Computational lower bound shakedown analysis with limited kinematic hardening is only safe if a specific hardening law is defined

Abstract

Lower bound shakedown analysis is a well accepted and very convenient tool to determine the load bearing capacity of engineering structures subjected to thermo-mechanical loadings. In order to achieve realistic results, limited kinematic hardening needs to be taken into account. In many cases, this is achieved by using two-surface models which consider only the initial and the ultimate yield surface. In previous works, I had shown already that the solution obtained from such an approach applied to unrestricted, limited kinematic hardening can appear to be path-dependent. Nonetheless, the two-surface model is still used frequently in the literature for these scenarios. Thus, the aim of this paper is to emphasize the implications from using unrestricted hardening. Most importantly, it should be highlighted that in some cases the obtained result for the shakedown loading factor might not be a lower bound such that it cannot be used in conservative structural design.