Exact solutions for large elastoplastic deformations of a thick-walled tube under internal pressure

Abstract

A rate-independent plasticity theory based on the concept of dual variables and dual derivatives is utilized to describe finite elastic-plastic deformations including kinematic and isotropic hardening effects. Application of this theory to the problem of the thick-walled tube under internal pressure leads to a system of partial differential equations of hyperbolic type. The existence and uniqueness of the solution of the boundary value problem is guaranteed, as well as the convergence of its numerical approximation. The exact solution of this problem is calculated by means of an extrapolation technique. This integration method turns out to be applicable for rather general hardening models of rate-independent plasticity. On the basis of the computed solutions the influence of the hardening parameters is investigated. As finite deformations are of special interest, this investigation is carried out not only for the partially yielded tube but also for the completely plastified tube. Furthermore, the onset of secondary plastic flow during unloading as well as residual stress distributions are studied.