Influence of the dispersion in the laws of continuum mechanics

Abstract

The work addresses to alternative formulation of equilibrium conditions as conditions of equilibrium angular moment for continuous mechanics. The equilibrium conditions of forces are the special case of more general conditions of equilibrium of angular moments. The modified equations are the conservation laws of density, linear moment, and energy. A new law for angular moment is suggested. One aim our analysis is to discuss the problems that can be appearing to consider the angular moment variation in an elementary volume. The theory by Bogolubov has difficulties to write the Boltzmann equation for nonhomogeneous gas. In this work influence of large gradients density, velocity or temperature on integral of collisions are investigated. Changing of Navie-Stokes equations as a function of the Boltzmann equation is determined. Usually mathematical modeling of processes in the mechanics of deformed solids is written without the angular moment variation in an elementary volume. Problem of compression of ideal hard plastic (the Prandtl problem) is considered with the angular moment.