Abstract

Surface stress, which is always neglected in classical elastic theories, has recently emerged as a key role in the mechanics of highly deformable soft solids. In this paper, the effect of surface stress on the deformation and instability of soft hollow cylinder is analyzed. By incorporating surface energy density function into the constitutive model of a hyper-elastic theory, explicit solutions are obtained for the large deformation of soft hollow cylinder under the uniform pressure loading and geometric everting. The surface tension and the residual surface stress have a significant effect on the large deformation and instability of the soft cylinder. When the pressure loading and geometric everting are applied on the soft hollow cylinder, significant changes in the critical condition of the creases are found by varying the surface parameters. Two models of instability, surface crease and global buckling behavior, will be generated on the soft hollow cylinder with the uniform pressure, and the formed instability model is dependent on the ratio of the thickness to the radius. The results in this work reveal that surface energy obviously influences both the deformation and the instability of soft hollow cylinder at finite deformation and will be helpful for understanding and predicting the mechanical behavior of soft structures accurately.

References

References
1.
Witten
,
T. A.
,
1999
, “
Insights From Soft Condensed Matter
,”
Rev. Mod. Phys.
,
71
(
2
), p.
S367
. 10.1103/RevModPhys.71.S367
2.
Levental
,
I.
,
Georges
,
P. C.
, and
Janmey
,
P. A.
,
2007
, “
Soft Biological Materials and Their Impact on Cell Function
,”
Soft Matter
,
3
(
3
), pp.
299
306
. 10.1039/B610522J
3.
Rus
,
D.
, and
Tolley
,
M. T.
,
2015
, “
Design, Fabrication and Control of Soft Robots
,”
Nature
,
521
(
7553
), pp.
467
475
. 10.1038/nature14543
4.
Zhang
,
R.
,
Wu
,
S.
,
Ze
,
Q.
, and
Zhao
,
R.
,
2020
, “
Micromechanics Study on Actuation Efficiency of Hard-Magnetic Soft Active Materials
,”
ASME J. Appl. Mech.
,
87
(
9
), p.
091008
. 10.1115/1.4047291
5.
Zhao
,
X.
,
2014
, “
Multi-scale Multi-Mechanism Design of Tough Hydrogels: Building Dissipation Into Stretchy Networks
,”
Soft Matter
,
10
(
5
), pp.
672
687
. 10.1039/C3SM52272E
6.
Hu
,
X.
,
Vatankhah-Varnoosfaderani
,
M.
,
Zhou
,
J.
,
Li
,
Q.
, and
Sheiko
,
S. S.
,
2015
, “
Weak Hydrogen Bonding Enables Hard, Strong, Tough, and Elastic Hydrogels
,”
Adv. Mater.
,
27
(
43
), pp.
6899
6905
. 10.1002/adma.201503724
7.
Stoyanov
,
H.
,
Kollosche
,
M.
,
Risse
,
S.
,
Wache
,
R.
, and
Kofod
,
G.
,
2013
, “
Soft Conductive Elastomer Materials for Stretchable Electronics and Voltage Controlled Artificial Muscles
,”
Adv. Mater.
,
25
(
4
), pp.
578
583
. 10.1002/adma.201202728
8.
Wang
,
Y.
,
Loh
,
L. Y. W.
,
Gupta
,
U.
,
Foo
,
C. C.
, and
Zhu
,
J.
,
2020
, “
Bio-inspired Soft Swim Bladders of Large Volume Change Using Dual Dielectric Elastomer Membranes
,”
ASME J. Appl. Mech.
,
87
(
4
), p.
041007
. 10.1115/1.4045901
9.
Kleman
,
M.
, and
Laverntovich
,
O. D.
,
2007
,
Soft Matter Physics: an Introduction
,
Springer Science & Business Media
,
New York
.
10.
Shariff
,
M. H. B. M.
,
2017
, “
On the Spectral Constitutive Modelling of Transversely Isotropic Soft Tissue: Physical Invariants
,”
Int. J. Eng. Sci.
,
120
, pp.
199
219
. 10.1016/j.ijengsci.2017.08.008
11.
Xiang
,
Y.
,
Zhong
,
D.
,
Rudykh
,
S.
,
Zhou
,
H.
,
Qu
,
S.
, and
Yang
,
W.
,
2020
, “
A Review of Physically Based and Thermodynamically Based Constitutive Models for Soft Materials
,”
ASME J. Appl. Mech.
,
87
(
11
), p.
110801
. 10.1115/1.4047776
12.
Altenbach
,
H.
, and
Morozov
,
N. F.
,
2013
,
Surface Effects in Solid Mechanics-Models, Simulations, and Applications
,
Springer
,
Berlin
.
13.
Style
,
R. W.
,
Boltyanskiy
,
R.
,
Che
,
Y.
,
Wettlaufer
,
J. S.
,
Wilen
,
L. A.
, and
Dufresne
,
E. R.
,
2013
, “
Universal Deformation of Soft Substrates Near a Contact Line and the Direct Measurement of Solid Surface Stresses
,”
Phys. Rev. Lett.
,
110
(
6
), p.
066103
. 10.1103/PhysRevLett.110.066103
14.
Assadi
,
A.
,
2013
, “
Size Dependent Forced Vibration of Nanoplates With Consideration of Surface Effects
,”
Appl. Math. Model.
,
37
(
5
), pp.
3575
3588
. 10.1016/j.apm.2012.07.049
15.
Wang
,
Y.
,
Feng
,
X.
,
Lu
,
B.
, and
Wang
,
G.
,
2013
, “
Surface Effects on the Mechanical Behavior of Buckled Thin Film
,”
ASME J. Appl. Mech.
,
80
(
2
), p.
021002
. 10.1115/1.4007681
16.
Attia
,
M. A.
,
2017
, “
On the Mechanics of Functionally Graded Nanobeams With the Account of Surface Elasticity
,”
Int. J. Eng. Sci.
,
115
, pp.
73
101
. 10.1016/j.ijengsci.2017.03.011
17.
Yang
,
S.
,
Zhao
,
X.
, and
Sharma
,
P.
,
2017
, “
Revisiting the Instability and Bifurcation Behavior of Soft Dielectrics
,”
ASME J. Appl. Mech.
,
84
(
3
), p.
031008
. 10.1115/1.4035499
18.
Jagota
,
A.
,
Paretkar
,
D.
, and
Ghatak
,
A.
,
2012
, “
Surface-Tension-Induced Flattening of a Nearly Plane Elastic Solid
,”
Phys. Rev. E
,
85
(
5
), p.
051602
. 10.1103/PhysRevE.85.051602
19.
Paretkar
,
D.
,
Xu
,
X.
,
Hui
,
C. Y.
, and
Jagota
,
A.
,
2014
, “
Flattening of a Patterned Compliant Solid by Surface Stress
,”
Soft Matter
,
10
(
23
), pp.
4084
4090
. 10.1039/C3SM52891J
20.
Duan
,
H. L.
,
Wang
,
J.
, and
Karihaloo
,
B. L.
,
2009
, “
Theory of Elasticity at the Nanoscale
,”
Adv. Appl. Mech.
,
42
, pp.
1
68
. 10.1016/S0065-2156(08)00001-X
21.
Andreotti
,
B.
,
Baumchen
,
O.
,
Boulogne
,
F.
,
Daniels
,
K. E.
,
Dufresne
,
E. R.
,
Perrin
,
H.
,
Salez
,
T.
,
Snoeijer
,
J. H.
, and
Style
,
R. W.
,
2016
, “
Solid Capillarity: When and How Does Surface Tension Deform Soft Solids?
Soft Matter
,
12
(
12
), pp.
2993
2996
. 10.1039/C5SM03140K
22.
Style
,
R. W.
,
Jagota
,
A.
,
Hui
,
C. Y.
, and
Dufresne
,
E. R.
,
2017
, “
Elastocapillarity: Surface Tension and the Mechanics of Soft Solids
,”
Annu. Rev. Condens. Matter Phys.
,
8
(
1
), pp.
99
118
. 10.1146/annurev-conmatphys-031016-025326
23.
Miller
,
R. E.
, and
Shenoy
,
V. B.
,
2000
, “
Size-Dependent Elastic Properties of Nanosized Structural Elements
,”
Nanotechnology
,
11
(
3
), pp.
139
147
. 10.1088/0957-4484/11/3/301
24.
Liu
,
M.
,
Wu
,
J.
,
Gan
,
Y.
, and
Chen
,
C. Q.
,
2016
, “
The Pore-Load Modulus of Ordered Nanoporous Materials With Surface Effects
,”
AIP Adv.
,
6
(
3
), p.
035324
. 10.1063/1.4945441
25.
Style
,
R. W.
,
Boltyanskiy
,
R.
,
Allen
,
B.
,
Jensen
,
K. E.
,
Foote
,
H. P.
,
Wettlaufer
,
J. S.
, and
Dufresne
,
E. R.
,
2014
, “
Stiffening Solids With Liquid Inclusions
,”
Nat. Phys.
,
11
(
1
), pp.
82
87
. 10.1038/nphys3181
26.
Mora
,
S.
,
Phou
,
T.
,
Fromental
,
J. M.
,
Pismen
,
L. M.
, and
Pomeau
,
Y.
,
2010
, “
Capillarity Driven Instability of a Soft Solid
,”
Phys. Rev. Lett.
,
105
(
21
), p.
214301
. 10.1103/PhysRevLett.105.214301
27.
Gibbs
,
J. W.
,
1906
,
The Scientific Papers of J. Willard Gibbs
,
Longmans-Green
,
London
.
28.
Shuttleworth
,
R.
,
1950
, “
The Surface Tension of Solids
,”
Proc. Phys. Soc. A
,
63
(
5
), p.
444
. 10.1088/0370-1298/63/5/302
29.
Gurtin
,
M. E.
, and
Murdoch
,
A. I.
,
1975
, “
A Continuum Theory of Elastic Material Surfaces
,”
Arch. Ration. Mech. Anal.
,
57
(
4
), pp.
291
323
. 10.1007/BF00261375
30.
Cammarata
,
R. C.
,
1994
, “
Surface and Interface Stress Effects in Thin Films
,”
Prog. Surf. Sci.
,
46
(
1
), pp.
1
38
. 10.1016/0079-6816(94)90005-1
31.
Xu
,
X.
,
Jagota
,
A.
, and
Hui
,
C. Y.
,
2014
, “
Effects of Surface Tension on the Adhesive Contact of a Rigid Sphere to a Compliant Substrate
,”
Soft Matter
,
10
(
26
), pp.
4625
4632
. 10.1039/C4SM00216D
32.
Giannakopoulos
,
A.
,
2003
, “
The Influence of Initial Elastic Surface Stresses on Instrumented Sharp Indentation
,”
ASME J. Appl. Mech.
,
70
(
5
), pp.
638
643
. 10.1115/1.1485756
33.
Wang
,
G. F.
, and
Niu
,
X. R.
,
2015
, “
Nanoindentation of Soft Solids by a Flat Punch
,”
Acta Mech. Sin.
,
31
(
4
), pp.
531
535
. 10.1007/s10409-015-0440-7
34.
Long
,
J.
,
Wang
,
G.
,
Feng
,
X.
, and
Yu
,
S.
,
2016
, “
Effects of Surface Tension on the Adhesive Contact Between a Hard Sphere and a Soft Substrate
,”
Int. J. Solids Struct.
,
84
, pp.
133
138
. 10.1016/j.ijsolstr.2016.01.021
35.
Style
,
R. W.
,
Wettlaufer
,
J. S.
, and
Dufresne
,
E. R.
,
2015
, “
Surface Tension and the Mechanics of Liquid Inclusions in Compliant Solids
,”
Soft Matter
,
11
(
4
), pp.
672
679
. 10.1039/C4SM02413C
36.
Liu
,
T.
,
Jagota
,
A.
, and
Hui
,
C. Y.
,
2017
, “
A Closed Form Large Deformation Solution of Plate Bending With Surface Effects
,”
Soft Matter
,
13
(
2
), pp.
386
393
. 10.1039/C6SM02398C
37.
Liu
,
Z.
,
Jagota
,
A.
, and
Hui
,
C. Y.
,
2020
, “
Modeling of Surface Mechanical Behaviors of Soft Elastic Solids: Theory and Examples
,”
Soft Matter
,
16
(
29
), pp.
6875
6889
. 10.1039/D0SM00556H
38.
Chang
,
G. H.
, and
Modarres-Sadeghi
,
Y.
,
2017
, “
Flow-Induced Buckling of Flexible Shells With Non-Zero Gaussian Curvatures and Thin Spots
,”
Soft Matter
,
13
(
13
), pp.
2465
2474
. 10.1039/C7SM00129K
39.
Li
,
G. Y.
,
He
,
Q.
,
Mangan
,
R.
,
Xu
,
G.
,
Mo
,
C.
,
Luo
,
J.
,
Destrade
,
M.
, and
Cao
,
Y.
,
2017
, “
Guided Waves in Pre-stressed Hyperelastic Plates and Tubes: Application to the Ultrasound Elastography of Thin-Walled Soft Materials
,”
J. Mech. Phys. Solids
,
102
, pp.
67
79
. 10.1016/j.jmps.2017.02.008
40.
Su
,
Y.
,
Zhou
,
W.
,
Chen
,
W.
, and
,
C.
,
2016
, “
On Buckling of a Soft Incompressible Electroactive Hollow Cylinder
,”
Int. J. Solids Struct.
,
97
, pp.
400
416
. 10.1016/j.ijsolstr.2016.07.008
41.
Zhu
,
Y.
,
Luo
,
X. Y.
, and
Ogden
,
R. W.
,
2010
, “
Nonlinear Axisymmetric Deformations of an Elastic Tube Under External Pressure
,”
Eur. J. Mech. A Solids
,
29
(
2
), pp.
216
229
. 10.1016/j.euromechsol.2009.10.004
42.
Emuna
,
N.
, and
Cohen
,
N.
,
2021
, “
Inflation Induced Twist in Geometrically Incompatible Isotropic Tubes
,”
ASME J. Appl. Mech.
,
88
(
3
), p.
031005
. 10.1115/1.4047980
43.
Zhu
,
Y.
,
Luo
,
X. Y.
, and
Ogden
,
R. W.
,
2008
, “
Asymmetric Bifurcations of Thick-Walled Circular Cylindrical Elastic Tubes Under Axial Loading and External Pressure
,”
Int. J. Solids Struct.
,
45
(
11–12
), pp.
3410
3429
. 10.1016/j.ijsolstr.2008.02.005
44.
Zhu
,
Y.
,
Luo
,
X. Y.
,
Wang
,
H. M.
,
Ogden
,
R. W.
, and
Berry
,
C.
,
2013
, “
Three-Dimensional Non-linear Buckling of Thick-Walled Elastic Tubes Under Pressure
,”
Int. J. Non-Linear Mech.
,
48
, pp.
1
14
. 10.1016/j.ijnonlinmec.2012.06.013
45.
Kozlovsky
,
P.
,
Zaretsky
,
U.
,
Jaffa
,
A. J.
, and
Elad
,
D.
,
2014
, “
General Tube Law for Collapsible Thin and Thick-Wall Tubes
,”
J. Biomech.
,
47
(
10
), pp.
2378
2384
. 10.1016/j.jbiomech.2014.04.033
46.
Haughton
,
D. M.
, and
Orr
,
A.
,
1995
, “
On the Eversion of Incompressible Elastic Cylinders
,”
Int. J. Non-Linear Mech.
,
30
(
2
), pp.
81
95
. 10.1016/0020-7462(94)00036-A
47.
Haughton
,
D. M.
, and
Orr
,
A.
,
1997
, “
On the Eversion of Compressible Elastic Cylinders
,”
Int. J. Solids Struct.
,
34
(
15
), pp.
1893
1914
. 10.1016/S0020-7683(96)00122-9
48.
Chen
,
Y. C.
, and
Haughton
,
D. M.
,
1997
, “
Existence of Exact Solutions for the Eversion of Elastic Cylinders
,”
J. Elasticity
,
49
(
1
), pp.
79
88
. 10.1023/A:1007431400648
49.
Liang
,
X.
,
Tao
,
F.
, and
Cai
,
S.
,
2016
, “
Creasing of an Everted Elastomer Tube
,”
Soft Matter
,
12
(
37
), pp.
7726
7730
. 10.1039/C6SM01381C
50.
Wang
,
L.
,
2020
, “
Axisymmetric Instability of Soft Elastic Tubes Under Axial Load and Surface Tension
,”
Int. J. Solids Struct.
,
191
, pp.
341
350
. 10.1016/j.ijsolstr.2020.01.015
51.
Mooney
,
M.
,
1940
, “
A Theory of Large Elastic Deformation
,”
J. Appl. Phys
,
11
(
9
), pp.
582
592
. 10.1063/1.1712836
52.
Huang
,
Z. P.
, and
Wang
,
J.
,
2006
, “
A Theory of Hyperelasticity of Multi-phase Media With Surface/Interface Energy Effect
,”
Acta Mechanica
,
182
(
3–4
), pp.
195
210
. 10.1007/s00707-005-0286-3
53.
Hong
,
W.
,
Zhao
,
X.
, and
Suo
,
Z.
,
2009
, “
Formation of Creases on the Surfaces of Elastomers and Gels
,”
Appl. Phys. Lett.
,
95
(
11
), p.
111901
. 10.1063/1.3211917
54.
Timoshenko
,
S. P.
, and
Gere
,
J. M.
,
1961
,
Theory of Elastic Stability
,
McGraw-Hill
,
New York
.
You do not currently have access to this content.