Blurred maximal cyclically monotone sets and bipotentials

Let X be a reflexive Banach space and Y its dual. In this paper we find necessary and sufficient conditions for the existence of a bipotential for a blurred maximal cyclically monotone graph. Equivalently, we find a necessary and sufficient condition on $\phi \in \Gamma_{0}(X)$ for that the differential inclusion $y \in \bar{B}(\epsilon) + \partial \phi(x)$ can be put in the form $y \in \partial b(\cdot, y)(x)$, with $b$ a bipotential.Comment: Revised version, corrections in theorem 6.

A variational formulation for constitutive laws described by bipotentials

Inspired by the algorithm of Berga and de Saxce for solving the discretisation in time of the evolution problem for an implicit standard material, we propose a general variational formulation in terms of bipotentials

Blurred constitutive laws and bipotential convex covers

In many practical situations, incertitudes affect the mechanical behaviour that is given by a family of graphs instead of a single one. In this paper, we show how the bipotential method is able to capture such blurred constitutive laws, using bipotential convex covers

FEM-based shakedown analysis of hardening structures

This paper develops a new finite element method (FEM)-based upper bound algorithm for limit and shakedown analysis of hardening structures by a direct plasticity method. The hardening model is a simple two-surface model of plasticity with a fixed bounding surface. The initial yield surface can translate inside the bounding surface, and it is bounded by one of the two equivalent conditions: (1) it always stays inside the bounding surface or (2) its centre cannot move outside the back-stress surface. The algorithm gives an effective tool to analyze the problems with a very high number of degree of freedom. Our numerical results are very close to the analytical solutions and numerical solutions in literature