A lagrangian density for the dynamics of elastic dielectrics

The equations governing the behaviour of an elastic dielectric in the quasi-static approximation are analysed in connection with the inverse problem of the calculus of variations. First, through compatibility with the potential conditions, the most general constitutive equations are derived which allow the model to admit a variational formulation. Then the explicit form of the Lagrangian density is determined. Consistent with the adoption of Lagrangian coordinates, the Lagrangian density ascribes to the dielectric the structure of a particle-like system.