The Γ-convergence of a sharp interface thin film model with nonconvex elastic energy

Pavel Bělík; Mitchell Luskin

doi:10.1137/050622596

The Γ-convergence of a sharp interface thin film model with nonconvex elastic energy

Pavel Bělík, Mitchell Luskin

School of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We give results for the Γ-limit of a scaled elastic energy of a film as the thickness h > 0 converges to zero. The elastic energy density models materials with multiple phases or variants and is thus nonconvex. The model includes an interfacial energy that allows sharp interfaces between the phases and variants and is proportional to the total variation of the deformation gradient.

Original language	English (US)
Pages (from-to)	414-433
Number of pages	20
Journal	SIAM Journal on Mathematical Analysis
Volume	38
Issue number	2
DOIs	https://doi.org/10.1137/050622596
State	Published - 2006

Keywords

Bounded variation
Martensite
Surface energy
Thin film
Γ-convergence

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10.1137/050622596

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abstract = "We give results for the Γ-limit of a scaled elastic energy of a film as the thickness h > 0 converges to zero. The elastic energy density models materials with multiple phases or variants and is thus nonconvex. The model includes an interfacial energy that allows sharp interfaces between the phases and variants and is proportional to the total variation of the deformation gradient.",

keywords = "Bounded variation, Martensite, Surface energy, Thin film, Γ-convergence",

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AU - Bělík, Pavel

AU - Luskin, Mitchell

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AB - We give results for the Γ-limit of a scaled elastic energy of a film as the thickness h > 0 converges to zero. The elastic energy density models materials with multiple phases or variants and is thus nonconvex. The model includes an interfacial energy that allows sharp interfaces between the phases and variants and is proportional to the total variation of the deformation gradient.

KW - Bounded variation

KW - Martensite

KW - Surface energy

KW - Thin film

KW - Γ-convergence

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JF - SIAM Journal on Mathematical Analysis

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ER -

The Γ-convergence of a sharp interface thin film model with nonconvex elastic energy

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