Asymptotic results for bifurcations in pure bending of rubber blocks
arXiv:0811.4022 · doi:10.1093/qjmam/hbn009
Abstract
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.