A local bounding principle for dissipation energy in shakedown of elastic-perfectly plastic solids

Abstract The paper deals with elastic-perfectly plastic solids which shake down to a purely elastic state under the action of quasi-static loads which vary arbitrarily remaining within a given domain. It presents a technique for bounding the dissipation energy which is done locally at a given point of the body during the adaptation process. This technique leads to a problem of finite plasticity which may be considered as the holonomic version of the original shakedown problem suitably perturbed. The holonomic solution can be directly used to construct the local bound which proves to be also the most stringent one. A simple example illustrates the method.