Asymptotic results for bifurcations in pure bending of rubber blocks

Coman, C.D. and Destrade, M. (2008) Asymptotic results for bifurcations in pure bending of rubber blocks. Quarterly Journal of Mechanics and Applied Mathematics, 61(3), pp. 395-414. (doi: 10.1093/qjmam/hbn009)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Coman, Dr Ciprian
• Authors: Coman, C.D., and Destrade, M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Quarterly Journal of Mechanics and Applied Mathematics
• ISSN: 0033-5614
• ISSN (Online): 1464-3855
• Published Online: 16 April 2008