Journal of Elasticity

, Volume 15, Issue 4, pp 369–387 | Cite as

Constitutive laws and existence questions in incompressible nonlinear elasticity

  • Hervé Le Dret
Article
Received:

Abstract

In this paper, we first give a justification of the specific form of the constitutive law of incompressible materials. The existence and uniqueness of the “indeterminate” pressure is established in general. In the framework of nonlinear incompressible elasticity, we then prove an existence and uniqueness result for the pure displacement boundary value problem with sufficiently small body forces.

Keywords

Specific Form Body Force Small Body Nonlinear Elasticity Displacement Boundary 
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Resumé

Dans cet article, on donne d'abord une justification de la forme que prend la loi de comportement d'un matériau incompressible. On établit l'existence et l'unicité de la pression “indéterminée” en général. On montre ensuite, dans le cadre de l'élasticité non linéaire incompressible, un résultat d'existence et d'unicité pour le problème aux limites “en déplacement pur” avec des forces volumiques suffisamment petites.

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Copyright information

© Martinus Nijhoff Publishers 1985

Authors and Affiliations

  • Hervé Le Dret
    • 1
  1. 1.Laboratoire d'Analyse Numérique (LA 189), Tour 55-65-5ème étageUniversité Pierre et Marie CurieParis Cedex 05France

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