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Research Papers

Third-Order Polynomials Model for Analyzing Multilayer Hard/Soft Materials in Flexible Electronics

[+] Author and Article Information
Xianhong Meng

School of Aeronautic Science and Engineering,
Beihang University,
Beijing 100191, China
e-mail: mxh@buaa.edu.cn

Boya Liu

School of Aeronautic Science and Engineering,
Beihang University,
Beijing 100191, China

Yu Wang

Department of Mechanical Engineering,
University of Colorado Boulder,
Boulder, CO 80309

Taihua Zhang

Academy of Opto-Electronics,
Chinese Academy of Sciences,
Beijing 100094, China

Jianliang Xiao

Department of Mechanical Engineering,
University of Colorado Boulder,
Boulder, CO 80309
e-mail: jianliang.xiao@colorado.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 21, 2016; final manuscript received May 31, 2016; published online June 16, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(8), 081011 (Jun 16, 2016) (10 pages) Paper No: JAM-16-1257; doi: 10.1115/1.4033754 History: Received May 21, 2016; Revised May 31, 2016

In flexible electronics, multilayer hard/soft materials are widely used to utilize both the superior electrical properties of inorganic semiconductors and robust mechanical properties of polymers simultaneously. However, the huge mismatch in mechanical properties of the hard and soft materials makes mechanics analysis challenging. We here present an analytical model to study the mechanics of multilayer hard/soft materials in flexible electronics. Third-order polynomials are adopted to describe the displacement field, which can be used to easily derive both strain and stress fields. Then, the principle of virtual work was used to derive the governing equations and boundary conditions, which can be solved numerically. Two types of loadings, pure bending and transverse shear, are studied. The normal strain distributions along thickness direction in the bimaterial regions clearly show zigzag profiles, due to the huge mismatch in the mechanical properties of the hard and soft materials. The effect of very different mechanical properties of the hard and soft materials on shear stress distributions can also be predicted by this model. The results from this analytical mode show good agreement with finite-element modeling (FEM). This model can be useful in systems with multilayer hard/soft materials, to predict mechanical behavior and to guide design and optimization.

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References

Figures

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Fig. 1

(a) Illustration of the layout of a typical flexible electronic system. (b) Cross section of one half of the unit cell.

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Fig. 2

Normal strain distributions of Si–NOA system subjected to bending moment

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Fig. 3

Shear stress distributions of Si–NOA system subjected to bending moment

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Fig. 4

Normal strain distributions of Si–PDMS system subjected to bending moment

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Fig. 5

Shear stress distributions of Si–PDMS system subjected to bending moment

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Fig. 6

Normal strain distributions of Si–NOA system subjected to transverse shear

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Fig. 7

Shear stress distributions of Si–NOA system subjected to transverse shear

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Fig. 8

Normal strain distributions of Si–PDMS system subjected to transverse shear

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Fig. 9

Shear stress distributions of Si–PDMS system subjected to transverse shear

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