NONPOTENTIALITY OF THE CAUCHY STRESS VECTOR WORK ON CHANGES IN THE DEFORMATION VECTOR UNDER VARIOUS STATES OF THE MEDIUM
A.I. Chanyshev1,2
1Chinakal Institute of Mining, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
2Novosibirsk State University of Economics and Management, Novosibirsk, Russia
Keywords: Stress vector, strain vector, work, potential, areas, octahedral areas, constitutive relations of the medium
Abstract
On a site with a unit normal, in addition to the stress vector, the deformation vector is set as a vector of relative displacements of the site points (it is equal to the ratio of the displacement vector to the distance from the offset reference point to the site). The deformation vector has properties similar to the Cauchy stress vector (the principal vector and the principal moment of the deformation vectors referred to the medium element vanish). For an initially isotropic medium, the work of the stress vector on the site is calculated on the basis of changes in the deformation vector. It is shown that it is non-potential, i.e. depends on the nature of the change in the stress vector. Work is potential for an isotropic medium only on areas equally inclined to the principal axes of the stress tensor, i.e. on octahedral sites. This position is valid for the states of elasticity, plasticity, extreme deformation.
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