We consider the axial buckling of a thin-walled cylinder fitted onto a mandrel core with a prescribed annular gap. The buckling pattern develops fully and uniformly to yield a surface texture of regular diamond-shaped buckles, which we propose for novel morphing structures. We describe experiments that operate well into the postbuckling regime, where a classical analysis does not apply; we show that the size of buckles depends on the cylinder radius and the gap width, but not on its thickness, and we formulate simple relationships from kinematics alone for estimating the buckle proportions during loading.

References

1.
Horton
,
W. H.
, and
Durham
,
S. C.
,
1965
, “
Imperfections, A Main Contributor to Scatter in Experimental Values of Buckling Load
,”
Int. J. Solids and Struct.
,
1
, pp.
59
72
.10.1016/0020-7683(65)90015-6
2.
Hutchinson
,
J. W.
,
2010
, “
Knockdown Factors for Buckling of Cylindrical and Spherical Shells Subject to Reduced Biaxial Membrane Stress
,”
Int. J. Solids and Struct.
,
47
, pp.
1443
1448
.10.1016/j.ijsolstr.2010.02.009
3.
Mandal
,
P. R.
, and
Calladine
,
C. R.
,
2000
, “
Buckling of Thin Cylindrical Shells Under Axial Compression
,”
Int. J. Solids and Struct.
,
37
, pp.
4509
4525
.10.1016/S0020-7683(99)00160-2
4.
Hunt
,
G. W.
,
Lord
,
G. J.
, and
Petelier
,
M. A.
,
2003
, “
Cylindrical Shell Buckling: A Characterization of Localization and Periodicity
,”
Discrete and Continuous Dynamical Systems—Series B
,
3
(
4
), pp.
505
518
.10.3934/dcdsb.2003.3.505
5.
Calladine
,
C. R.
,
1983
,
Theory of Shell Structures
,
Cambridge University Press
,
Cambridge, UK
.
6.
Hunt
,
G. W.
, and
Ario
,
I.
,
2005
, “
Twist Buckling and the Foldable Cylinder: An Exercise in Origami
,”
Int. J. Non-Linear Mech.
,
40
(
6
), pp.
833
843
.10.1016/j.ijnonlinmec.2004.08.011
7.
Cai
,
S.
,
Breid
,
D.
,
Crosby
,
A. J.
,
Suo
,
Z.
, and
Hutchinson
,
J. W.
,
2011
, “
Periodic Patterns and Energy States of Buckled Films on Compliant Substrates
,”
J. Mech. Phys. Solids
,
59
, pp.
1094
1114
.10.1016/j.jmps.2011.02.001
8.
Mahadevan
,
L.
, and
Rica
,
S.
,
2005
, “
Self-Organised Origami
,”
Science
,
307
, p.
1740
.10.1126/science.1105169
9.
Audoly
,
B.
, and
Boudaoud
,
A.
,
2008
, “
Buckling of a Thin Film Bound to a Compliant Substrate (Part 1). Formulation, Linear Stability of Cylindrical Patterns, Secondary Bifurcations
,”
J. Mech. Phys. Solids
,
56
(
7
), pp.
2401
2421
.10.1016/j.jmps.2008.03.003
10.
Hure
,
J.
,
Roman
,
B.
, and
Bico
,
J.
,
2012
, “
Stamping and Wrinkling of Elastic Plates
,”
Phys. Rev. Lett.
,
109
, p.
054302
.10.1103/PhysRevLett.109.054302
11.
Mansfield
,
E. H.
,
1989
,
The Bending and Stretching of Plates
,
Cambridge University Press
,
Cambridge, UK
.
12.
Johnson
,
W.
,
Soden
,
P. D.
, and
Al-Hassani
,
S. T. S.
,
1977
, “
Inextensional Collapse of Thin-Walled Tubes Under Axial Compression
,”
IMechE J. Strain Analysis
,
12
(
4
), pp.
317
339
.10.1243/03093247V124317
13.
Guest
,
S. D.
, and
Pellegrino
,
S.
,
1994
, “
The Folding of Triangulated Cylinders, Part II: The Folding Process
,”
ASME J. Appl. Mech.
,
61
, pp.
777
783
.10.1115/1.2901554
14.
Shyer
,
A.
,
Tallinen
,
T.
,
Nerurkar
,
N.
,
Wei
,
Z.
,
Kim
,
E.
,
Kaplan
,
D.
,
Tabin
,
C.
,
Mahadevan
,
L.
,
2013
, “
Villification: How the Gut gets Its Villi
,”
Science
,
342
, pp.
212
218
.10.1126/science.1238842
You do not currently have access to this content.