Exponential estimates of perturbations of rigid-plastic spreading-sink of an annulus

Abstract

The time evolution of the plane picture of small perturbations imposed on the radial spreading or sink of an annulus made of incompressible ideally rigid-plastic material obeying the Mises–Hencky plasticity criterion is studied. The adhesion conditions are posed on the extending (contracting) boundaries of the annulus in both the ground and perturbed processes. The method of integral relations, which is based on variational inequalities in the corresponding complex Hilbert space, is used to reduce the linearized problem in perturbations to a single relation for quadratic functionals, which permits deriving new exponential upper bounds for the growth or decay of kinematic perturbations. It is shown that the evolution of angular harmonics with distinct numbers is qualitatively distinct.