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Experimental Study of Elastic Constants of a Dense Foam with Weak Cosserat Coupling

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Abstract

A dense closed cell foam is studied to determine which continuum theory of elasticity is applicable. Size effects inconsistent with classical elasticity are observed. The material exhibits a characteristic length scale considerably larger, by more than a factor 6, than the largest observable structure size. The Cosserat coupling number \(N\) is shown to be small, via measurements of size effects in square section bars, comparison with size effects in round section bars, and determination of warp of a square section bar in torsion. For this material, the couple stress theory is excluded and the modified couple stress theory is excluded. Theories that force constants to their thermodynamic limits do not apply to this foam. The role of other generalized continuum theories is considered.

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Acknowledgements

Partial support of the National Science Foundation under Grant CMMI-1361832 is gratefully acknowledged. We thank W.J. Drugan for application of the full analysis of [7] to interpret square section results.

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  1. Department of Engineering Physics, University of Wisconsin-Madison, 1500 Engineering Drive, Madison, WI, 53706, USA

    Z. Rueger & R. S. Lakes

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  1. Z. Rueger
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  2. R. S. Lakes
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Correspondence to R. S. Lakes.

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Rueger, Z., Lakes, R.S. Experimental Study of Elastic Constants of a Dense Foam with Weak Cosserat Coupling. J Elast 137, 101–115 (2019). https://doi.org/10.1007/s10659-018-09714-8

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