Asymptotic results for bifurcations in pure bending of rubber blocks

Ciprian D. Coman, Michel Destrade

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

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.

LanguageEnglish
Pages395-414
Number of pages20
JournalQuarterly Journal of Mechanics and Applied Mathematics
Volume61
Issue number3
DOIs
Publication statusPublished - 16 Apr 2008
Externally publishedYes

Fingerprint

Rubber
buckling
Buckling
rubber
Bifurcation
Singular Perturbation Method
equilibrium equations
Eigenproblem
Turning Point
Direct numerical simulation
direct numerical simulation
Fourth Order
Euler
perturbation
Direct numerical Simulation
Experience

Cite this

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Asymptotic results for bifurcations in pure bending of rubber blocks. / Coman, Ciprian D.; Destrade, Michel.

In: Quarterly Journal of Mechanics and Applied Mathematics, Vol. 61, No. 3, 16.04.2008, p. 395-414.

Research output: Contribution to journalArticle

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