INTERNAL VARIABLE FORMULATIONS OF ELASTIC-PLASTIC DYNAMIC PROBLEMS

The paper reviews work that has been carried out in recent pears in th e Centre for Research in Computational and Applied Mechanics (CERECAM) at the University of Cape Town on the compact internal variable formu lation of the problem of an elastic-plastic body subject to incrementa l loading. The fundamental problem is expressed as a convex nonlinear programming problem. The simplest two step algorithm for the solution of this programming problem is shown to be the standard Newton-Raphson algorithm, and the formulation permits a discussion of the convergenc e of the iterative solution procedure. It is shown that this static fo rmulation is readily extended to include inertia and linear damping te rms, leading to an identical basic formulation in which the stiffness matrix and the residual are redefined for the dynamic problem. The sta tic problem, and hence any software written for its solution, can thus be simply modified to include dynamic effects. The essential analogy between the static and dynamic problems was first presented as a maste r's thesis (R.D. Isted, 1988); subsequently there have been a number o f additional contributions to the basic formulation for static problem s, in which the internal variable framework was extended and clarified . Further contributions have also been made in respect of the dynamic problem, and these developments are summarised. Some of this later wor k has been directed at improvements in the implicit solution algorithm s. These aspects will not be discussed in detail, however the main pur pose of this review is to demonstrate the formal relationship between the static and dynamic problems. Copyright (C) 1996 Elsevier Science L td.