT ≠ 0 for a class of an EME material parallel to an equation Tb - 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.