Calculus of Variations and Geometric Measure Theory
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G. Gargiulo - E. Zappale - H. Zorgati

Curved thin films made of second grade materials

created by zappale on 18 Feb 2009

[BibTeX]

Published Paper

Inserted: 18 feb 2009

Journal: Advances in Mathematical Science and Applications
Volume: 18
Number: 2
Pages: 319-336
Year: 2008

Abstract:

We consider a curved thin film made of a non simple second grade material. The behavior of the film is described by a non convex bulk energy depending on the second order derivatives of the deformation. When the thickness of the curved film goes to zero, we show using $\Gamma$-convergence arguments that the quasiminimizers of the three-dimensional energy converge to the minimizers of an energy whose density has been '${\cal A}$-quasiconvexified' depending on a two-dimensional deformation and a Cosserat vector.

Keywords: Dimensional Reduction, A-quasiconvexity, Curved thin films, Non simple materials

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