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Derivation of Elastic Theories for Thin Sheets and the Constraint of Incompressibility

In: Analysis, Modeling and Simulation of Multiscale Problems

Author

Listed:
  • Sergio Conti

    (Universität Duisburg-Essen, Fachbereich Mathematik)

  • Georg Dolzmann

    (University of Maryland, Mathematics Department)

Abstract

Summary We discuss the derivation of two-dimensional models for thin elastic sheets as Γ-limits of three-dimensional nonlinear elasticity. We briefly review recent results and present an extension of the derivation of a membrane theory, first obtained by LeDret and Raoult in 1993, to the case of incompressible materials. The main difficulty is the construction of a recovery sequence which satisfies pointwise the nonlinear constraint of incompressibility.

Suggested Citation

  • Sergio Conti & Georg Dolzmann, 2006. "Derivation of Elastic Theories for Thin Sheets and the Constraint of Incompressibility," Springer Books, in: Alexander Mielke (ed.), Analysis, Modeling and Simulation of Multiscale Problems, pages 225-247, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-35657-8_9
    DOI: 10.1007/3-540-35657-6_9
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