The effect of transverse strains in the mechanics of a solid medium

Abstract

The effect of transverse strains for elastic and plastic bodies is discussed. It is shown that for plastic bodies transverse strains have the same nature as longitudinal strains — rotation of elastic elements cut out by Lüders lines. For elastic bodies longitudinal (active) and transverse (passive) strains have a different nature, and the emergence of internal forces is connected with the gradients of the active but not total displacements. Accordingly the equations of state are written in the form of connections of the stresses with the active strains, and connections of the stresses with the passive strains. It is shown that the connection between stresses and strains calculated with respect to an arbitrary plane has a physical meaning only for certain (defining) planes. The strains calculated on the rest of the planes have no physical meaning; their role is reduced to an invariant description of the processes taking place on the defining planes. Therefore, for the description of the processes taking place on all planes, a single strain tensor is insufficient. It is shown that, in the case of a linearly elastic body, a tensor of the active and a tensor of the passive strains are sufficient.