An Eulerian formulation of nonlinear thermomechanics and electrodynamics of moving anisotropic elastic solids

In this paper, the formulation of nonlinear thermomechanics and electrodynamics of deformable materials proposed by Eringen and Maugin (1990) is restructured using the thermomechanical formulation of Green and Naghdi (1977, 1978). Constitutive equations for thermoelastic solids are typically proposed using Lagrangian forms of deformation variables. Consequently, previous developments of constitutive equations for thermoelastic electrodynamic materials proposed Lagrangian forms of electrodynamic quantities. In contrast, here, an Eulerian formulation is proposed which naturally unifies the constitutive modeling. In particular, the formulation does not use electrodynamic body force or body couple terms and the nonlinear constitutive equations for thermomechanical and electrodynamic variables are determined by derivatives of a single Helmholtz free energy function. Also, the constitutive equations for electrodynamic contributions to the stress tensor, the polarization and magnetization vectors depend naturally on the specific functional form of the Helmholtz free energy and need not be proposed independently.