Technical Brief

Torsional Buckling by Joining Prestrained and Unstrained Elastomeric Strips With Application as Bilinear Elastic Spring

[+] Author and Article Information
Raudel Avila

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: roavila@u.northwestern.edu

Yeguang Xue

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: yeguang-xue@u.northwestern.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 7, 2017; final manuscript received July 19, 2017; published online August 3, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(10), 104502 (Aug 03, 2017) (5 pages) Paper No: JAM-17-1358; doi: 10.1115/1.4037347 History: Received July 07, 2017; Revised July 19, 2017

Controlled formation of complex three-dimensional (3D) geometries has always attracted wide interest especially in micro/nanoscale where traditional fabrication techniques fail to apply. Recent advances employed buckling as a promising complementary assembling technique and the method can be used for high-performance electronics materials, such as silicon. This paper describes a new buckling pattern generated by joining multiple prestrained and unstrained elastomeric strips. After releasing, periodic twisting of the system along the releasing direction is generated and bilinear force–displacement relationship is revealed from finite element analysis (FEA). The finding enriches the classes of geometries that can be achieved from structural buckling. Also, compared to other buckling phenomena, the lateral dimension of the system does not change during the buckling process, which makes the structure perfect for elastic spring elements that can be arranged closely to each other without interference.

Copyright © 2017 by ASME
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Armon, S. , Efrati, E. , Kupferman, R. , and Sharon, E. , 2011, “ Geometry and Mechanics in the Opening of Chiral Seed Pods,” Science, 333(6050), pp. 1726–1730. [CrossRef] [PubMed]
Savin, T. , Kurpios, N. A. , Shyer, A. E. , Florescu, P. , Liang, H. Y. , Mahadevan, L. , and Tabin, C. J. , 2011, “ On the Growth and Form of the Gut,” Nature, 476(7358), pp. 57–62. [CrossRef] [PubMed]
Huang, J. S. , Liu, J. , Kroll, B. , Bertoldi, K. , and Clarke, D. R. , 2012, “ Spontaneous and Deterministic Three-Dimensional Curling of Pre-Strained Elastomeric Bi-Strips,” Soft Matter, 8(23), pp. 6291–6300. [CrossRef]
Liu, J. , Huang, J. S. , Su, T. X. , Bertoldi, K. , and Clarke, D. R. , 2014, “ Structural Transition From Helices to Hemihelices,” PLoS One, 9(4), p. e0139525.
Reis, P. M. , 2015, “ A Perspective on the Revival of Structural (In) Stability With Novel Opportunities for Function: From Buckliphobia to Buckliphilia,” ASME J. Appl. Mech., 82(11), p. 111001. [CrossRef]
Huang, Z. Y. , Hong, W. , and Suo, Z. , 2005, “ Nonlinear Analyses of Wrinkles in a Film Bonded to a Compliant Substrate,” J. Mech. Phys. Solids, 53(9), pp. 2101–2118. [CrossRef]
Jiang, H. Q. , Khang, D. Y. , Song, J. Z. , Sun, Y. G. , Huang, Y. G. , and Rogers, J. A. , 2007, “ Finite Deformation Mechanics in Buckled Thin Films on Compliant Supports,” Proc. Natl. Acad. Sci. U.S.A., 104(40), pp. 15607–15612. [CrossRef] [PubMed]
Raayai-Ardakani, S. , Yague, J. L. , Gleason, K. K. , and Boyce, M. C. , 2016, “ Mechanics of Graded Wrinkling,” ASME J. Appl. Mech., 83(12), p. 121011. [CrossRef]
Liu, Y. L. , Li, M. J. , Liu, J. R. , and Chen, X. , 2017, “ Mechanism of Surface Wrinkle Modulation for a Stiff Film on Compliant Substrate,” ASME J. Appl. Mech., 84(5), p. 051011. [CrossRef]
Lee, W. K. , Jung, W. B. , Nagel, S. R. , and Odom, T. W. , 2016, “ Stretchable Superhydrophobicity From Monolithic, Three-Dimensional Hierarchical Wrinkles,” Nano Lett., 16(6), pp. 3774–3779. [CrossRef] [PubMed]
Xu, S. , Yan, Z. , Jang, K. I. , Huang, W. , Fu, H. R. , Kim, J. , Wei, Z. , Flavin, M. , McCracken, J. , Wang, R. , Badea, A. , Liu, Y. , Xiao, D. Q. , Zhou, G. Y. , Lee, J. , Chung, H. U. , Cheng, H. Y. , Ren, W. , Banks, A. , Li, X. L. , Paik, U. , Nuzzo, R. G. , Huang, Y. G. , Zhang, Y. H. , and Rogers, J. A. , 2015, “ Assembly of Micro/Nanomaterials Into Complex, Three-Dimensional Architectures by Compressive Buckling,” Science, 347(6218), pp. 154–159. [CrossRef] [PubMed]
Zhang, Y. H. , Yan, Z. , Nan, K. W. , Xiao, D. Q. , Liu, Y. H. , Luan, H. W. , Fu, H. R. , Wang, X. Z. , Yang, Q. L. , Wang, J. C. , Ren, W. , Si, H. Z. , Liu, F. , Yang, L. H. , Li, H. J. , Wang, J. T. , Guo, X. L. , Luo, H. Y. , Wang, L. , Huang, Y. G. , and Rogers, J. A. , 2015, “ A Mechanically Driven Form of Kirigami as a Route to 3D Mesostructures in Micro/Nanomembranes,” Proc. Natl. Acad. Sci. U.S.A., 112(38), pp. 11757–11764. [CrossRef] [PubMed]
Hanna, B. H. , Magleby, S. P. , Lang, R. J. , and Howell, L. L. , 2015, “ Force-Deflection Modeling for Generalized Origami Waterbomb-Base Mechanisms,” ASME J. Appl. Mech., 82(8), p. 081001. [CrossRef]
Yan, Z. , Zhang, F. , Wang, J. C. , Liu, F. , Guo, X. L. , Nan, K. W. , Lin, Q. , Gao, M. Y. , Xiao, D. Q. , Shi, Y. , Qiu, Y. T. , Luan, H. W. , Kim, J. H. , Wang, Y. Q. , Luo, H. Y. , Han, M. D. , Huang, Y. G. , Zhang, Y. H. , and Rogers, J. A. , 2016, “ Controlled Mechanical Buckling for Origami-Inspired Construction of 3D Microstructures in Advanced Materials,” Adv. Funct. Mater., 26(16), pp. 2629–2639. [CrossRef] [PubMed]
Chen, Y. L. , Zhu, Y. , Chen, X. , and Liu, Y. L. , 2016, “ Mechanism of the Transition From In-Plane Buckling to Helical Buckling for a Stiff Nanowire on an Elastomeric Substrate,” ASME J. Appl. Mech., 83(4), p. 041011. [CrossRef]
Wang, A. , Avila, R. , and Ma, Y. J. , 2017, “ Mechanics Design for Buckling of Thin Ribbons on an Elastomeric Substrate Without Material Failure,” ASME J. Appl. Mech., 84(9), p. 094501. [CrossRef]
Wang, F. , Guo, X. G. , Xu, J. X. , Zhang, Y. H. , and Chen, C. Q. , 2017, “ Patterning Curved Three-Dimensional Structures With Programmable Kirigami Designs,” ASME J. Appl. Mech., 84(6), p. 061007. [CrossRef]
Ma, Y. J. , Feng, X. , Rogers, J. A. , Huang, Y. G. , and Zhang, Y. H. , 2017, “ Design and Application of ‘J-Shaped’ Stress-Strain Behavior in Stretchable Electronics: A Review,” Lab Chip, 17(10), pp. 1689–1704. [CrossRef] [PubMed]
Ma, Y. J. , Jang, K. I. , Wang, L. , Jung, H. N. , Kwak, J. W. , Xue, Y. G. , Chen, H. , Yang, Y. Y. , Shi, D. W. , Feng, X. , Rogers, J. A. , and Huang, Y. G. , 2016, “ Design of Strain-Limiting Substrate Materials for Stretchable and Flexible Electronics,” Adv. Funct. Mater., 26(29), pp. 5345–5351. [CrossRef]
Dassault Systèmes, 2015, “ ABAQUS 2016 Analysis User's Manual,” Dassault Systèmes, Providence, RI.


Grahic Jump Location
Fig. 1

Process to form the buckling pattern. (a) Prepare two different types of strips: type A strips with rectangular cross section (W×H) and length L and type B strip with square cross section (W′×W′) and length L′. (b) Elongate type B strip to the same length as type A strip and their width exactly match after elongation. (c) Attach type A strips to each side of the center type B strip and release the system after bonding to form the buckling pattern.

Grahic Jump Location
Fig. 2

(a) Buckling pattern predicted from FEA by releasing from the original length 100 mm to 91 mm. (b) A snapshot of the details of periodic buckling pattern. Twisting occurs along the stretching direction and the twisting angle ranges between −ϕ0 and +ϕ0. (c) Buckling pattern generated by replacing center strip of square-shaped cross section to hexagon-shaped cross section. The left side is the cross section of bonded system.

Grahic Jump Location
Fig. 3

Bilinear force–displacement relationship of the system by symmetrically attaching unstrained strips to a prestrained center strip. (a) The distance from the transition point to the fully released state (zero cross-sectional net force) is controlled by the prestress σpre in the center strip and (b) the tensile stiffness ratio of nonbuckling to buckling states knonbuckle/kbuckle can be tuned by changing H/W.



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