EXACT-SOLUTIONS FOR LARGE ELASTOPLASTIC DEFORMATIONS OF A THICK-WALLED TUBE UNDER INTERNAL-PRESSURE

A rate-independent plasticity theory based on the concept of dual vari ables and dual derivatives is utilized to describe finite elastic-plas tic deformations including kinematic and isotropic hardening effects. Application of this theory to the problem of the thick-walled tube und er internal pressure leads to a system of partial differential equatio ns 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 me thod turns out to be applicable for rather general hardening models of rate-independent plasticity. On the basis of the computed solutions t he influence of the hardening parameters is investigated. As finite de formations are of special interest, this investigation is carried out not only for the partially yielded tube but also for the completely pl astified tube. Furthermore, the onset of secondary plastic flow during unloading as well as residual stress distributions are studied.