A new approach to shakedown analysis for non-standard elastoplastic material by the bipotential

On the basis of the implicit standard materials that introduces a function, called bipotential, depending on both the stress and plastic strain rate, this paper is devoted to present a new approach of shakedown analysis for non standard elastoplastic materials. The bipotential theory was successfully applied to geomaterials with non-associated flow rule and Coulomb's dry friction law. The present analysis is different to the Melan's potential and it is based on a corner stone inequality satisfied by the bipotential and the existence of time-independent residual stress field. The deduction of bound theorems, static and kinematic, is detailed in the present article