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Asymptotic results for bifurcations in pure bending of rubber blocks. (English) Zbl 1147.74022
Summary: We consider the bifurcation of an incompressible neo-Hookean thick block with the ratio of thickness to length \({\eta}\), subject to pure bending. 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 \({\eta} \to {\infty}\) degenerates into a surface instability. Singular perturbation methods enable us to capture this transition, while direct numerical simulations corroborate the analytical results.

MSC:
74G60 Bifurcation and buckling
74B20 Nonlinear elasticity
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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