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Representing a non-associated constitutive law by a bipotential issued from a Fitzpatrick sequence

Vallée C., Lerintiu C., Fortuné D., Atchonouglo K., Ban M.

Archives of Mechanics

2009

Vol. 61, nr 3-4

325-340

We analyze the relation between Géry de Saxcé's bipotentials representing non-associated constitutive laws and Fitzpatrick's functions representing maximal monotone multifunctions. We illustrate by two examples (one linear and monotone, the other non-linear and non-monotone) the fact that Fitzpatrick's representation coming from convex analysis provides a constructive method to discover the "best" bipotential modelling of a given Implicit Standard Material.