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

Sergio Conti () and Georg Dolzmann ()
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Sergio Conti: Universität Duisburg-Essen, Fachbereich Mathematik
Georg Dolzmann: University of Maryland, Mathematics Department

A chapter in Analysis, Modeling and Simulation of Multiscale Problems, 2006, pp 225-247 from Springer

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.

Keywords: Lipschitz Domain; Thin Membrane; Incompressible Material; Recovery Sequence; Rigorous Derivation (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-35657-8_9

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DOI: 10.1007/3-540-35657-6_9

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