Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-25T20:43:54.665Z Has data issue: false hasContentIssue false
  • English
  • Français

Circular Auxetic Plates

Published online by Cambridge University Press:  16 October 2012

T.-C. Lim
T.-C. Lim*
Affiliation:
School of Science and Technology, SIM University, S 599491, Republic of Singapore
*
*Corresponding author (alan_tc_lim@yahoo.com)
Get access

Abstract

This paper investigates the suitability of auxetic materials for load-bearing circular plates. It is herein shown that the optimal Poisson's ratio for minimizing the bending stresses is strongly dependent on the final deformed shape, load distribution, and the type of edge supports. Specifically, the use of auxetic material for circular plates is recommended when (a) the plate is bent into a spherical or spherical-like cap, (b) a point load is applied to the center of the plate regardless of the edge conditions, and (c) a uniform load is applied on a simply-supported plate. However, auxetic materials are disadvantaged when a flat plate is to be bent into a saddle-like shell. The optimal Poisson's ratios concept recommended in this paper is useful for providing an added design consideration. In most cases, the use of auxetic materials for laterally loaded circular plates is more advantageous compared to the use of materials with conventional Poisson's ratio, with other factors fixed. This is achieved through materials-based stress re-distribution in addition to the common practices of dimensioning-based stress redistribution and materials strengthening.

Keywords

Auxetic materialsCircular platesMechanical properties
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 1 , March 2013 , pp. 121 - 133
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Popereka, M. Y. A. and Balagurov, V. G., “Ferromagnetic Films Having a Negative Poisson Ratio”, Fizika Tverdogo Tela, 11, pp. 3507–3513 (1969).Google Scholar
2. Milstein, F. and Huang, K., “Existence of a Negative Poisson Ratio in FCC Crystals”, Physical Review B, 19, pp. 2030–2033 (1979).Google Scholar
3. Wojciechowski, K. W., “Two-Dimensional Isotropic System with a Negative Poisson Ratio”, Physics Letters A, 137, pp. 60–64 (1989).Google Scholar
4. Wojciechowski, K. W. and Branka, A. C., “Negative Poisson's Ratio in Isotropic Solids”, Physical Review A, 40, pp. 7222–7225 (1989).Google Scholar
5. Lakes, R., “Foam Structures with Negative Poisson's Ratio”, Science, 235, pp. 1038–1040 (1987).Google Scholar
6. Lakes, R., “Negative Poisson's Ratio Materials”, Science, 238, p. 551 (1987).Google Scholar
7. Caddock, B. D. and Evans, K. E., “Microporous Materials with Negative Poisson's Ratios I: Microstructure and Mechanical Properties”, Journal of Physics D: Applied Physics, 22, pp. 1877–1882 (1989).Google Scholar
8. Evans, K. E. and Caddock, B. D., “Microporous Materials with Negative Poisson's Ratios II: Mechanisms And Interpretation”, Journal of Physics D: Applied Physics, 22, pp. 1883–1887 (1989).Google Scholar
9. Choi, J. B. and Lakes, R. S., “Design of a Fastener Based on Negative Poisson's Ratio Foam”, Cellular Polymers, 10, pp. 205–212 (1991).Google Scholar
10. Caddock, B. D. and Evans, K. E., “Negative Poisson Ratios and Strain-Dependent Mechanical Properties in Arterial Prostheses”, Biomaterials, 16, pp. 1109–1115 (1995).Google Scholar
11. Martz, E. O., Lakes, R. S., Goel, V. K. and Park, J. B., “Design of an Artificial Intervertebral Disc Exhibiting a Negative Poisson's Ratio”, Cellular Polymers, 24, pp. 127–138 (2005).Google Scholar
12. Dolla, W. J. S., Fricke, B. A. and Becker, B. R., “Structural and Drug Diffusion Models of Conventional and Auxetic Drug-eluting Stents”, Journal of Medical Devices, 1, pp.47–55 (2007).Google Scholar
13. Scarpa, F., “Auxetic Materials for Bioprostheses”, IEEE Signal Processing Magazine, 25, pp.125–126 (2008).Google Scholar
14. Lakes, R. S. and Lowe, A., “Negative Poisson's Ratio Foam as Seat Cushion Material”, Cellular Polymers, 19, pp. 157–167 (2000).Google Scholar
15. Wang, Y. C. and Lakes, R. S., “Analytical Parametric Analysis of the Contact Problem of Human Buttocks and Negative Poisson's Ratio Foam Cushions”, International Journal of Solids and Structures, 39, pp. 4825–4838 (2002).Google Scholar
16. Alderson, A., Rasburn, J., Ameer-Bag, S., Mullarkey, P. G., Perrie, W. and Evans, K. E., “An Auxetic Filter: A Tuneable Filter Displaying Enhanced Size Selectivity or De-fouling Properties”, Industrial & Engineering Chemistry Research, 39, pp. 654–655 (2000).CrossRefGoogle Scholar
17. Alderson, A., Davies, P. J., Evans, K. E., Alderson, K. L. and Grima, J. N., “Modelling of the Mechanical and Mass Transport Properties of Auxetic Molecular Sieves: An Idealised Inorganic (Zeolitic) Host-Guest System”, Molecular Simulation, 31, pp. 889–896 (2005).Google Scholar
18. Alderson, A., Davies, P. J., Williams, M. R., Evans, K. E., Alderson, K. L. and Grima, J. N., “Modelling of the Mechanical and Mass Transport Properties of Auxetic Molecular Sieves: An Idealised Organic (Polymeric Honeycomb) Host-Guest System”, Molecular Simulation, 31, pp. 897–905 (2005).Google Scholar
19. Lim, T. C. and Acharya, R. U., “Performance Evaluation of Auxetic Molecular Sieves with Re-Entrant Structures”, Journal of Biomedical Nanotechnology, 6, pp. 718–724 (2010).Google Scholar
20. Scarpa, F., Giacomin, J., Zhang, Y. and Pastorino, P., “Mechanical Performance of Auxetic Polyurethane Foam for Antivibration Glove Applications”, Cellular Polymers, 24, pp. 253–268 (2005).Google Scholar
21. Alderson, A. and Alderson, K., “Expanding Materials and Application: Exploiting Auxetic Textiles”, Technical Textiles International, 14, pp. 29–34 (2005).Google Scholar
22. Park, K. O., Choi, J. B., Lee, S. J., Choi, H. H. and Kim, J. K., “Polyurethane Foam with Negative Poisson's Ratio for Diabetic Shoe”, Key Engineering Materials, 288&289, pp. 677–680 (2005).Google Scholar
23. Ellul, B., Muscat, M. and Grima, J. N., “On the Effect of the Poisson's Ratio (Positive and Negative) on the Stability of Pressure Vessel Heads”, Physics Status Solidi B, 246, pp. 2025–2032 (2009).Google Scholar
24. Salit, V. and Weller, T., “On the Feasibility of Introducing Auxetic Behavior Into Thin Walled Structures”, Acta Materialia, 57, pp. 125–135 (2009).Google Scholar
25. Whitty, J. P. M., Henderson, B., Myler, P. and Chirwa, C., “Crash Performance of Cellular Foams with Reduced Relative Density Part 2: Rib Deletion”, International Journal of Crashworthiness, 12, pp. 689–698 (2007).Google Scholar
26. Park, K. O., Choi, J. B., Park, J. C., Park, D. J. and Kim, J. K., “An Improvement in Shock Absorbing Behavior of Polyurethane Foam with a Negative Poisson Effect”, Key Engineering Materials, 342, pp. 845–848 (2007).CrossRefGoogle Scholar
27. Alderson, K. L., Weber, R. S. and Evans, K. E., “Microstructural Evolution in the Processing of Auxetic Microporous Polymers”, Physica Status Solidi B, 244, pp. 828–841 (2007).Google Scholar
28. Grima, J. N. and Evans, K. E., “Auxetic Behavior from Rotating Squares”, Journal of Materials Science Letters, 19, pp. 1563–1565 (2000).Google Scholar
29. Grima, J. N. and Evans, K. E., “Auxetic Behavior from Rotating Triangles”, Journal of Materials Science Letters, 41, pp. 3193–3196 (2006).Google Scholar
30. Grima, J. N., Zammit, V., Gatt, R., Alderson, A. and Evans, K. E., “Auxetic Behaviour from Rotating Semi-Rigid Units”, Physica Status Solidi B, 244, pp. 866–882 (2007).Google Scholar
31. Liu, Y. and Hu, H., “A Review on Auxetic Structures and Polymeric Materials”, Scientific Research Essays, 5, pp. 1052–1063 (2010).Google Scholar
32. Bianchi, M., Scarpa, F., Banse, M. and Smith, C. W., “Novel Generation of Auxetic Open Cell Foams for Curved And Arbitrary Shapes”, Acta Materialia, 59, pp. 686–691 (2011).Google Scholar
33. Gaspar, N., Smith, C. W., Alderson, A., Grima, J. N. and Evans, K. E., “A Generalised Three-Dimensional Tethered-Nodule Model for Auxetic Materials”, Journal of Materials Science, 46, pp. 372–384 (2011).Google Scholar
34. Grima, J. N., Manicaro, E. and Attard, D., “Auxetic Behaviour from Connected Different-Sized Squares and Rectangles”, Proceedings of the Royal Society A, 467, pp. 439–458 (2011).Google Scholar
35. Taylor, C. M., Smith, C. W., Miller, W. and Evans, K. E., “The Effects of Hierarchy on the In-Plane Elastic Properties of Honeycombs”, International Journal of Solids and Structures, 48, pp. 1330–1339 (2011).Google Scholar
36. Lim, T. C. and Acharya, R. U., “An Hexagonal Array of Fourfold Interconnected Hexagonal Nodules for Modeling Auxetic Microporous Polymers: A Comparison of 2D and 3D Models”, Journal of Materials Science, 44, pp. 4491–4494 (2009).Google Scholar
37. Bianchi, M., Scarpa, F., Smith, C. W. and Whittell, G. R., “Physical and Thermal Effects on the Shape Memory Behaviour of Auxetic Open Cell Foams”, Journal of Materials Science, 45, pp. 341–347 (2010).Google Scholar
38. Scarpa, F. and Tomlinson, G., “Theoretical Characteristics of the Vibration of Sandwich Plates with In-Plane Negative Poisson's Ratio Values”, Journal of Sound and Vibration, 230, pp. 45–67 (2000).CrossRefGoogle Scholar
39. Ruzzene, M., Mazzarella, L., Tsopelas, P. and Scarpa, F., “Wave Propagation in Sandwich Plates with Periodic Auxetic Core”, Journal of Intelligent Material Systems and Structures, 13, pp. 587–597 (2002).CrossRefGoogle Scholar
40. Bullar, S. K., Wegner, J. L., and Mioduchowski, A., “Auxetic Behavior of a Thermoelastic Layered Plate”, Journal of Engineering Technology Research, 2, pp. 161–167 (2010).Google Scholar
41. Bullar, S. K., Wegner, J. L., and Mioduchowski, A., “Strain Energy Distribution in an Auxetic Plate with a Crack”, Journal of Engineering Technology Research, 2, pp. 118–126 (2010).Google Scholar
42. Strek, T., Maruszewski, B., Narojczyk, J. and Wojciechowski, K. W., “Finite Element Analysis of Auxetic Plate Deformation”, Journal of Non-Crystalline Solids, 354, pp. 4475–4480 (2008).Google Scholar
43. Poźniak, A. A., Kamiński, H., Kędziora, P., Maruszewski, B., Stręk, T. and Wojciechowski, K. W., “Anomalous Deformation of Constrained Auxetic Square”, Reviews on Advanced Materials Science, 23, pp. 169–174 (2010).Google Scholar
44. Kolat, P., Maruszewski, B. M. and Wojciechowski, K. W., “Solitary Waves in Auxetic Plates”, Journal of Non-Crystalline Solids, 356, pp. 2001–2009 (2010).Google Scholar
45. Timoshenko, S. P. and Woinowsky-Krieger, S., Theory of Plates and Shells, 2nd Ed., McGraw-Hill, New York, Chap. 5 (1964).Google Scholar
46. Ugural, A. C., Stresses in Plates and Shells, 2nd Ed., McGraw-Hill, New York (1998).Google Scholar
47. Ventsel, E. and Krauthammer, T., Thin Plates and Shells: Theory, Analysis and Applications, Marcel Dekker, New York (2001).Google Scholar
48. Reddy, J. N., Theory and Analysis of Elastic Plates and Shells, 2nd Ed., CRC Press, Boca Raton (2006).CrossRefGoogle Scholar
49. Woinowsky-Krieger, S., “Der Spannungszustand in Dicken Elastischen Platen II”, Ingenieur Archiv, 4, pp. 305–331. (In German for: “The State of Stress in Thick Elastic Plates - Part 2”) (1933).Google Scholar
50. Almgren, R. F., “An Isotropic Three Dimensional Structure with Poisson's Ratio = −1”, Journal of Elasticity, 15, pp. 427–430 (1985).Google Scholar
51. Haeri, A. Y., Weidner, D. J. and Parise, J. B., “Elasticity of Alpha-Cristobalite: A Silicon Dioxide with a Negative Poisson's Ratio”, Science, 257, pp. 650–652 (1992).Google Scholar
52. Warren, T. L., “Negative Poisson Ratio in a Tranversely Isotropic Foam Structure”, Journal of Applied Physics, 67, pp. 7591–7594 (1990).Google Scholar
53. Ugbolue, S. C., Kim, Y. K., Warner, S. B., Fan, Q., Yang, C. L., Kyzymchuk, O., Feng, Y. and Lord, J., “The Formation and Performance of Auxetic Textiles. Part II: Geometry and Structural Properties”, Journal of the Textile Institute, 102, pp. 424–433 (2011).CrossRefGoogle Scholar
54. Sloan, M. R., Wright, J. R. and Evans, K. E., “The Helical Auxetic Yarn – A Novel Structure for Composites and Textiles; Geometry, Manufacture and Mechanical Properties”, Mechanical Materials, 43, pp. 476–486 (2011).Google Scholar
55. Lira, C., Scarpa, F. and Rajasekaran, R., “A Gradient Cellular Core for Aeroengine Fan Blades Based on Auxetic Configurations” Journal of Intelligent Material Systems and Structures, 22, pp. 907–917 (2011).Google Scholar
56. Dos Reis, F. and Ganghoffer, J. F., “Equivalent Mechanical Properties of Auxetic Lattices from Discrete Homogenization”, Computational Materials Science, 51, pp. 314–321 (2012).Google Scholar