Energy-momentum tensors in nonsimple elastic dielectrics

Abstract

Abstract. We use Noether's theorem to derive energy-momentum tensors for a simple elastic material, a nonsimple elastic material of grade two, a simple elastic dielectric and a nonsimple elastic dielectric of grade two. The technique is easily extendable to a nonsimple elastic dielectric of any grade.

On the spatial and material motion problems in nonlinear electro-elastostatics with consideration of free space

“…Based on the basic laws of electricity and elasticity, the general equations and some analyses for the boundary-value problems of nonlinear electro-elasticity have been well established, see for example [1][2][3][4][5][6]. The material motion problem in nonlinear electro-elasticity has also received considerable attention [7][8][9][10][11][12][13][14]. Nevertheless, until recently the contribution of the free space in formulating the problem of nonlinear electro-elastostatics was often of minor interest.…”

Lie Point Symmetries, Conservation and Balance Laws in Linear Gradient Elastodynamics

“…It only contains higher gradients of the displacement vector. Here such gradient theory is called gradient elasticity of form C. Gradient elasticity of form C has been investigated by Huang and Batra [12], Maugin and Trimarco [21], Maugin [22], Mindlin and Eshel [27], Mindlin [28] and Kalpakides and Agiasofitou [14].…”

“…Maugin and Trimarco [21], Maugin [22] gave the Eshelby stress tensor for a simple gradient elastodynamics of grade-2. Gradient elasticity and elastodynamics coupled with electric fields were investigated by Huang and Batra [12] and Kalpakides and Agiasofitou [14], respectively. But these authors have assumed the usual form of the kinetic energy neglecting terms which are obtained in the limit from a restricted Mindlin continuum to gradient elastodynamics.…”

Theoretical and numerical aspects of the material and spatial settings in nonlinear electro-elastostatics

“…This material form of the balance equation of linear momentum has proved to be very useful in fracture mechanics. Concerning with material defects, the problem of material forces in nonlinear electro-elasticity was also studied by many other authors (Epstein and Maugin 1990;Epstein and Maugin 1991;Huang and Batra 1996;Kalpakides and Agiasofitou 2002;Maugin and Epstein 1991;Pak and Herrmann 1986a, b;Trimarco 2007). In a recent study , the material force problem in nonlinear electro-elastostatics was revisited.…”