Numerical modeling of a composite auxetic metamaterials using micro-dilatation theory

  • Yury SolyaevEmail author
  • Sergey Lurie
  • Anastasia Ustenko
Original Article


Micro-dilatation theory of elasticity is the simplest special case of the micromorphic theory, assuming that the micro-deformation tensor has the spherical form. Recently, it was shown that the micro-dilatation theory can be efficiently used as the continuum model of cellular auxetic metamaterials with re-entrant type lattice structure. Here, we provide a further development of this subject and present the results of numerical three-dimensional modeling of composite cellular metamaterials using the conventional lattice model and the corresponding continuum micro-dilatation model. We consider the two-phase metastructures which behave like a heterogeneous auxetic material under tension/compression and, at the same time, like a homogeneous material under shear. These results are achieved due to the absence of coupling between the microstructural micro-dilatation effects and the macroscopic shear properties of the metamaterial. The positive size effect for the apparent Young’s modulus of the considered composite structures is shown. Additionally, the simple way for the finite-element implementation of the micro-dilatation theory in the Comsol system is described.


Micro-dilatation elasticity Auxetic metamaterial Micromorphic continuum Finite element simulation 


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This work was partially supported by the Grants RFBR 18-01-00553-a, RFBR 18-08-00643-a, MK-1336.2017.8 and the funding of the IAM RAS program.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Applied Mechanics of Russian Academy of Sciences and Moscow Aviation InstituteMoscowRussia
  2. 2.Institute of Applied Mechanics of Russian Academy of Sciences and Lomonosov Moscow State UniversityMoscowRussia
  3. 3.Institute of Applied Mechanics of Russian Academy of SciencesMoscowRussia

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