Laminated ribbons have been widely adopted for structures of flexible electronics to simultaneously achieve the electronic functions and mechanical performances. Their effective tensile stiffness and bending stiffness, which are extensively used as fundamental parameters in the mechanical analysis, are usually obtained by the plane-strain hypothesis for simplicity. However, it is found that the practical condition is usually closer to the traction free, even for the cases with a relatively large width. Here, a traction-free model is proposed to analytically obtain the effective tensile stiffness and bending stiffness of laminated ribbons, which can be used directly in the mechanical analysis of flexible electronics. The prediction of the traction-free model agrees very well with the precise result obtained by 3D finite element analysis (FEA) for the cases that are in the range of structure designs of flexible electronics. It is found that the tensile/bending stiffness of traction-free model is between the plane-stress model and plane-strain model, but is closer to the plane-stress model. The use of the plane-strain model sometimes may yield a considerable error in the mechanical analysis of flexible electronics. The parameter study shows that this model is very important for the problems with advanced materials, such as metamaterials with negative Poisson's ratio. This work provides a theoretical basis for the mechanical analysis of flexible electronics.
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Research-Article
A Traction-Free Model for the Tensile Stiffness and Bending Stiffness of Laminated Ribbons of Flexible Electronics
Shizhen Yin,
Shizhen Yin
State Key Laboratory of Nonlinear Mechanics,
Chinese Academy of Sciences,
Beijing 100190,
Institute of Mechanics
,Chinese Academy of Sciences,
Beijing 100190,
China
;School of Engineering Science,
Beijing 100049,
e-mail: yinshizhen@imech.ac.cn
University of Chinese Academy of Sciences
,Beijing 100049,
China
e-mail: yinshizhen@imech.ac.cn
Search for other works by this author on:
Yewang Su
Yewang Su
1
State Key Laboratory of Nonlinear Mechanics,
Chinese Academy of Sciences,
Beijing 100190,
Institute of Mechanics
,Chinese Academy of Sciences,
Beijing 100190,
China
;School of Engineering Science,
Beijing 100049,
University of Chinese Academy of Sciences
,Beijing 100049,
China
;Beijing Key Laboratory of Engineered Construction and Mechanobiology,
Beijing 100190,
e-mail: yewangsu@imech.ac.cn
Institute of Mechanics, Chinese Academy of Sciences
,Beijing 100190,
China
e-mail: yewangsu@imech.ac.cn
1Corresponding author.
Search for other works by this author on:
Shizhen Yin
State Key Laboratory of Nonlinear Mechanics,
Chinese Academy of Sciences,
Beijing 100190,
Institute of Mechanics
,Chinese Academy of Sciences,
Beijing 100190,
China
;School of Engineering Science,
Beijing 100049,
e-mail: yinshizhen@imech.ac.cn
University of Chinese Academy of Sciences
,Beijing 100049,
China
e-mail: yinshizhen@imech.ac.cn
Yewang Su
State Key Laboratory of Nonlinear Mechanics,
Chinese Academy of Sciences,
Beijing 100190,
Institute of Mechanics
,Chinese Academy of Sciences,
Beijing 100190,
China
;School of Engineering Science,
Beijing 100049,
University of Chinese Academy of Sciences
,Beijing 100049,
China
;Beijing Key Laboratory of Engineered Construction and Mechanobiology,
Beijing 100190,
e-mail: yewangsu@imech.ac.cn
Institute of Mechanics, Chinese Academy of Sciences
,Beijing 100190,
China
e-mail: yewangsu@imech.ac.cn
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received January 26, 2019; final manuscript received February 17, 2019; published online March 16, 2019. Assoc. Editor: Yong Zhu.
J. Appl. Mech. May 2019, 86(5): 051011 (8 pages)
Published Online: March 16, 2019
Article history
Received:
January 26, 2019
Revision Received:
February 17, 2019
Accepted:
February 18, 2019
Citation
Yin, S., and Su, Y. (March 16, 2019). "A Traction-Free Model for the Tensile Stiffness and Bending Stiffness of Laminated Ribbons of Flexible Electronics." ASME. J. Appl. Mech. May 2019; 86(5): 051011. https://doi.org/10.1115/1.4042920
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