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Representing a non-associated constitutive law by a bipotential issued from a Fitzpatrick sequence
Arch. Mech. 61 (3-4), 325-340, 2009
Keywords: Generalized Standard Materials; non-associated material laws; Implicit Standard Materials; constitutive laws; point-to-set functions; multifunctions; maximal monotone operators; Fitzpatrick functions; Fitzpatrick sequences; bipotentials
Abstract
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.