Jerky flow model as a basis for research in deformation instabilities

Abstract

A phenomenological jerky flow model was developed in which macroscale plastic strain rates are defined by dislocation kinetics. The model takes into account destructive processes governed by shear and bulk defect accumulation. At the heart of the model lie equations of solid mechanics and relaxation-type constitutive equations. A loaded elastoplastic solid is treated as a nonlinear dynamic system whose evolution, according to synergetic laws, is much contributed by negative and positive feedbacks expressed, respectively, through constitutive equations of the first group (relaxation equations) and constitutive equations of the second group (kinetic equations for deformation defect and damage accumulation rates). The negative feedback stabilizes deformation by relaxation, bringing the process to some local dynamic equilibrium. The positive feedback destabilizes deformation, driving the system to a critical state. Numerical experiment was performed in 2D and 3D statements. Statistical analysis of stress fluctuations about the average trend shows that the jerky flow model of an elastoplastic medium demonstrates evolution characteristic of nonlinear dynamic systems: through states of dynamic chaos and self-organized criticality to a global catastrophe.