Asymptotic results for bifurcations in pure bending of rubber blocks

Ciprian Coman (1) , Michel Destrade (2)

1 Departments of Mathematics
2 DALEMBERT - Institut Jean Le Rond d'Alembert

The bifurcation of an incompressible neo-Hookean thick block with a ratio of thickness to length {eta}, 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 < {eta} < {infty}, the block experiences an Euler-type buckling instability which in the limit {eta} -> {infty} degenerates into a surface instability. Singular perturbation methods enable us to capture this transition, while direct numerical simulations corroborate the analytical results.

Mots clés: hyperelastic plates; incremental equations; turning points; boundary layers

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

Ciprian Coman, Michel Destrade. Asymptotic results for bifurcations in pure bending of rubber blocks. Quarterly Journal of Mechanics and Applied Mathematics, 2008, 61 (3), pp.395-414. ⟨10.1093/qjmam/hbn009⟩. ⟨hal-00341387⟩