  Thermo-elastic behavior of perfect single crystal is considered. The crystal
is represented as a set of interacting particles (atoms). The approach for
determination of equivalent continuum values for the discrete system is
proposed. Averaging of equations of particles' motion and long wave
approximation are used in order to make link between the discrete system and
equivalent continuum. Basic balance equations for equivalent continuum are
derived from microscopic equations. Macroscopic values such as Piola and Cauchy
stress tensors and heat flux are represented via microscopic parameters.
Connection between the heat flux and temperature is discussed. Equation of
state in Mie-Gruneisen form connecting Cauchy stress tensor with deformation
gradient and thermal energy is obtained from microscopic considerations.

Materials Science;Mesoscale and Nanoscale Physics;Classical Physics;Computational Physics