Research Papers

Localized Deformation in Plastic Liquids on Elastomers

[+] Author and Article Information
Xavier P. Morelle

School of Engineering and Applied Sciences,
Kavli Institute for Bionano
Science and Technology,
Harvard University,
29, Oxford Street,
Cambridge, MA 02138
e-mail: morelle.xavier@gmail.com

Ruobing Bai

School of Engineering and Applied Sciences,
Kavli Institute for Bionano
Science and Technology,
Harvard University,
29, Oxford Street,
Cambridge, MA 02138
e-mail: ruobing1220@gmail.com

Zhigang Suo

Fellow ASME
School of Engineering and Applied Sciences,
Kavli Institute for Bionano
Science and Technology,
Harvard University,
29, Oxford Street,
Cambridge, MA 02138
e-mail: suo@seas.harvard.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 27, 2017; final manuscript received July 23, 2017; published online August 18, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(10), 101002 (Aug 18, 2017) (5 pages) Paper No: JAM-17-1341; doi: 10.1115/1.4037410 History: Received June 27, 2017; Revised July 23, 2017

A plastic liquid such as toothpaste and butter deforms like an elastic solid under a small stress and like a plastic solid under a large stress. Recently, plastic liquids have been used as compliant electrodes for elastomeric transducers. Here, we study the deformation of a plastic liquid adherent on an elastomer when the elastomer is stretched monotonically. We observe that deformation in the plastic liquid localized into shear bands and necks. We further observe that the plastic liquid slips near the interface between the plastic liquid and the elastomer. Each pulling edge of the plastic liquid develops a shear tail, a thin layer of the plastic liquid adherent to the elastomer. As the elastomer is stretched, the tail conforms to the deformation of the elastomer, and the plastic liquid above the tail slips. Finite element simulations confirm that localization occurs even for a relatively simple elastic–plastic model, but require a boundary condition that allows the near-interface slip.

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Bingham, E. C. , 1916, “ An Investigation of the Laws of Plastic Flow,” Bulletin of the Bureau of Standards, Vol. 13 (Scientific Paper 278), U.S. National Bureau of Standards, Gaithersburg, MD, pp. 309–353. http://nvlpubs.nist.gov/nistpubs/bulletin/13/nbsbulletinv13n2p309_A2b.pdf
Larson, R. G. , 1999, The Structure and Rheology of Complex Fluids, Oxford University Press, New York, pp. 801–802.
Barnes, H. A. , 1999, “ The Yield Stress—A Review or ‘παντα ρει’—Everything Flows?” J. Non-Newtonian Fluid Mech., 81(1–2), pp. 133–178. [CrossRef]
Balmforth, N. J. , Frigaard, I. A. , and Ovarlez, G. , 2014, “ Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics,” Annu. Rev. Fluid Mech., 46(1), pp. 121–146. [CrossRef]
Ovarlez, G. , Rodts, S. , Chateau, X. , and Coussot, P. , 2009, “ Phenomenology and Physical Origin of Shear Localization and Shear Banding in Complex Fluids,” Rheol. Acta, 48(8), pp. 831–844. [CrossRef]
Olmsted, P. D. , 2008, “ Perspectives on Shear Banding in Complex Fluids,” Rheol. Acta, 47(3), pp. 283–300. [CrossRef]
Radulescu, A. V. , and Radulescu, I. , 2006, “ Rheological Models for Lithium and Calcium Greases,” Mechanika, 59(3), pp. 67–70. https://www.researchgate.net/publication/268349397_Rheological_models_for_lithium_and_calcium_greases
Coussot, P. , 2014, “ Yield Stress Fluid Flows: A Review of Experimental Data,” J. Non-Newtonian Fluid Mech., 211, pp. 31–49. [CrossRef]
German, G. , and Bertola, V. , 2010, “ Formation of Viscoplastic Drops by Capillary Breakup,” Phys. Fluids, 22(3), p. 033101. [CrossRef]
Pelrine, R. , Kornbluh, R. , Pei, Q. , and Joseph, J. , 2000, “ High-Speed Electrically Actuated Elastomers With Strain Greater Than 100%,” Science, 287(5454), pp. 836–839. [CrossRef] [PubMed]
Keplinger, C. , Sun, J.-Y. , Foo, C. C. , Rothemund, P. , Whitesides, G. M. , and Suo, Z., 2013, “ Stretchable, Transparent, Ionic Conductors,” Science, 341(6149), pp. 984–987. [CrossRef] [PubMed]
Pelrine, R. , Kornbluh, R. D. , Eckerle, J. , Jeuck, P. , Oh, S. , Pei, Q. , and Stanford, S. , 2001, “ Dielectric Elastomers: Generator Mode Fundamentals and Applications,” Proc. SPIE, 4329, p. 148.
Koh, S. J. A. , Zhao, X. , and Suo, Z. , 2009, “ Maximal Energy That can be Converted by a Dielectric Elastomer Generator,” Appl. Phys. Lett., 94(26), p. 262902. [CrossRef]
O'Brien, B. , Thode, J. , Anderson, I. , Calius, E. , Haemmerle, E. , and Xie, S. , 2007, “ Integrated Extension Sensor Based on Resistance and Voltage Measurement for a Dielectric Elastomer,” Proc. SPIE, 6524, p. 652415.
Huang, J. , Yang, J. , Jin, L. , Clarke, D. R. , and Suo, Z. , 2016, “ Pattern Formation in Plastic Liquid Films on Elastomers by Ratcheting,” Soft Matter, 12(16), pp. 3820–3827. [CrossRef] [PubMed]
AGS-Company, 2016, “ Safety Data Sheet of Lith-Ease White Lithium Grease-WL-14, WL-15,” AGS-Company, Muskegon, MI, accessed Jan. 21, 2016, http://agscompany.com/images/stories/MSDS/English/White-Lithium-Lith-Ease-Grease_WL-14-15_English.pdf
3M, 2015, “ VHB Tape Specialty Tapes—Technical Data,” 3M, London, ON, Canada, accessed Aug. 8, 2017, http://multimedia.3m.com/mws/media/1235574O/specialty-tapes-vhb-technical-data-sheet.pdf
Wong, W. , Guo, T.F., Zhang, Y.W., and Cheng, L., 2010, “ Surface Instability Maps for Soft Materials,” Soft Matter, 6(22), pp. 5743–5750. [CrossRef]
Li, T. , Huang, Z. , Suo, Z. , Lacour, S.P., and Wagner S., 2004, “ Stretchability of Thin Metal Films on Elastomer Substrates,” Appl. Phys. Lett., 85(16), pp. 3435–3437. [CrossRef]
Lu, N. , Suo, Z. , and Vlassak, J. J. , 2010, “ The Effect of Film Thickness on the Failure Strain of Polymer-Supported Metal Films,” Acta Mater., 58(5), pp. 1679–1687. [CrossRef]
Jørgensen, L. , Le Merrer, M. , Delanoë-Ayari, H. , and Barentin, C. , 2015, “ Yield Stress and Elasticity Influence on Surface Tension Measurements,” Soft Matter, 11(25), pp. 5111–5121. [CrossRef] [PubMed]
Li, T. , Huang, Z. Y. , Xi, Z. C. , Lacour, S. P. , Wagner, S. , and Suo, Z. , 2005, “ Delocalizing Strain in a Thin Metal Film on a Polymer Substrate,” Mech. Mater., 37(2), pp. 261–273. [CrossRef]
Coussot, P. , Raynaud, J. S. , Bertrand, F. , Moucheront, P. , Guilbaud, J. P. , Huynh, H. T. , Jarny, S. , and Lesueur, D. , 2002, “ Coexistence of Liquid and Solid Phases in Flowing Soft-Glassy Materials,” Phys. Rev. Lett., 88(21), p. 218301. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

(a) A plastic liquid deforms like an elastic solid of Young's modulus E when the stress is small and like a plastic solid when the stress is above the yield stress σy. Some strain hardening can be observed. (b) Examples of applications of plastic liquids.

Grahic Jump Location
Fig. 2

(a) Microstructure of the lithium grease; (b) stress–strain curves of the lithium grease loaded at several strain rates [15]

Grahic Jump Location
Fig. 3

Experimental setup. A schematic (a) and a photo (b) of a layer of lithium grease on a sheet of VHB elastomer. When the elastomer is stretched, the deformation in the grease is recorded by the cameras from the front and the side.

Grahic Jump Location
Fig. 4

When W/H is large, numerous shear bands form. When W/H is small, a single neck forms.

Grahic Jump Location
Fig. 5

The formation of shear bands in a slender plastic liquid (W/H ≥ 5). The initial dimensions of the plastic liquid are H = 3 mm, W = 22.75 mm, and L = 32.7 mm.

Grahic Jump Location
Fig. 6

Zoom-in on the surface morphology of the shear bands in an optical microscope. The initial dimensions of the lithium grease layer are H = 6.5 mm, W = 31.2 mm and L = 23 mm.

Grahic Jump Location
Fig. 7

The formation of neck in a plastic liquid layer (W/H ≤ 5). The initial dimensions of the lithium grease layer are H = 6.5 mm, W = 18.8 mm, and L = 33 mm.

Grahic Jump Location
Fig. 8

The formation of shear tails. At each pulling edge of the grease, a thin layer of the grease remains adherent to the elastomer. Relative to the thin layer, a block of the grease slips. (a) A thin specimen (H = 3 mm, W = 22.75 mm, and L = 32.7 mm). (b) A thick specimen (H = 6.5 mm, W = 18.8 mm, and L = 33 mm). The side view also shows that the grease/elastomer interface remains flat.

Grahic Jump Location
Fig. 9

The effect of boundary conditions on localization. (a) In the reference state, the grease is represented by a rectangle, with top surface perturbed into a sinusoidal shape. (b) Under the no slip condition, the deformation does not localize even at λ = 2.5. (c) Under the free slip condition, deformation localizes at λ = 1.6. (d) Under the frictional slip condition, deformation also localizes at λ = 1.6.




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