Asymptotic results for bifurcations in pure bending of rubber blocks

The bifurcation of an incompressible neo-Hookean thick block with a ratio of thickness to length η, subject to pure bending, is considered. The two incremental equilibrium equations corresponding to a nonlinear pre-buckling state of strain are reduced to a fourth-order linear eigenproblem that displ...

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Bibliographic Details
Published in:Quarterly journal of mechanics and applied mathematics 2008-08, Vol.61 (3), p.395-414
Main Authors: Coman, Ciprian D., Destrade, Michel
Format: Article
Language:English
Subjects:
Applied sciences
Buckling
Elastomers
Engineering Sciences
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Industrial polymers. Preparations
Materials and structures in mechanics
Mathematical methods in physics
Mechanics
Numerical approximation and analysis
Numerical simulation, solution of equations
Physics
Polymer industry, paints, wood
Solid mechanics
Structural and continuum mechanics
Technology of polymers
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Summary:The bifurcation of an incompressible neo-Hookean thick block with a ratio of thickness to length η, subject to pure bending, is considered. The two incremental equilibrium equations corresponding to a nonlinear pre-buckling state of strain are reduced to a fourth-order linear eigenproblem that displays a multiple turning point. It is found that for 0 
ISSN:0033-5614
1464-3855
DOI:10.1093/qjmam/hbn009