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Research Papers

Large Deflection of Circular Auxetic Membranes Under Uniform Load

[+] Author and Article Information
Teik-Cheng Lim

School of Science and Technology,
SIM University,
Singapore 599491
e-mail: alan_tc_lim@yahoo.com

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received February 29, 2016; final manuscript received April 27, 2016; published online July 8, 2016. Assoc. Editor: Huiling Duan.

J. Eng. Mater. Technol 138(4), 041011 (Jul 08, 2016) (7 pages) Paper No: MATS-16-1077; doi: 10.1115/1.4033636 History: Received February 29, 2016; Revised April 27, 2016

Currently, available results for the large deflection of circular isotropic membranes are valid for Poisson's ratio of 0.2, 0.3, and 0.4 only. This paper explores the deflection of circular membranes when the membrane material is auxetic, i.e., when they possess negative Poisson's ratio and compared against conventional ones. Due to the multistage calculations involved in the exact method, a generic semi-empirical model is proposed to facilitate convenient and direct computation of the membrane deflection as a function of the radial distance; additionally, a specific semi-empirical model is given to provide a more accurate maximum deflection. Comparison of deflection distributions verifies the validity of the semi-empirical model vis-à-vis the exact model. The deflection of circular membrane increases with the diminishing effect as the Poisson's ratio of the membrane material becomes more negative.

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Figures

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Fig. 1

A circular membrane of thickness h and effective radius R with Young's modulus E and Poisson's ratio v (left) under a uniform load p (top right) and its corresponding deflection w (bottom right)

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Fig. 2

Comparison of the truncated analytical deflection (dashed curve) and the semi-empirical deflection (continuous curve) against the exact analytical deflection (circles)

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Fig. 3

Comparison between the dimensionless deflection distributions between the exact model (discrete data points) and the semi-empirical model (continuous curves) for (a) v=−1, −0.8, −0.6, −0.4, −0.2, 0, 0.2, and 0.4 and (b) v=−0.9, −0.7, −0.5, −0.3, −0.1, 0.1, 0.3, and 0.5

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Fig. 4

Loci of dimensionless deflection versus dimensionless radial distance for the auxetic and conventional regions

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Fig. 5

Plots of dimensionless maximum membrane deflection versus the dimensionless radial distance: (a) generic and specific semi-empirical results compared against exact solution and (b) percentage error of generic and specific semi-empirical with reference to the exact solution

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Fig. 6

Comparison of the normalized deflection distributions between infinitesimal deformation theory of plates with the large deformation theory of membranes: (a) v=0.5, (b) v=0, (c) v=−0.5, and (d) v=−1

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