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Models and auxetic characteristics of a simple cubic lattice of spherical particles

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Abstract

For a simple cubic lattice of spherical particles with three translational and three rotational degrees of freedom, using the method of structural modeling, discrete, long-wavelength continuum and higher-order gradient models are developed. The higher-order gradient model of such a medium is compared with the Lame equations for cubic symmetry media. From this comparison, the relationships are established between the second-order elastic constants and the microstructure parameters of this medium such as the size of particles and the parameters of their force and torque interactions. Based on the dependences found, the relationship between Poisson’s ratios of the considered anisotropic material and its structural parameters is analyzed. It is found that, at some values of the microstructure parameters, this medium can manifest the auxetic properties.

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Acknowledgements

The research was carried out under the financial support of the Russian Science Foundation (Grant No. 21-19-00813).

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Authors and Affiliations

  1. Mechanical Engineering Research Institute of the Russian Academy of Sciences– Branch of Federal Research Center “Institute of Applied Physics of the RAS”, Nizhny Novgorod, Russia, 603024

    I. S. Pavlov, S. V. Dmitriev & A. V. Muravieva

  2. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia, 603950

    I. S. Pavlov & A. V. Muravieva

  3. Institute of Molecule and Crystal Physics, UFRC, Russian Academy of Sciences, Ufa, Russia, 450001

    S. V. Dmitriev

  4. Tver State University, Tver, Russia, 170102

    A. A. Vasiliev

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Pavlov, I.S., Dmitriev, S.V., Vasiliev, A.A. et al. Models and auxetic characteristics of a simple cubic lattice of spherical particles. Continuum Mech. Thermodyn. 34, 1669–1685 (2022). https://doi.org/10.1007/s00161-022-01157-w

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