We provide a rigorous derivation by Γ-convergence of an effective theory of thin films in hyperelastic regime in the so-called discrete to continuous framework. By considering a discrete thin film obtained piling up at microscopic distance a finite number M of copies of a discrete monolayer ω, we provide a continuum description analogous to that in the dimension-reduction theories for continuum thin films. Our energetic description of the continuum limit model accounts for microscopic effects and in particular depends in a non-trivial way on M. We also consider the problem of homogenization and discuss several cases of interest when an explicit formula for the homogenized energy density can be obtained, with an interpretation in terms of the Cauchy-Born rule. © 2008 Springer-Verlag.

Continuum limits of discrete thin films with superlinear growth densities / Alicandro, R.; Braides, A.; Cicalese, M.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 33:3(2008), pp. 267-297. [10.1007/s00526-008-0159-4]

Continuum limits of discrete thin films with superlinear growth densities

Alicandro R.;Braides A.;Cicalese M.
2008-01-01

Abstract

We provide a rigorous derivation by Γ-convergence of an effective theory of thin films in hyperelastic regime in the so-called discrete to continuous framework. By considering a discrete thin film obtained piling up at microscopic distance a finite number M of copies of a discrete monolayer ω, we provide a continuum description analogous to that in the dimension-reduction theories for continuum thin films. Our energetic description of the continuum limit model accounts for microscopic effects and in particular depends in a non-trivial way on M. We also consider the problem of homogenization and discuss several cases of interest when an explicit formula for the homogenized energy density can be obtained, with an interpretation in terms of the Cauchy-Born rule. © 2008 Springer-Verlag.
2008
33
3
267
297
Alicandro, R.; Braides, A.; Cicalese, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/139531
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