Global bifurcation of anti-plane shear fronts
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
TL;DR
This paper investigates the global bifurcation phenomena of anti-plane shear fronts in an incompressible elastic solid, revealing unbounded solution curves with large deformations through advanced mathematical analysis.
Contribution
It introduces a novel application of global bifurcation theory to construct unbounded solution curves for anti-plane shear fronts in elastic solids.
Findings
Existence of unbounded solution curves with large deformations
Construction of front-type solutions using bifurcation theory
Solutions include arbitrarily large deformations
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.
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