A total-variation surface energy model for thin films of martensitic crystals
type: Item
instance of: scholarly article
title: A total-variation surface energy model for thin films of martensitic crystals
zbMATH Open document ID: 1014.49013
DOI: 10.4171/IFB/53
author: Pavel Bȩlík
author: Mitchell Luskin
published in: Interfaces and Free Boundaries
publication date: 2003-02-18T00:00:00Z
review text: The authors build a thin-film model for martensitic crystals, which differs from that introduced by \textit{K. Bhattacharya} and \textit{R. D. James} [J. Mech. Phys. Solids 47, No.~3, 531-576 (1999; Zbl 0960.74046)], as they start from the energy functional \(\kappa \int_{\Omega _{h}}|D\left( \nabla u\right) |dx\), which represents the total variation of the deformation gradient inside the domain \(\Omega _{h}=S\times \left( -h/2,h/2\right) \). The deformation is supposed to be known on the lateral boundary \(\Gamma _{h}=\gamma \times \left( -h/2,h/2\right) \). Assuming that the plane domain \(S\) is smooth enough and using the properties of functions having bounded variation, the authors prove the existence of a minimizer of this model. They then let \(h\) go to 0 and derive a limit surface energy of this thin-film model which is similar to that of Bhattacharya and James. A finite element approximation of this thin-film model is finally presented.
reviewed by: Alain Brillard
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 74N15
Mathematics Subject Classification ID: 49J10
Mathematics Subject Classification ID: 74G65
zbMATH DE Number: 1749687
zbMATH Keywords: thin-film surface energy
zbMATH Keywords: bounded variation
zbMATH Keywords: martensite
zbMATH Keywords: energy functional
zbMATH Keywords: total variation
zbMATH Keywords: deformation gradient
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1749687