Micromechanical Modelling and Computation of Shakedown with Nonlinear Kinematic Hardening — Including Examples for 2D-Problems

Abstract

A static shakedown theorem is presented using a micromechanical overlay model which simulates elastic-plastic material behaviour with nonlinear kinematic hardening. It is a generalization of the Melan theorem for unlimited, linear kinematic hardening material. The new model is an extension of the one-dimensional Masing overlay model. It is shown that the necessary shakedown conditions for general nonlinear kinematic hardening materials are also sufficient ones for the proposed material model. Numerical solutions of 2-D problems were developed using finite element discretization and advanced optimization techniques. Three examples for plates and shells show the influence of the type of strainhardening on the magnitude of shakedown loads and the behaviour of failure.