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 displays a multiple turning point. It is found that for 0 < η < ∞, the block experiences an Euler-type buckling instability which in the limit η → ∞ degenerates into a surface instability. Singular perturbation methods enable us to capture this transition, while direct numerical simulations corroborate the analytical results.