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The Dirichlet–Neumann problem revisited after modelling a new class of non-smooth phenomena

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Annals of Solid and Structural Mechanics

Abstract

Generalized Standard Materials are governed by maximal cyclically monotone operators and modelled by convex potentials. Géry de Saxcé’s Implicit Standard Materials are modelled by biconvex bipotentials. Analyzing the intermediate class of n-monotone materials governed by maximal n-monotone operators and modelled by Fitzpatrick’s functions, we find out that n-monotonicity is a relevant criterion for the materials characterisation and classification. Additionally, the Fitzpatrick’s functions allow to describe the thermal or mechanical equilibrium equations of n-monotone materials by primal–dual two-fields variational principles. In doing so, we are led to Dirichlet–Neumann problems that we solve by Uzawa-type algorithms.

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Authors and Affiliations

  1. Département de Physique, Faculté des Sciences, Université Ibn Zohr, Cité Dakhla, BP 8106, Agadir, Morroco

    J. Chaoufi

  2. Institut Pprime, UPR 3346, Université de Poitiers, 11 boulevard M. et P. Curie, BP 30179, 86962, Futuroscope-Chasseneuil Cedex, France

    C. Vallée & C. Lerintiu

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  1. C. Vallée
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  2. J. Chaoufi
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  3. C. Lerintiu
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Correspondence to J. Chaoufi.

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Vallée, C., Chaoufi, J. & Lerintiu, C. The Dirichlet–Neumann problem revisited after modelling a new class of non-smooth phenomena. Ann. Solid Struct. Mech. 6, 29–36 (2014). https://doi.org/10.1007/s12356-014-0036-0

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  • DOI: https://doi.org/10.1007/s12356-014-0036-0

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