Material electromagnetic fields and material forces

Abstract

Electromagnetic fields address configurational forces in a natural way through an energy-stress tensor, which reduces to the Maxwell tensor in the simplest case. This tensor is related to physical forces and to the Cauchy traction in a continuum. Material forces, as opposed to physical forces, are of a different nature as they act upon a site of a continuum where the possible material inhomogeneity is located. A material energy-stress tensor, which is reminiscent of the Maxwell stress, is associated with these forces. Through appropriate balance laws, a material momentum is also associated with material forces. The material momentum is of particular interest in electromagnetic materials as it is intimately related to the pseudomomentum of light

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.…”

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.…”

Configurational forces and gauge conditions in electromagnetic bodies

“…The treatment parallels the classical approach to some extent. However, the gauge conditions for the material potentials cannot be a formal replica of the classical Coulomb or Lorenz-Lorentz gauge conditions of electrodynamics (Jackson 2002, Trimarco 2007a. The problem has not an obvious solution and seems to represent an open issue in deformable solids.…”

“…In this context, the lack of uniqueness of the vector potential affects the unique definition of the Eshelby stress and that of material momentum, which are derived as canonical quantities from a suitable expression of the Lagrangian density. Differently, the physical electromagnetic stress (a Cauchy-like stress) and momentum do not depend explicitly upon the electromagnetic potentials and are thus uniquely defined (Trimarco 2007a).…”