On the bifurcations of the Lamé solutions in plane-strain elasticity

Ciprian D. Coman, Xiang Liu

Research output: Contribution to journalArticle

Abstract

We consider the in-plane bifurcations experienced by the Lamé solutions corresponding to an elastic annulus subjected to radial tension on the curved boundaries. Numerical investigations of the relevant incremental problem reveal two main bifurcation modes: a long-wave local deformation around the central hole of the domain, or a material wrinkling-type instability along the same boundary. Strictly speaking, the latter scenario is related to the violation of the ShapiroLopatinskij condition in an appropriate traction boundary-value problem. It is further shown that the main features of this material instability mode can be found by using a singular-perturbation strategy.

LanguageEnglish
Pages135-143
Number of pages9
JournalInternational Journal of Non-Linear Mechanics
Volume47
Issue number2
Early online date2 Apr 2011
DOIs
Publication statusPublished - Mar 2012
Externally publishedYes

Fingerprint

Plane Strain
Elasticity
Bifurcation
Wrinkling
Curved Boundary
Singular Perturbation
Ring or annulus
Numerical Investigation
Boundary value problems
Strictly
Boundary Value Problem
Scenarios
Strategy

Cite this

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title = "On the bifurcations of the Lam{\'e} solutions in plane-strain elasticity",
abstract = "We consider the in-plane bifurcations experienced by the Lam{\'e} solutions corresponding to an elastic annulus subjected to radial tension on the curved boundaries. Numerical investigations of the relevant incremental problem reveal two main bifurcation modes: a long-wave local deformation around the central hole of the domain, or a material wrinkling-type instability along the same boundary. Strictly speaking, the latter scenario is related to the violation of the ShapiroLopatinskij condition in an appropriate traction boundary-value problem. It is further shown that the main features of this material instability mode can be found by using a singular-perturbation strategy.",
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On the bifurcations of the Lamé solutions in plane-strain elasticity. / Coman, Ciprian D.; Liu, Xiang.

In: International Journal of Non-Linear Mechanics, Vol. 47, No. 2, 03.2012, p. 135-143.

Research output: Contribution to journalArticle

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