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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.

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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