Global Bifurcation of Anti-plane Shear Fronts

Robin Ming Chen; Samuel Walsh; Miles Wheeler

doi:10.1007/s00332-021-09684-7

Global Bifurcation of Anti-plane Shear Fronts

Robin Ming Chen, Samuel Walsh, Miles Wheeler

Department of Mathematical Sciences

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Abstract

We consider anti-plane shear deformations of an incompressible elastic solid whose reference configuration is an infinite cylinder with a cross section that is unbounded in one direction. For a class of generalized neo-Hookean strain energy densities and live body forces, we construct unbounded curves of front-type solutions using global bifurcation theory. Some of these curves contain solutions with deformations of arbitrarily large magnitude.

Original language	English
Article number	28
Journal	Journal of Nonlinear Science
Volume	31
Issue number	2
Early online date	26 Feb 2021
DOIs	https://doi.org/10.1007/s00332-021-09684-7
Publication status	Published - 30 Apr 2021

Funding

The research of RMC is supported in part by the NSF through DMS-1907584. The research of SW is supported in part by the NSF through DMS-1812436.

Keywords

global bifurcation
nonlinear elasticity
front
anti-plane shear

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This is a post-peer-review, pre-copyedit version of an article published in Journal of Nonlinear Science. The final authenticated version is available online at: https://doi.org/10.1007/s00332-021-09684-7
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Cite this

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AB - We consider anti-plane shear deformations of an incompressible elastic solid whose reference configuration is an infinite cylinder with a cross section that is unbounded in one direction. For a class of generalized neo-Hookean strain energy densities and live body forces, we construct unbounded curves of front-type solutions using global bifurcation theory. Some of these curves contain solutions with deformations of arbitrarily large magnitude.

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Global Bifurcation of Anti-plane Shear Fronts

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