Quasi-Bifurcation in Dynamics of Elastic-Plastic Continua

Abstract

In this study, a stability concept in terms of the properties of an effective force field is introduced. A criterion for determining certain infinitesimal disturbances which may amplify with time in an elastic-plastic body subject to prescribed initial, kinematic, and time-dependent traction boundary conditions is introduced and developed. The body may be made of a general work-hardening continuum having a piecewise continuous motion and finite deformation. The transition from the dynamic criterion to Hill’s quasi-static bifurcation criterion is indicated.