On Foundations of the Biot's Theory. New Interpretation on the Basis of the Generalized Variational Principle

Abstract

Consistent approach for description of multiple-phase media can be formulated on the basis of the generalized variational principle for dissipative continuum mechanics. An important element of this approach is a physical mean of variables in which terms the theory is formulated. The consistent statement has to be formulated in terms of variables dealt with integrals of motion of material points, representing a continuum. The various definitions of mean velocities of phases are available for multiple-phase media in dependence on interpretation of temperature. [The correct account of this circumstance allows to overcome contradictions of the Biot's theory dealt with non-additive forms of kinetic and potential energies and to evaluate simultaneously some coefficients which should be determined experimentally in the framework of the original Biot's theory.] As illustration of the new approach, the simplest double-phase media (such as suspension and rod structures filled by fluid) are considered by uniform way in the report.