Advertisement

Set-Valued Analysis

, Volume 10, Issue 2–3, pp 165–183 | Cite as

Linearized Elasticity as Γ-Limit of Finite Elasticity

  • G. Dal Maso
  • M. Negri
  • D. Percivale
Article

Abstract

Linearized elastic energies are derived from rescaled nonlinear energies by means of Γ-convergence. For Dirichlet and mixed boundary value problems in a Lipschitz domain Ω, the convergence of minimizers takes place in the weak topology of H1(Ω,R n ) and in the strong topology of W1,q(Ω,R n ) for 1≤q<2.

linearized elasticity Γ-convergence 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adams, R. A.: Sobolev Spaces, Academic Press, New York, 1975.Google Scholar
  2. 2.
    Ciarlet, P. G.: Three Dimensional Elasticity, North-Holland, Amsterdam, 1988.Google Scholar
  3. 3.
    Dal Maso, G.: An Introduction to ΓConvergence, Birkhäuser, Boston, 1993.Google Scholar
  4. 4.
    Friesecke, G., James, R. D. and Müller, S.: Rigorous derivation of nonlinear plate theory and geometric rigidity, C.R. Acad. Sci. Paris Sér. I Math. 334 (2002), 173-178.Google Scholar
  5. 5.
    Gurtin, M. E.: An Introduction to Continuum Mechanics, Academic Press, New York, 1981.Google Scholar
  6. 6.
    Temam, R.: Problè mes Mathématiques en Plasticité, Gauthier-Villars, Paris, 1983.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • G. Dal Maso
    • 1
  • M. Negri
    • 1
  • D. Percivale
    • 2
  1. 1.International School for Advanced Studies (SISSA)TriesteItaly
  2. 2.Dipartimento di Metodi e Modelli Matematici, Piazzale KennedyUniversità degli Studi di GenovaGenovaItaly

Personalised recommendations