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Extremal hinged lattices do not obey the theory of elasticity

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Abstract

Hinged lattices that attain extremal values of Poisson’s ratio do not in general obey the theory of elasticity. Hinged structures that attain a Poisson’s ratio of − 1 are easy to stretch or deform volumetrically but they resist bending, in contrast to the predictions of elasticity theory. Their behavior corresponds to that of a Cosserat solid with divergent characteristic length. Hinged structures that attain a maximum Poisson’s ratio are rigid with respect to hydrostatic tension, are easy to shear or to stretch but are unstable with respect to hydrostatic compression.

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Acknowledgements

We acknowledge partial support by the National Science Foundation via Grant No. CMMI -1906890.

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  1. Department of Engineering Physics and Department of Materials Science, University of Wisconsin, Madison, WI , 53706, USA

    R. S. Lakes

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Lakes, R.S. Extremal hinged lattices do not obey the theory of elasticity. Z. Angew. Math. Phys. 73, 27 (2022). https://doi.org/10.1007/s00033-021-01664-x

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