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Negative Poisson’s ratio in 2D Voronoi cellular solids by biaxial compression: a numerical study

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Abstract

A 2D (two-dimensional) random cellular solid model was built using FEM (finite element method) based on a modified Voronoi tessellation technique. A sequence of permanent biaxial compression deformations was applied on the model to obtain a series of re-entrant random cellular solid structures with different area compression ratios. The Poisson’s ratio and energy absorption capacity of cellular solid models with different initial relative densities (0.032 and 0.039) were studied at different area compression ratios. The results showed that the Poisson’s ratio first decreased and then increased with increasing compression strain. A minimum Poisson’s ratio of approximately −0.38 was achieved with an appropriate compression strain. An empirical fitting rule was established which can best fit the 2D simulation to 3D experimental results for foams. The cellular solids with minimum negative Poisson’s ratio can exhibit the highest energy absorption capacity. Furthermore, mechanical properties of the random cellular solid model were compared with 2D regular honeycomb models with both concave- and convex-shaped cells. Results showed that the energy absorption capacity of the three models increased with an increasing dynamic compression velocity. The random foam model exhibited the highest increase rate in energy absorption capacity with the increasing compression velocity.

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Acknowledgements

This work was supported by “The National Natural Science Foundation of China (11304033) and the Fundamental Research Funds for the Central Universities (N150504006)”. The first author would also like to thank the financial support from the China Scholars Council (File No. 201506085013).

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Authors and Affiliations

  1. College of Sciences, Northeastern University, Shenyang, 110819, People’s Republic of China

    Dong Li & Jianhua Yin

  2. Materials Science and Engineering, University of Virginia, Charlottesville, VA, 22904, USA

    Liang Dong

  3. Department of Engineering Physics, University of Wisconsin, Madison, WI, 53706-1687, USA

    Roderic S. Lakes

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  1. Dong Li
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  2. Liang Dong
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  3. Jianhua Yin
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  4. Roderic S. Lakes
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Correspondence to Dong Li.

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Li, D., Dong, L., Yin, J. et al. Negative Poisson’s ratio in 2D Voronoi cellular solids by biaxial compression: a numerical study. J Mater Sci 51, 7029–7037 (2016). https://doi.org/10.1007/s10853-016-9992-6

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  • DOI: https://doi.org/10.1007/s10853-016-9992-6

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