Internal variable formulations of problems in elastoplastic dynamics

Abstract

The fundamental problem of an elastic-plastic body subjected to incremental loading is reviewed using a compact internal variable approach which is expressed as a convex nonlinear mathematical programming problem. The approach is based on work carried out by Martin and co-workers [1–6] at the University of Cape Town. Additional contributions are introduced in the area of solution algorithms. Algorithms are developed aimed at approximating kinematic variables. Static and dynamic differential equations of motion and algorithms in form of a convex nonlinear mathematical programming problem are developed using the application of Liapunov functions. Stability analysis via energy methods with the help of Liapunov functions is performed to determine integration parameters.