A framework was developed for electromechanical behaviour of dielectric crystalline solids subjected to finite deformations. The theory was formulated in the context of electrostatics; however, vacancies in the lattice might carry an electric charge, and their concentrations might be large. The material was treated as a continuous body with a continuous distribution of point vacancies, but volumes and charges of individual defects enter the description. The deformation gradient was decomposed multiplicatively into terms accounting for recoverable thermoelasticity and irreversible volume changes associated with vacancies. Thermodynamic arguments led to constitutive relations among electromechanical quantities framed in the elastically unloaded intermediate configuration, with the Cauchy stress tensor consistently non-symmetric as a result of electrostatic effects. The requirement of non-negative dissipation imposes constraints on vacancy migration. Following postulation of a quadratic form for the free energy potential, a kinetic equation for vacancy flux was derived in the intermediate configuration, with diffusion driven by gradients of vacancy concentration, electrostatic potential, hydrostatic pressure, and crystal structure. Effects of geometric non-linearity (i.e. finite elastic strains and large vacancy concentrations) were found to affect vacancy diffusion in a body subjected to biaxial lattice strain, for example a film device with lattice mismatch at its interfaces.

A Non-Linear Model for Elastic Dielectric Crystals with Mobile Vacancies. J.D.Clayton: International Journal of Non-Linear Mechanics, 2009, 44[6], 675-88