Coninuum Approximation of the Self-Consistent Einstein Model under an External Force: Basic Equations for Thermo-Elasticity and Lattice Vibration

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Abstract
The following are studied in this paper: (1) The continuum approximation of the self-consistent Einstein model subjected to an external force is proposed with the aid of the finite deformation theory. (2) The field equations and the boundary condition which describe consistently both deformations and vibrations of lattices are derived by using the coutinuum approximation. (3) The linearized basic equations are explicitly derived. These equations can be regarded as an extension of the phenomenological elastic theory and of the lattice vibration theory with no deformation. A simple illustrative example is also investigated in order to show characteristic features of the basic equations.