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.
Issue Section:
Research Papers
References
1.
Witten
, T. A.
, 1999
, “Insights From Soft Condensed Matter
,” Rev. Mod. Phys.
, 71
(2
), p. S367
. 10.1103/RevModPhys.71.S3672.
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/B610522J3.
Rus
, D.
, and Tolley
, M. T.
, 2015
, “Design, Fabrication and Control of Soft Robots
,” Nature
, 521
(7553
), pp. 467
–475
. 10.1038/nature145434.
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
. 10.1115/1.40472915.
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/C3SM52272E6.
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.2015037247.
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.2012027288.
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
. 10.1115/1.40459019.
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.2017.08.00811.
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
. 10.1115/1.404777612.
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.110.06610314.
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.2012.07.04915.
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
. 10.1115/1.400768116.
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.2017.03.01117.
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
. 10.1115/1.403549918.
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.85.05160219.
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/C3SM52891J20.
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-X21.
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/C5SM03140K22.
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-031016-02532623.
Miller
, R. E.
, and Shenoy
, V. B.
, 2000
, “Size-Dependent Elastic Properties of Nanosized Structural Elements
,” Nanotechnology
, 11
(3
), pp. 139
–147
. 10.1088/0957-4484/11/3/30124.
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
. 10.1063/1.494544125.
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/nphys318126.
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.105.21430127.
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
. 10.1088/0370-1298/63/5/30229.
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/BF0026137530.
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)90005-131.
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/C4SM00216D32.
Giannakopoulos
, A.
, 2003
, “The Influence of Initial Elastic Surface Stresses on Instrumented Sharp Indentation
,” ASME J. Appl. Mech.
, 70
(5
), pp. 638
–643
. 10.1115/1.148575633.
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/s10409-015-0440-734.
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.2016.01.02135.
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/C4SM02413C36.
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/C6SM02398C37.
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/D0SM00556H38.
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/C7SM00129K39.
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.2017.02.00840.
Su
, Y.
, Zhou
, W.
, Chen
, W.
, and Lü
, C.
, 2016
, “On Buckling of a Soft Incompressible Electroactive Hollow Cylinder
,” Int. J. Solids Struct.
, 97
, pp. 400
–416
. 10.1016/j.ijsolstr.2016.07.00841.
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.2009.10.00442.
Emuna
, N.
, and Cohen
, N.
, 2021
, “Inflation Induced Twist in Geometrically Incompatible Isotropic Tubes
,” ASME J. Appl. Mech.
, 88
(3
), p. 031005
. 10.1115/1.404798043.
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.2008.02.00544.
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.2012.06.01345.
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.2014.04.03346.
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-A47.
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)00122-948.
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:100743140064849.
Liang
, X.
, Tao
, F.
, and Cai
, S.
, 2016
, “Creasing of an Everted Elastomer Tube
,” Soft Matter
, 12
(37
), pp. 7726
–7730
. 10.1039/C6SM01381C50.
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.2020.01.01551.
Mooney
, M.
, 1940
, “A Theory of Large Elastic Deformation
,” J. Appl. Phys
, 11
(9
), pp. 582
–592
. 10.1063/1.171283652.
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/s00707-005-0286-353.
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
. 10.1063/1.321191754.
Timoshenko
, S. P.
, and Gere
, J. M.
, 1961
, Theory of Elastic Stability
, McGraw-Hill
, New York
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