Shakedown analysis: Comparison between models with the linear unlimited, linear limited and non-linear kinematic hardening

In this paper, shakedown analysis for plasticity models with hardening is considered by using the framework of implicit standard materials. It is shown that the concept of bipotential allows not only to retrieve some classical results in associated plasticity but also to consider non-associated laws e.g. the non-linear kinematic hardening rule. Furthermore, the comparison of the shakedown load for the three kinds of hardening on an example shows substantial differences and thus the importance of considering the non-linear kinematic hardening in shakedown analysis.