Towards thermodynamics of elastic electric conductors
We discuss some problems of equilibrium shapes and possible morphological patterns of crystalline deformable conductors. To this end we propose a master system describing quasistatic evolution of shapes of such conductors owing to rearrangement of their material particles. The driving force of the evolution is the diminishing of the total energy of the system consisting of the elastic, electrostatic and surface energies. The proposed master system is based on the assumption that the characteristic time scale of establishing equilibrium with respect to rearrangement of materials particles is much greater than the time scales of establishing equilibrium with respect to mechanical and electrostatic degrees of freedom. The proposed system is based on principles and notions of the exact nonlinear continuum mechanics in the Eulerian description. We use the exact master system to derive an explicit formula of increment or decrement in the growth of small disturbances of an isotropic, uniformly stressed elastic halfplane in a uniform electrostatic field. In the case of small deviations from the unstressed state we express the coefficients of the dispersion relation in terms of the Lamé and Poisson modules. After establishing the key dispersion equationon the solid basis ofthe nonlinear theory, we show some modifications ofthe master system that will allow us to establish the same dispersion equations without any appeal to the notions and concepts of the exact theory. Finally we apply our system to the case of incompressible substances and demonstrate that the suggested master system leads to the same (in)stability criterion as that established long ago for a liquid conductor in an electrostatic field.