Asymptotic results for bifurcations in pure bending of rubber blocks
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COMAN, C., DESTRADE, M. (2008) 'Asymptotic results for bifurcations in pure bending of rubber blocks'. Quarterly Journal of Mechanics and Applied Mathematics, 61 :395-414.
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.