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A Simple Model of the Treloar—Kearsley Instability

Department of Mechanical Engineering, University of California, Berkeley, CA, 94720

The Treloar—Kearsley instability is studied in the framework of membrane theory. The phenomenon considered is the bifurcation of an equibiaxial stretch of a thin square elastic sheet, in equilibrium under equibiaxial dead loads, to a rectangle at a critical value of the load. The membrane setting, in which the sheet is regarded as an elastic surface, leads to sharper results on the stability of equilibria than those delivered by conventional elasticity theory. Further, definite conclusions can be drawn under weaker constitutive hypotheses. These are illustrated through the use of a particular strain-energy function which renders the analysis nearly trivial.

Key Words: stability • bifurcation • elastic membranes

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This version was published on December 1, 2007

Mathematics and Mechanics of Solids, Vol. 12, No. 6, 611-622 (2007)
DOI: 10.1177/1081286506066090


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This Article Abstract Free Full Text (Free PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in Web of Science Alert me to new issues of the journal Add to Saved Citations Download to citation manager Request Permissions Request Reprints Add to My Marked Citations Citing Articles Citing Articles via Google Scholar Citing Articles via Scopus Google Scholar Articles by Steigmann, D. J. Search for Related Content Social Bookmarking                         What's this?