  In the present chapter, we discuss an approach for transition from discrete
to continuum description of thermomechanical behavior of solids. The transition
is carried out for several anharmonic systems: one-dimensional crystal,
quasi-one-dimensional crystal (a chain possessing longitudinal and transversal
motions), two- and tree-dimensional crystals with simple lattice. Macroscopic
balance equations are derived from equations of motion for particles.
Macroscopic parameters, such as stress, heat flux, deformation, thermal energy,
etc., are represented via parameters of the discrete system. Closed form
equations of state relating thermal pressure, thermal energy and specific
volume are derived. Description of the heat transfer in harmonic approximation
is discussed. Unsteady ballistic heat transfer in a harmonic one-dimensional
crystal is considered. The heat transfer equation for this system is rigorously
derived.
