Modelling of Implicit Standard Materials. Application to Linear Coaxial Non-Associated Constitutive Laws

We analyze the relation between Gery de Saxce's bipotentials representing non-associated constitutive laws and Fitzpatrick's functions representing maximal monotone multifunctions. Revisiting the model of elastic materials initiated by Robert Hooke, we illustrate that Fitzpatrick's representation of monotone operators coming from convex analysis provides a constructive method to discover the best bipotential for modelling an Implicit Standard Material.