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

Ciprian D. Coman; Xiang Liu

doi:10.1016/j.ijnonlinmec.2011.03.015

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

Ciprian D. Coman, Xiang Liu

Research output: Contribution to journal › Article

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	135-143
Number of pages	9
Journal	International Journal of Non-Linear Mechanics
Volume	47
Issue number	2
Early online date	2 Apr 2011
DOIs	https://doi.org/10.1016/j.ijnonlinmec.2011.03.015
Publication status	Published - Mar 2012
Externally published	Yes

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

Coman, C. D., & Liu, X. (2012). On the bifurcations of the Lamé solutions in plane-strain elasticity. International Journal of Non-Linear Mechanics, 47(2), 135-143. https://doi.org/10.1016/j.ijnonlinmec.2011.03.015

Coman, Ciprian D. ; Liu, Xiang. / On the bifurcations of the Lamé solutions in plane-strain elasticity. In: International Journal of Non-Linear Mechanics. 2012 ; Vol. 47, No. 2. pp. 135-143.

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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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Coman, CD & Liu, X 2012, 'On the bifurcations of the Lamé solutions in plane-strain elasticity', International Journal of Non-Linear Mechanics, vol. 47, no. 2, pp. 135-143. https://doi.org/10.1016/j.ijnonlinmec.2011.03.015

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 journal › Article

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AU - Coman, Ciprian D.

AU - Liu, Xiang

PY - 2012/3

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N2 - 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.

AB - 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.

KW - Incremental elasticity

KW - Loss of ellipticity

KW - Singular perturbations

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