Abstract
This chapter lays down the foundation for elastic stability of columns, circular plates, rectangular plates, cylindrical shells and spherical shells that possess negative Poisson’s ratio . Results show that the plate Poisson’s ratio has no effect on the elastic stability of rectangular plates under in-plane biaxial loadings when the critical buckling load is expressed in terms of plate flexural rigidity, but the Poisson’s ratio plays a greater role for circular plate buckling. In the elastic stability study of spherical shells, the critical buckling stress is directly proportional to the shell thickness for Poisson’s ratio of 0 and proportional to the square of the shell thickness as the Poisson’s ratio approaches −1. Thereafter a summary of results by Miller et al. (Compos Sci Technol 70:1049–1056, 2010) for flatwise buckling optimization of hexachiral and tetrachiral honeycombs is furnished. Finally examples are given for square plates with array of perforations such that imposition of uniaxial compressive buckling leads to 2D auxeticity.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bertoldi K, Reis PM, Willshaw S, Mullin T (2010) Negative Poisson’s ratio behavior induced by an elastic instability. Adv Mater 22(3):361–366
Haghpanah B, Papadopoulos J, Mousanezhad D, Nayeb-Hashemi H, Vaziri A (2014) Buckling of regular, chiral and hierarchical honeycombs under a general macroscopic stress state. Proc Roy Soc A 470(2167):20130856
Karnessis N, Burriesci G (2013) Uniaxial and buckling mechanical response of auxetic cellular tubes. Smart Mater Struct 22(8):084008
Kerr AD (1962) On the stability of circular plates. J Aerosp Sci 29(4):486–487
Lim TC (2013) Circular auxetic plates. J Mech 29(1):121–133
Lim TC (2014) Buckling and vibration of circular auxetic plates. ASME J Eng Mater Technol 136(2):021007
Miller W, Smith CW, Scarpa F, Evans KE (2010) Flatwise buckling optimization of hexachiral and tetrachiral honeycombs. Compos Sci Technol 70(7):1049–1056
Mises RV (1914) The critical external pressure of cylindrical tubes. Zeitschrift des Vereines Deutscher Ingenieurs 58(19):750
Reddy JN (2007) Theory and analysis of elastic plates and shells, 2nd edn, Chap. 5. CRC Press, Boca Raton
Reismann H (1952) Bending and buckling of an elastically restrained circular plate. ASME J Appl Mech 19:167–172
Shim J, Shan S, Kosmrlj A, Kang SH, Chen ER, Weaver JC, Bertoldi K (2013) Harnessing instabilities for design of soft reconfigurable auxetic/chiral materials. Soft Matter 9(34):8198–8202
Timoshenko SP, Gere JM (1961) Theory of elastic stability, 2nd edn. McGraw-Hill, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media Singapore
About this chapter
Cite this chapter
Lim, TC. (2015). Elastic Stability of Auxetic Solids. In: Auxetic Materials and Structures. Engineering Materials. Springer, Singapore. https://doi.org/10.1007/978-981-287-275-3_10
Download citation
DOI: https://doi.org/10.1007/978-981-287-275-3_10
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-287-274-6
Online ISBN: 978-981-287-275-3
eBook Packages: EngineeringEngineering (R0)