Asymptotic results for bifurcations in pure bending of rubber blocks

Details Asymptotic results for bifurcations in pure bending of rubber blocks Asymptotic results for bifurcations in pure bending of rubber blocks

2008-11-25

arxiv.org/abs/0811.4022v1

The Quarterly Journal of Mechanics and Applied Mathematics 61, 3 (2008) 395-414

Physics

Classical Physics

Scientific paper

10.1093/qjmam/hbn009

The bifurcation of an incompressible neo-Hookean thick block with a ratio of thickness to length {eta}, 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 < {eta} < {infty}, the block experiences an Euler-type buckling instability which in the limit {eta} -> {infty} degenerates into a surface instability. Singular perturbation methods enable us to capture this transition, while direct numerical simulations corroborate the analytical results.

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