On electric body forces and Maxwell stresses in nonlinearly electroelastic solids

We review in detail two concepts that appear in the theory that governs the interaction between electric fields and deformable media, namely the ‘Maxwell stress’ and the ‘total stress’. We focus on the quasi-static context, based on the force, couple and energy balance equations, with particular reference to boundary conditions. Equivalent formulations of the governing equations expressed in terms of different measures of stress are highlighted and connections with a principle of virtual work and a variational principle are noted.