The behavior of a curved thin film made of a nonsimple grade two material is described by a nonconvex bulk energy depending on the first and second order derivatives of the deformation. We show using Γ-convergence arguments that the quasiminimizers of the three-dimensional energy converge, when the thickness of the curved film vanishes, to the minimizers of an energy which is a function of a two-dimensional deformation and of a Cosserat vector. Part of the energy density is obtained by A-quasiconvexification arguments.
Curved nonsimple grade-two thin films / Gargiulo, Giuliano; Zappale, Elvira; Zorgati, Hamdi. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 344:5(2007), pp. 343-347. [10.1016/j.crma.2007.01.018]
Curved nonsimple grade-two thin films
Zappale, Elvira
;
2007
Abstract
The behavior of a curved thin film made of a nonsimple grade two material is described by a nonconvex bulk energy depending on the first and second order derivatives of the deformation. We show using Γ-convergence arguments that the quasiminimizers of the three-dimensional energy converge, when the thickness of the curved film vanishes, to the minimizers of an energy which is a function of a two-dimensional deformation and of a Cosserat vector. Part of the energy density is obtained by A-quasiconvexification arguments.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
