Abstract
In a recent paper by Ting and Chen [18] it was shown by examples that Poisson’s ratio can have no bounds for all anisotropic elastic materials. With the exception of cubic materials, the examples presented involve a very large transverse strain. We show here that a very large Poisson’s ratio with a bounded transverse strain exists for all anisotropic elastic materials. The large Poisson’s ratio with a bounded transverse strain occurs when the axial strain is in the direction very near or at the direction along which Young’s modulus is very large. In fact the transverse strain has to be very small for the material to be stable. If the non-dimensionalized Young’s modulus is of the order δ−1, where δ is very small, the axial strain, the transverse strain and Poisson’s ratio are of the order δ, δ1/2 and δ−1/2, respectively.
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Mathematics Subject Classifications (2000)
74B05, 74E10.
T.C.T. Ting: Professor Emeritus of University of Illinois at Chicago and Consulting Professor of Stanford University.
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Ting, T.C.T. Very Large Poisson’s Ratio with a Bounded Transverse Strain in Anisotropic Elastic Materials. J Elasticity 77, 163–176 (2004). https://doi.org/10.1007/s10659-005-2156-6
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DOI: https://doi.org/10.1007/s10659-005-2156-6