Global bifurcation of anti-plane shear fronts

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.

arXiv comment21 pages, 2 figures

References in corpus (6)

• Existence and qualitative theory for stratified solitary water waves
• Center manifolds without a phase space for quasilinear problems in elasticity, biology, and hydrodynamics
• Global bifurcation of anti-plane shear fronts
• Classical Injective Solutions in the Large in Incompressible Nonlinear Elasticity
• Global bifurcation for monotone fronts of elliptic equations
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Cited by in corpus (4)

• Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study
• Center manifolds without a phase space for quasilinear problems in elasticity, biology, and hydrodynamics
• Global bifurcation of anti-plane shear fronts
• Global bifurcation of solitary waves to the Boussinesq $abcd$ system