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Universal relations in nonlinear electro-magneto-elasticity

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Abstract

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.

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Authors and Affiliations

  1. Department of Applied Mechanics, Indian Institute of Technology, Delhi, 110016, India

    Deepak Kumar

  2. Department of Mechanical Engineering, Indian Institute of Technology, Patna, 801103, India

    Deepak Kumar & Somnath Sarangi

  3. Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, 721302, India

    Ranjan Bhattacharyya

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  1. Deepak Kumar
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  2. Somnath Sarangi
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  3. Ranjan Bhattacharyya
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Kumar, D., Sarangi, S. & Bhattacharyya, R. Universal relations in nonlinear electro-magneto-elasticity. Arch Appl Mech 90, 1643–1657 (2020). https://doi.org/10.1007/s00419-020-01688-1

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