Asymptotic results for bifurcations in pure bending of rubber blocks

Abstract

The bifurcation of an incompressible neo-Hookean thick block with a ratio of thickness to length n, 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. Singular perturbation methods enable us to capture this transition, while direct numerical simulations corroborate the analytical results.