Modeling of primary instability forms of softening elastic-plastic bodies

Abstract

The origin of macroscopical defects in an initially continuous softening elastic-plastic body, which is exposed to shift deformation, is investigated. It is supposed that body deformations are homogeneous up to stability loss, then displacements representing the form of the loss of stability are added to the displacement corresponding to homogeneous deformation. In continual elastic-plastic fracture mechanics, it is supposed that the origin of macrodefects of continua occurs in zones of the localization of the deformations arising at a loss of stability. In this work the condition characterizing primary forms of loss of stability, which appear before the others in the course of a deformation, is prescribed, based on a functional, the positive definiteness of which is equivalent to the stability of a mechanical system. The algorithm for searching primary forms of the loss of stability is constructed for the first time. It is established that primary forms of loss of stability for the considered simplified mathematical model of elastic-plastic bodies have a structure corresponding to the numerous experimental data received in natural and laboratory conditions.