A structured phase transition for the antiplane shear of an elastic circular tube

Roger Fosdick, Ying Zhang

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Abstract

We consider the radially symmetric axial shear of an elastic circular tube. The strain-energy function for the material is non-convex, and the potential energy contains a penalty contribution for large strain gradients. We study the corresponding problem of minimum potential energy, and give a detailed analysis of its solution for the particular case of a trilinear material. In this case, the relevant Euler-Lagrange equation can be completely analysed in terms of special functions. We study the limiting behaviour of the solution as the penalty parameter is made infinitesimally small. Finally, we present numerical results for this solution and, for reasons of comparison, also for the solution in the case of a cubic material.

Original languageEnglish (US)
Pages (from-to)189-210
Number of pages22
JournalQuarterly Journal of Mechanics and Applied Mathematics
Volume48
Issue number2
DOIs
StatePublished - May 1995

Bibliographical note

Funding Information:
We wish to acknowledge the NSF under grant MSS-9024637 for their support of this research. We also gratefully acknowledge the partial support of Alliant Techsystems Inc. and the support of a contract between the Army Research Office and the University of Minnesota for the Army High Performance Computing Research Center. Comments from the reviewers were most helpful and greatly appreciated.

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