Basic equations for shocks in nonlinear electroelastic materials

Abstract

The complete set of balance equations and jump relations useful in the study of the propagation of strong discontinuities of the shock-wave type is deduced both in its Eulerian form and material form (the latter being the most useful one) for nonlinear anisotropic electroelastic materials such as piezoelectric ceramics. In particular, the relevant form of the so-called Hugoniot equation is obtained, and all expressions are given a useful form in terms of the displacement gradient and the material electric field (or the gradient of electric potential in the quasielectrostatic approximation). The equations obtained are based on a strict use of nonlinear continuum mechanics and the electrodynamics of continua with electromechanical interactions.