Research Papers

A Prenecking Strategy Makes Stretched Membranes With Clamped Ends Wrinkle-Free

[+] Author and Article Information
Ming Li, Yangjun Luo, Yanzhuang Niu, Tengfei Zhao, Jian Xing

State Key Laboratory of Structural Analysis for
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China

HuaPing Wu, Kai Zhu

Key Laboratory of E&M,
Zhejiang University of Technology,
Hangzhou 310032, China

Zhan Kang

State Key Laboratory of Structural Analysis for
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China
e-mail: zhankang@dlut.edu.cn

1M. Li and Y. J. Luo contribute equally to this work.

2Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 24, 2017; final manuscript received April 4, 2017; published online April 20, 2017. Assoc. Editor: Harold S. Park.

J. Appl. Mech 84(6), 061006 (Apr 20, 2017) (10 pages) Paper No: JAM-17-1163; doi: 10.1115/1.4036416 History: Received March 24, 2017; Revised April 04, 2017

For both polyimide membranes in aerospace and graphene membranes in nanoelectronics with surface accuracy requirements, wrinkles due to the extreme out-of-plane flexibility yield inverse influences on the properties and applications of membranes. In this study, on the basis of discrete topology optimization, we propose a prenecking strategy by adopting elliptical free edges to suppress the stretch-induced wrinkling. This prenecking strategy with the computer-aided-design (CAD)-ready format is versatile to eliminate wrinkles in stretched membranes with clamped ends and achieve wrinkle-free performances. The wrinkle-free capability of the prenecking strategy, capable of satisfying the shape accuracy requirements, indicates that by suffering insignificant area loss, concerning of wrinkling problems in membranes is no further required. As compared with the existing researches focusing on studying wrinkling behaviors, the prenecking strategy offers a promising solution to the stretch-induced wrinkling problem by eliminating wrinkles through design optimization.

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Grahic Jump Location
Fig. 5

Nanoscale MD verifications for stretch-induced mechanical wrinkling-suppression capability of the prenecking strategy in graphene membranes with different prenecking ratios, namely (a) αp= 2%, (b) αp= 5%, (c) αp= 20%, and (d) αp= 90%

Grahic Jump Location
Fig. 6

Thermal wrinkling and thermal vibration-suppression capability of the prenecking strategy: (a) Distributions of compressive σmin in a polyimide membrane with different prenecking ratios under uniform thermal shrinkage, (b) fundamental natural frequencies of membranes with the increase of αp, (c) out-of-plane accelerations in center of a polyimide membrane subjected to a sudden uniform thermal variation

Grahic Jump Location
Fig. 4

Macroscale experimental verifications for stretch-induced mechanical wrinkling-suppression capability of the prenecking strategy in polyimide membranes. (a) Deformed membranes and (b) wrinkle profiles with 0%≤αp≤90% when ε=7.5%. The wrinkle profiles and deformed morphologies of a membrane with αp  = 10% under different tensile strains are shown in the bottom frame of (b) and (c), respectively.

Grahic Jump Location
Fig. 1

Stretch-induced mechanical wrinkling behaviors in (a) a polyimide membrane (40 mm × 20 mm × 12.5 μm) in the macroscale physical experiment and (b) a nanoscale graphene membrane (300 nm × 150 nm × 0.335 nm) in the nanoscale MD simulation

Grahic Jump Location
Fig. 2

(a) Maximum lateral displacement of the free edge dmax as a function of tensile strain ε for the studied graphene membrane (300 nm × 150 nm × 0.335 nm) and (b) distributions of minimum principal stresses σmin in a membrane under increasing stretching strain in FEA, the stress contours are plotted on the initial configuration of the membrane, and the gray color denotes the positive σmin

Grahic Jump Location
Fig. 3

Prenecking strategy to suppress stretch-induced mechanical wrinkling: (a) Optimal designs in topology optimization corresponding to typical admissible area ratios, (b) normalized concave free edge, elliptical curve and necking configuration of a rectangular membrane under 1% stretch, (c) stress distributions of σmin with prenecking ratio αp falling into different regimes, (d) evolutions of min(σmin) with the increase of prenecking ratio αp, (e) critical prenecking ratio for wrinkle-free regime as a function of Poisson's ratio v



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