This note derives an analytical relationship for an inextensible network when it buckles. According to the relationship, the applied compressive force can be determined according to the maximum absolute values of deflection and angle of deflection in the network’s wrinkles.
Issue Section:
Brief Notes
1.
Cerda
, E.
, and Mahadevan
, L.
, 2003
, “Geometry and Physics of Wrinkling
,” Phys. Rev. Lett.
, 90
, 074302
074302
.2.
Cerda
, E.
, Ravi-Chandar
, K.
, and Mahadevan
, L.
, 2002
, “Thin Films: Wrinkling of an Elastic Sheet Under Tension
,” Nature (London)
, 419
, pp. 579
–580
.3.
Simmonds
, J. G.
, 1985
, “The Strain Energy Density of Rubber-Like Shells
,” Int. J. Solids Struct.
, 21
, pp. 67
–77
.4.
Wang
, W.-B.
, and Pipkin
, A. C.
, 1986
, “Inextensible Networks With Bending Stiffness
,” Q. J. Mech. Appl. Math.
, 39
, pp. 343
–359
.5.
Wang
, W.-B.
, and Pipkin
, A. C.
, 1986
, “Plane Deformations of Nets With Bending Stiffness
,” Acta Mech.
, 65
, pp. 263
–279
.6.
Hilgers
, M. G.
, and Pipkin
, A. C.
, 1992
, “Elastic Sheets With Bending Stiffness
,” Q. J. Mech. Appl. Math.
, 45
, pp. 57
–75
.7.
Hilgers
, M. G.
, and Pipkin
, A. C.
, 1992
, “Bending Energy of Highly Elastic Membranes
,” Q. Appl. Math.
, 50
, pp. 389
–400
.8.
Hilgers
, M. G.
, and Pipkin
, A. C.
, 1993
, “Energy Minimizing Deformations of Elastic Sheets With Bending Stiffness
,” J. Elast.
, 31
, pp. 125
–139
.9.
Hilgers
, M. G.
, and Pipkin
, A. C.
, 1996
, “Bending Energy of Highly Elastic Membranes II
,” Q. Appl. Math.
, 54
, pp. 307
–316
.10.
Hilgers
, M. G.
, and Pipkin
, A. C.
, 1997
, “Plane Infinitesimal Waves in Elastic Sheets With Bending Stiffness
,” Math. Mech. Solids
, 2
, pp. 75
–89
.11.
Luo, C., and Steigmann, D. J., 2001, “Bending and Twisting Effects in the Three-Dimensional Finite Deformations of an Inextensible Network,” Advances in the Mechanics of Plates and Shells, Kluwer Academic Publishers, Boston, pp. 213–228.
12.
Synge, J. L., and Griffith, B. A., 1949, Principles of Mechanics, Second Ed., McGraw-Hill, New York, pp. 370–372.
13.
Timoshenko, S., 1936, Theory of Elastic Stability, First Ed., McGraw-Hill, New York, pp. 69–75.
Copyright © 2004
by ASME
You do not currently have access to this content.