Asymptotic results for bifurcations in pure bending of rubber blocks |
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Authors: | Coman Ciprian D; Destrade Michel |
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Institution: | (
Department of Mathematics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, United Kingdom
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Abstract: | The bifurcation of an incompressible neo-Hookean thick blockwith a ratio of thickness to length , subject to pure bending,is considered. The two incremental equilibrium equations correspondingto a nonlinear pre-buckling state of strain are reduced to afourth-order linear eigenproblem that displays a multiple turningpoint. It is found that for 0 < < , the block experiencesan Euler-type buckling instability which in the limit degeneratesinto a surface instability. Singular perturbation methods enableus to capture this transition, while direct numerical simulationscorroborate the analytical results. |
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