Research Papers

Shear Deformation in Rectangular Auxetic Plates

[+] Author and Article Information
Teik-Cheng Lim

School of Science and Technology,
SIM University,
461 Clementi Road,
S599491, Singapore
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 March 21, 2014; final manuscript received May 7, 2014; published online June 5, 2014. Assoc. Editor: Tetsuya Ohashi.

J. Eng. Mater. Technol 136(3), 031007 (Jun 05, 2014) (6 pages) Paper No: MATS-14-1065; doi: 10.1115/1.4027711 History: Received March 21, 2014; Revised May 07, 2014

Solids that exhibit negative Poisson's ratio are called auxetic materials. This paper examines the extent of transverse shear deformation with reference to bending deformation in simply supported auxetic plates as a ratio of Mindlin-to-Kirchhoff plate deflection for polygonal plates in general, with special emphasis on rectangular plates. Results for square plates show that the Mindlin plate deflection approximates the Kirchhoff plate deflection not only when the plate thickness is negligible, as is obviously known, but also when (a) the Poisson's ratio of the plate is very negative under all load distributions, as well as (b) at the central portion of the plate when the load is uniformly distributed. Hence geometrically thick plates are mechanically equivalent to thin plates if the plate Poisson's ratio is sufficiently negative. The high suppression of shear deformation in favor of bending deformation in auxetic plates suggests its usefulness for bending-based plate sensors that require larger difference in the in-plane strains between the opposing plate surfaces with minimal transverse deflection.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Lakes, R., 1987, “Negative Poisson's Ratio Materials,” Science, 238(4826), pp. 551. [CrossRef]
Wojciechowski, K. W., and Branka, A. C., 1989, “Negative Poisson's Ratio in Isotropic Solids,” Phys. Rev. A, 40(12), pp. 7222–7225. [CrossRef] [PubMed]
Evans, K. E., and Caddock, B. D., 1989, “Microporous Materials With Negative Poisson's Ratios II: Mechanisms and Interpretation,” J. Phys. D: Appl. Phys., 22(12), pp. 1883–1887. [CrossRef]
Lakes, R. S., 1992, “Saint-Venant End Effects for Materials With Negative Poisson's Ratios,” ASME J. Appl. Mech., 59(4), pp. 744–746. [CrossRef]
Lakes, R. S., 1993, “Design Considerations for Materials With Negative Poisson's Ratios,” ASME J. Mech. Des., 115(4), pp. 696–700. [CrossRef]
Phan-Thien, N., and Karihaloo, B. L., 1994, “Materials With Negative Poisson's Ratio: A Qualitative Microstructural Model,” ASME J. Appl. Mech., 61(4), pp. 1001–1004. [CrossRef]
Chen, C. P., and Lakes, R. S., 1996, “Micromechanical Analysis of Dynamic Behavior of Conventional and Negative Poisson's Ratio Foams,” ASME J. Eng. Mater. Technol., 118(3), pp. 285–288. [CrossRef]
Ting, T. C. T., and Barnett, D. M., 2005, “Negative Poisson's Ratios in Anisotropic Linear Elastic Media,” ASME J. Appl. Mech., 72(6), pp. 929–931. [CrossRef]
Lim, T. C., 2010, “In-Plane Stiffness of Semi-Auxetic Laminates,” ASCE J. Eng. Mech., 136(9), pp. 1176–1180. [CrossRef]
Bornengo, D., Scarpa, F., and Remillat, C., 2005, “Evaluation of Hexagonal Chiral Structure for Morphine Airfoil Concept,” IMechE J. Aerosp. Eng., 219(3), pp. 185–192. [CrossRef]
Alderson, A., and Alderson, K. L., 2007, “Auxetic Materials,” IMechE J. Aerosp. Eng., 221(4), pp. 565–575. [CrossRef]
Dolla, W. J. S., Fricke, B. A., and Becker, B. R., 2007, “Structural and Drug Diffusion Models of Conventional and Auxetic Drug-Eluting Stents,” ASME J. Med. Dev., 1(1), pp. 47–55. [CrossRef]
Tan, T. W., Douglas, G. R., Bond, T., and Phani, A. S., 2011, “Compliance and Longitudinal Strain of Cardiovascular Stents: Influence of Cell Geometry,” ASME J. Med. Dev., 5(4), p. 041002. [CrossRef]
Conn, A. T., and Rossiter, J., 2012, “Smart Radially Folding Structures,” IEEE/ASME Trans. Mechatron.17(5), pp. 968–975. [CrossRef]
Scarpa, F., and Tomlinson, G., 2000, “On Static and Dynamic Design Criteria of Sandwich Plate Structures With a Negative Poisson's Ratio Core,” Appl. Mech. Eng., 5(1), pp. 207–222. Available at: http://www.ijame.uz.zgora.pl/ijame_files/archives/v5n1.htm#A16
Scarpa, F., and Tomlinson, G., 2000, “Theoretical Characteristics of the Vibration of Sandwich Plates With In-Plane Negative Poisson's Ratio Values,” J. Sound Vib., 230(1), pp. 45–67. [CrossRef]
Ruzzene, M., Mazzarella, L., Tsopelas, P., and Scarpa, F., 2002, “Wave Propagation in Sandwich Plates With Periodic Auxetic Core,” J. Intell. Mater. Syst. Struct., 13(9), pp. 587–597. [CrossRef]
Strek, T., Maruszewski, B., Narojczyk, and Wojciechowski, K. W., 2008, “Finite Element Analysis of Auxetic Plate Deformation,” J. Non-Cryst. Solids, 354(35-39), pp. 4475–4480. [CrossRef]
Kolat, P., Maruszewski, B. M., and Wojciechowski, K. W., 2010, “Solitary Waves in Auxetic Plates,” J. Non-Cryst. Solids, 356(37–40), pp. 2001–2009. [CrossRef]
Lim, T. C., 2013, “Optimal Poisson's Ratios for Laterally Loaded Rectangular Plates,” IMechE J. Mater.: Des. Appl., 227(2), pp. 111–123. [CrossRef]
Lim, T. C., 2013, “Circular Auxetic Plates,” J. Mech., 29(1), pp. 121–133. [CrossRef]
Lim, T. C., 2014, “Flexural Rigidity of Thin Auxetic Plates,” Int. J. Appl. Mech., 6(2), p. 1450012. [CrossRef]
Lim, T. C., 2013, “Thermal Stresses in Thin Auxetic Plates,” J. Therm. Stresses, 36(11), pp. 1131–1140. [CrossRef]
Maruszewski, B. T., Drzewiecki, A., and Starosta, R., 2013, “Thermoelastic Damping in an Auxetic Rectangular Plate With Thermal Relaxation—Free Vibrations,” Smart Mater. Struct., 22(8), p. 084003. [CrossRef]
Lim, T. C., 2014, “Buckling and Vibration of Circular Auxetic Plates,” ASME J. Eng. Mater. Technol., 136(2), p. 021007. [CrossRef]
Lim, T. C., 2014, “Elastic Stability of Thick Auxetic Plates,” Smart Mater. Struct., 23(4), p. 045004. [CrossRef]
Lim, T. C., “Shear Deformation in Beams With Negative Poisson's Ratio,” IMechE J. Mater.: Des. Appl. (in press). [CrossRef]
Lim, T. C., 2013, “Shear Deformation in Thick Auxetic Plates,” Smart Mater. Struct., 22(8), p. 084001. [CrossRef]
Reddy, J. N., Lee, K. H., and Wang, C. M., 2000, Shear Deformable Beams and Plates: Relationships With Classical Solutions, Elsevier, New York.
Mindlin, R. D., 1951, “Influence of Rotary Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates,” ASME J. Appl. Mech., 18, pp. 31–38.
Reissner, E., 1945, “The Effect of Transverse Shear Deformation on the Bending of Elastic Plates,” ASME J. Appl. Mech., 12, pp. 69–77.
Wittrick, W. H., 1987, “Analytical, Three-Dimensional Elasticity Solutions to Some Plate Problems, and Some Observations on Mindlin's Plate Theory,” Int. J. Solids Struct., 23(4), pp. 441–464. [CrossRef]
Timoshenko, S., and Woinowsky-Krieger, S., 1959, Theory of Plates and Shells, 2nd ed., McGraw-Hill, Singapore.
Koenders, M. A., 1997, “Evolution of Spatially Structured Elastic Material Using a Harmonic Density Function,” Phys. Rev. E, 56(5), pp. 5585–5593. [CrossRef]
Gaspar, N., 2001, “Structures and Heterogeneity in Deforming, Density Packed Granular Materials,” PhD thesis, Kingston University, London.
Gaspar, N., Smith, C. W., and Evans, K. E., 2003, “Effect of Heterogeneity on the Elastic Properties of Auxetic Materials,” J. Appl. Phys., 94(9), pp. 6143–6149. [CrossRef]
Lakes, R. S., 1983, “Size Effects and Micromechanics of a Porous Solid,” J. Mater. Sci., 18(9), pp. 2572–2580. [CrossRef]


Grahic Jump Location
Fig. 1

A family of Mindlin-to-Kirchhoff deflection ratio curves of a simply supported square plate under sinusoidal load

Grahic Jump Location
Fig. 2

Plots of Mindlin-to-Kirchhoff deflection ratio of the center of a simply supported square plate under uniform load, taking into consideration based on (a) κ = 5/6 and (b) κ = 5/(6-v)

Grahic Jump Location
Fig. 3

A graphical comparison on the Mindlin-to-Kirchhoff deflection ratio versus plate Poisson's ratio at the center of a simply supported square plate under sinusoidal and uniform loads at various dimensionless plate thickness

Grahic Jump Location
Fig. 4

Mindlin-to-Kirchhoff deflection ratio of simply supported square plate under sinusoidal load (with m = n = 1) and under uniform load: (a) comparison from center to middle of plate side parallel to either axes, (b) comparison along plate diagonal from center to corner, and (c) boundary of equal Mindlin-to-Kirchhoff deflection ratio for both types of load distributions




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In