An existence theory for nonlinear elasticity that allows for cavitation
type: Item
instance of: scholarly article
title: An existence theory for nonlinear elasticity that allows for cavitation
zbMATH Open document ID: 0836.73025
DOI: 10.1007/BF00386070
published in: Archive for Rational Mechanics and Analysis
publication date: 1996-04-29T00:00:00Z
review text: In this long paper of mathematical style the existence of minimizers in nonlinear elasticity is proved under assumptions on the stored energy that permit the formation of new holes in the body -- cavitation. The corresponding fully three-dimensional problem is considered, and an additional, physically motivated, energy term proportional to the area of the boundary of the deformed body is included. This extends some work of \textit{J. Ball} [Philos. Trans. R. Soc. Lond., Ser. A 306, No. 2, 557-611 (1982; Zbl 0513.73020)]and makes use of some ideas of \textit{V. Sverak} [Arch. Ration. Mech. Anal. 100, No. 2, 105-127 (1988; Zbl 0659.73038)]. The minimizers obtained lie in a subclass of maps in \(W^{1,p}\), \(2 < p < 3\), that are one-to-one everywhere and preserve orientation.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 49J20
zbMATH DE Number: 797107
zbMATH Keywords: minimizers
zbMATH Keywords: stored energy
zbMATH Keywords: energy term
author: Stefan Müller
author: Scott J. Spector
reviewed by: Gérard A. Maugin
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00386070
OpenAlex ID: W2004217808
description: scientific article; zbMATH DE number 797107