Asymptotic results for bifurcations in pure bending of rubber blocks

Ciprian D. Coman, Michel Destrade

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


The bifurcation of an incompressible neo-Hookean thick block with a ratio of thickness to length η, 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. It is found that for 0 < η < ∞, the block experiences an Euler-type buckling instability which in the limit η → ∞ degenerates into a surface instability. Singular perturbation methods enable us to capture this transition, while direct numerical simulations corroborate the analytical results.

Original languageEnglish
Pages (from-to)395-414
Number of pages20
JournalQuarterly Journal of Mechanics and Applied Mathematics
Issue number3
Publication statusPublished - 16 Apr 2008
Externally publishedYes


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