Condition of plasticity in energy models mechanics

Abstract

Alyushin Y. A. Condition of plasticity in energy models mechanics // Material working by pressure.  – 2019. – № 2 (49). - P. 3-15.

The dependence of the volume energy density and its rate of change on the characteristics of the stress and strain States in the Euler and Lagrange spaces is investigated. The popular plasticity conditions and the stress state criterion are interpreted from the positions of the energy model of mechanics. It is shown that the level of volume energy density of a particle determines the average Cauchy stress, and the rate of its change is the second invariant of the deviator or the intensity of tangent stresses. It is noted that the intensity of the shear strain rate depends on the rotor of the velocity vector and the divergence of the acceleration vector, which makes it possible to transform the potential velocity field into a vortex field and Vice versa without changing the energy costs. The equation with the participation of invariants of the equations of motion is justified, which allows us to explain the mechanism of transition from reversible to irreversible deformations with energy dissipation and an increase in the temperature of the material when irreversible deformations occur. From the point of view of energy models of solid mechanics conditions yield maximum intensity values of the tangential stresses can be interpreted as the presence of each material physical property that determines the maximum speed of a transfer (or change) of energy depending on the achieved level of volumetric energy density, the excess of which leads to conversion of excess energy in the temperature as in heat stroke. These relations do not contradict the known equations of mechanics, are consistent with experimental observations and can contribute to the further development of the theory of plasticity and metal processing by pressure.