Energy approach to modeling dynamic processes in heterogeneous elastic media (Q2754673)

It is assumed that characteristic dimensions of heterogenuities in mixture are of the same order and significantly exceed intermolecular dimensions. Under force loading, interaction between phases is determined by the volume transmission of impulse, and the surface forces can be neglected as compared to the volume ones. Equations of mechanics of continuum are formulated in space, at each point of which two sets of field characteristic functions are prescribed. The model is based on the equation of balance of total mechanical energy. Basic relationships of the model are constructed in the Lagrangian coordinate system with orientation to the geometrical configuration at the initial time instant. As a result, equations of Lamé type, and initial and boundary conditions for two displacement fields are derived.