Block Structure and Mora Circles for Stresses and Deformations

Abstract

Displacements associated with deformations are considered. The deformation vector at an arbitrary area with the normal is defined as the ratio of the displacement vector of the site points to the distance from the site to the displacement reference point. The deformation vectors related to an arbitrary element of the medium have properties: their principal vector and principal moment are zero. For the strain vector, Mohr’s circles are constructed similarly to the stress vector. It is shown that, for an arbitrary area with a normal , the work of forces corresponding to the stress vector on the relative displacements determined by the deformation vector depends, in the general case, on the loading path even in the case of applying the relations of Hooke’s law. The only areas where this effect does not exist are the stresses and deformations of the site that are equally inclined to the main axes. On this basis, a block model of materials (such as metals) is constructed, where the elements have the form of octahedrons.