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

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Authors

  • C. Vallée Solid Mechanics Laboratory, UMR CNRS 6610, Poitiers University, France
  • C. Lerintiu Solid Mechanics Laboratory, UMR CNRS 6610, Poitiers University, France
  • D. Fortuné Solid Mechanics Laboratory, UMR CNRS 6610, Poitiers University, France
  • K. Atchonouglo Solid Mechanics Laboratory, UMR CNRS 6610, Poitiers University, France
  • M. Ban Institute for General Mechanics, RWTH Aachen, Germany

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.

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