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Research Papers

Anisotropic Mechanics of Cellular Substrate Under Finite Deformation

[+] Author and Article Information
Feng Zhu

School of Logistics Engineering,
Wuhan University of Technology,
Wuhan 430063, China;
Departments of Civil and Environmental
Engineering,
Mechanical Engineering,
and Materials Science and Engineering,
Center for Bio-Integrated Electronics,
Northwestern University,
Evanston, IL 60208

Hanbin Xiao

School of Logistics Engineering,
Wuhan University of Technology,
Wuhan 430063, China

Yeguang Xue

Departments of Civil and Environmental
Engineering, Mechanical Engineering,
and Materials Science and Engineering,
Center for Bio-Integrated Electronics,
Northwestern University,
Evanston, IL 60208

Xue Feng

Department of Engineering Mechanics,
Interdisciplinary Research Center for Flexible
Electronics Technology,
Tsinghua University,
Beijing 100084, China

Yonggang Huang

Departments of Civil and Environmental
Engineering, Mechanical Engineering, and
Materials Science and Engineering,
Center for Bio-Integrated Electronics,
Northwestern University,
Evanston, IL 60208

Yinji Ma

Department of Engineering Mechanics,
Interdisciplinary Research Center for Flexible
Electronics Technology,
Tsinghua University,
Beijing 100084, China
e-mail: mayinji@gmail.com

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 25, 2018; final manuscript received April 11, 2018; published online May 8, 2018. Special Editor: Pradeep Sharma.

J. Appl. Mech 85(7), 071007 (May 08, 2018) (7 pages) Paper No: JAM-18-1172; doi: 10.1115/1.4039964 History: Received March 25, 2018; Revised April 11, 2018

The use of cellular substrates for stretchable electronics minimizes not only disruptions to the natural diffusive or convective flow of bio-fluids, but also the constraints on the natural motion of the skin. The existing analytic constitutive models for the equivalent medium of the cellular substrate under finite stretching are only applicable for stretching along the cell walls. This paper aims at establishing an analytic constitutive model for the anisotropic equivalent medium of the cellular substrate under finite stretching along any direction. The model gives the nonlinear stress–strain curves of the cellular substrate that agree very well with the finite element analysis (FEA) without any parameter fitting. For the applied strain <10%, the stress–strain curves are the same for different directions of stretching, but their differences become significant as the applied strain increases, displaying the deformation-induced anisotropy. Comparison of the results for linear and nonlinear elastic cell walls clearly suggests that the nonlinear stress–strain curves of the cellular substrate mainly result from the finite rotation of cell walls.

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Figures

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Fig. 1

(a) Schematic illustration of cellular substrate, (b) mechanics model of a basic unit, and (c) normalized nominal stress (T̂3) versus engineering strain (ε) of the equivalent medium for the cellular substrate, obtained by FEA along x- and y-directions at different porosities ϕ = 60%, 70%, 80%, and 90%

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Fig. 2

Beam model for the cellular walls under finite deformation in the global and local coordinate systems

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Fig. 3

Illustration of the effective cell lengths along the (a) x- and (b) y-directions

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Fig. 4

The normalized nominal stress (T̂3) versus engineering strain (ε) of the equivalent medium for the cellular substrate with linear elastic cell walls under stretching along the cell walls (α = 0 deg) at different porosities ϕ = 60%, 70%, 80%, and 90%

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Fig. 5

The normalized nominal stress (T̂3) versus engineering strain (ε) of the equivalent medium for the cellular substrate with linear elastic cell walls stretched in different directions α = 0 deg, 10 deg, 20 deg and 30 deg at porosity ϕ = 80%

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Fig. 10

Projected length of the basic unit normal to the stretching direction

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Fig. 9

Schematic illustration and equilibrium of forces normal to the stretching direction for (a) solid and (b) cellular substrate

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Fig. 8

Distribution of interfacial shear stress between PDMS (0.3 mm thick, elastic modulus 500 kPa, outer contour 3.4 mm×3.4 mm) and skin (1 mm thick, elastic modulus 130 kPa) for ((a) and (b)) solid PDMS; ((c) and (d)) cellular PDMS (porosity ϕ = 80%, cell size d = 0.52 mm); and ((e) and (f)) equivalent medium of the cellular PDMS for stretching of the skin along x- (α = 0 deg) and y-directions (α = 30 deg) under 15% applied strain

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Fig. 7

(a) Solid and (b) cellular PDMS bonded to the skin

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Fig. 6

The normalized nominal stress (T̂3) versus engineering strain (ε) of the equivalent medium for the cellular substrate with linear elastic cell or nonlinear elastic (Mooney–Rivlin) cell walls stretched along (α = 0 deg) and normal to cell walls (30 deg) at porosity ϕ = 80%

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