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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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Figures

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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.

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Fig. 2

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

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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.

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Fig. 4

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

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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.

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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.

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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.

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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.

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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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