Boundary layers and stress concentration in the circular shearing of annular thin films

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 463, Issue 2087, 2007, Pages 3037-3053

  Coman, Ciprian D ^a   Bassom, Andrew P ^b  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Boundary layers; Circular shearing; Thin films; Wrinkling

Indexed keywords

EID: 36349023336     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2007.0106     Document Type: Article

References (27)

1. Bernal, R., Tassius, C., Melo, F. & Géminard, J. C. 2007 Mechanical characterisation of elastic membranes: cell mechanics applications. Appl. Phys. Lett. 90, 063903. (doi:10.1063/1.2437672)
2. Boal, D. 2002 Mechanics of the cell. Cambridge, UK: Cambridge University Press.
3. Bucciarelli, L. 1969 Torsional stability of shallow shells of revolution. AIAA J. 7, 648-653.
4. Burton, K. & Taylor, D. L. 1997 Traction forces of cytokinesis measured using optically modified elastic substrata. Nature 385, 450-454. (doi:10.1038/385450a0)
5. Coman, C. D. 2007 Edge-buckling in stretched thin films under in-plane bending. Z. Angew. Math. Phys. 58, 510-525. (doi:10.1007/s00033- 006-6036-0)
6. Coman, C. D. & Bassom, A. P. 2007a On the wrinkling of a pre-stressed annular thin film in tension. J. Mech. Phys. Solids 55, 1601-1617. (doi:10.1016/j.jmps.2007.01.006)
7. Coman, C. D. & Bassom, A. P. 2007b Wrinkling of pre-stressed annular thin films under azimuthal shearing. Math. Mech. Solids. (doi:10.1177/1081286507077107)
8. Coman, C. D. & Bassom, A. P. In press. Higher-order asymptotics for pre-stressed thin films under in-plane bending. J. Eng. Math.
9. Coman, C. D. & Haughton, D. M. 2006 Localized wrinkling instabilities in radially stretched annular thin films. Acta Mech. 185, 179-200. (doi:10.1007/s00707-005-0307-2)
10. Dean, W. R. 1924 The elastic stability of an annular plate. Proc. R. Soc. A 106, 268-284. (doi:10.1098/rspa.1924.0068)
11. Géminard, J. C., Bernal, R. & Melo, F. 2004 Wrinkle formations in axis-symmetrically stretched membranes. Eur. Phys. J. E 15, 117-126. (doi:10.1140/epje/i2004-10041-1)
12. Haseganu, E. M. & Steigmann, D. J. 1994 Theoretical flexural response of a pressurized cylindrical membrane. Int. J. Solids Struct. 31, 27-50. (doi:10.1016/0020-7683(94)90173-2)
13. Haughton, D. M. & Lindsay, K. A. 1993 The second-order deformation of a finite compressible isotropic elastic annulus subjected to circular shearing. Proc. R. Soc. A 442, 621-639. (doi:10.1098/rspa.1993.0125)
14. Haughton, D. M. & McKay, B. A. 1995 Wrinkling of annular discs subjected to radial displacements. Int. J. Eng. Sci. 33, 335-350. (doi:10.1016/0020-7225(94)00068-U)
15. Iwasa, T., Natori, M. C. & Higuchi, K. 2004 Evaluation of tension field theory for wrinkling analysis with respect to the post-buckling study. ASME J. Appl. Mech. 71, 532-540. (doi:10.1115/1.1767171)
16. Joseph, D. D. & Fosdick, R. L. 1973 The free surface on a liquid between cylinders rotating at different speeds (part 1). Arch. Rat. Mech. Anal. 49, 321-380. (doi:10.1007/BF00253044)
17. Joseph, D. D., Beavers, G. S. & Fosdick, R. L. 1973 The free surface on a liquid between cylinders rotating at different speeds (part 2). Arch. Rat. Mech. Anal. 49, 381-401. (doi:10.1007/BF00253045)
18. Li, X. & Steigmann, D. J. 1993 Finite plane twist of an annular membrane. Q. J. Mech. Appl. Math. 46, 601-625. (doi:10.1093/qjmam/46.4.601)
19. Li, X. & Steigmann, D. J. 1995 Point loads on a hemispherical elastic membrane. Int. J. Non-Linear Mech. 30, 569-581. (doi:10.1016/0020-7462(95)00019-K)
20. Lindsay, K. A. 1992 The second-order deformation of an incompressible isotropic slab under torsion. Q. J. Mech. Appl. Math. 45, 529-544. (doi:10.1093/qjmam/45.4.529)
21. Miyamura, T. 2000 Wrinkling on stretched circular membrane under in-plane torsion: bifurcation analyses and experiments. Eng. Struct. 22, 1407-1425. (doi:10.1016/S0141-0296(99)00101-7)
22. Reiner, M. 1958 Rheology. In Handbuch der Physik, vol. 6 (ed. S. Flügge). Elasticity and plasticity, pp. 434-550. Berlin, Germany: Springer.
23. Roxburgh, D. G., Steigmann, D. J. & Tait, R. J. 1995 Azimuthal shearing and transverse deflection of an annular elastic membrane. Int. J. Eng. Sci. 33, 27-43. (doi:10.1016/0020-7225(94)E0035-H)
24. Southwell, R. V. & Skan, S. W. 1924 On the stability under shearing forces of a flat elastic strip. Proc. R. Soc. A 105, 582-607. (doi:10.1098/rspa.1924.0040)
25. Steigmann, D. J. 1990 Tension field theory. Proc. R. Soc. A 429, 141-173. (doi:10.1098/rspa.1990.0055)
26. Stein, M. & Hedgepeth, J. M. 1961 Analysis of partly wrinkled membranes. NASA technical note NASA-TN D-813.
27. Timoshenko, S. 1921 Über die Stabilität versteifter Platten. Der Eisenbau 12, 147-163.