Modeling of primary instability forms of the softening elastic-plastic bodies

Origin of macroscopical defects in 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 to the displacement corresponding to homogeneous deformation, the displacement representing the form of loss of stability are added. In continual elastic-plastic fracture mechanics it is supposed that origin of macrodefects of the continua occurs in zones of localization of the deformations arising at loss of stability.
In this work on the basis of a functional which positive definiteness is equivalent to stability of mechanical system, the condition characterising primary forms of loss of stability which appear before the others in the course of deformation is received. For the first time the algorithm of search of primary forms of loss of stability is constructed. It is established that primary forms of loss of stability for considered simplified mathematical model of elastic-plastic bodies have structure corresponding to the numerous experimental data received in natural and laboratory conditions.