Influence of unit cell parameters of tetrachiral mechanical metamaterial on its effective properties

Authors

  • Linar R. Akhmetshin National Research Tomsk State University, 36, pr. Lenina, Tomsk, 634050, Russian Federation; Institute of Strength Physics and Materials Science SB RAS, 2/4, pr. Akademicheskii, Tomsk, 634055, Russian Federation
  • Igor Yu. Smolin National Research Tomsk State University, 36, pr. Lenina, Tomsk, 634050, Russian Federation; Institute of Strength Physics and Materials Science SB RAS, 2/4, pr. Akademicheskii, Tomsk, 634055, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2021.113

Abstract

In the paper, we study the mechanical behavior of a three-dimensional chiral mechanical metamaterial using numerical modeling. A feature of chiral structures is that during their uniaxial loading a twisting is observed along the loading axis. A rod of the mechanical metamaterial composed of 3 × 3 × 9 unit cells along the corresponding three orthogonal axes. The relative strain of uniaxial compression of the sample in the simulation did not exceed 3.3%. The simulation was performed by the finite element method in a threedimensional case. Original results on the dependencies of the rotation angle and the reaction of the rigidly fixed support of the metamaterial sample on the parameters characterizing the structure of the unit cell of the metamaterial are presented in this context. All the dependencies, except one, are nonlinear with portions of large and small changes.

Keywords:

numerical modeling, finite-element method, metamaterial, structure-property relation, chiral structure, uniaxial deformation, rotation

Downloads

Download data is not yet available.
 

References

Литература

1. Kweun J.M., Lee H. J., Oh J.H., Seung H.M., Kim Y.Y. Transmodal Fabry-P´erot resonance: Theory and realization with elastic metamaterials. Phys. Rev. Lett. 118, 205901-1–205901-6 (2017). https://doi.org/10.1103/PhysRevLett.118.205901

2. Evans K.E., Nkansah M.A., Hutchinson I. J., Rogers S.C. Molecular network design. Nature 353 (6340), 124–125 (1991). https://doi.org/10.1038/353124a0

3. Lesieutre G., Browne J.A., Frecker M. Scaling of performance, weight, and actuation of a 2-D compliant cellular frame structure for a morphing wing. Journal of Intelligent Material Systems and Structures 22 (10), 979–986 (2011). https://doi.org/10.1177/1045389X11412641

4. Olympio K.R., Gandhi F. Flexible Skins for Morphing Aircraft Using Cellular Honeycomb Cores. Journal of Intelligent Material Systems and Structures 21 (17), 1719–1735 (2010). https://doi.org/10.1177/1045389X09350331

5. Bubert E.A., Woods B.K., Lee K., Kothera C. S., Wereley N.M. Design and fabrication of a passive 1D morphing aircraft skin. Journal of Intelligent Material Systems and Structures 21 (17), 1699–1717 (2010). https://doi.org/10.1177/1045389X10378777

6. Heo H., Ju J., Kim D.-M., Jeon C.-S. Passive Morphing Airfoil with Honeycombs. Proceedings of the ASME 2011 International Mechanical Engineering Congress and Exposition. Volume 1: Advances in Aerospace Technology; Energy Water Nexus; Globalization of Engineering; Posters. Denver, Colorado, USA, 263–271 (2011). https://doi.org/10.1115/IMECE2011-64350

7. Ju J., Ananthasayanam J., Summers J.D., Joseph P. Design of cellular shear bands of a nonpneumatic tire-Investigation of contact pressure. SAE International Journal of Passenger Cars - Mechanical Systems 3 (1), 598–606 (2010). https://doi.org/10.4271/2010-01-0768

8. Ju J., Kim D.-M., Kim K. Flexible cellular solid spokes of a non-pneumatic tire. Composite Structures 94 (8), 2285–2295 (2012). https://doi.org/10.1016/j.compstruct.2011.12.022

9. Goldstein R.V., Gorodtsov V.A., Lisovenko D. S., Volkov M.A. Negative Poisson’s ratio for cubic crystals and nano/microtubes. Phys. Mesomech. 17 (2), 97–115 (2014). https://doi.org/10.1134/S102995991402002

10. Goldstein R.V., Gorodtsov V.A., Lisovenko D. S., Volkov M.A. Thin Homogeneous TwoLayered Plates of Cubic Crystals with Different Layer Orientation. Phys. Mesomech. 22 (4), 261–268 (2019). https://doi.org/10.1134/S1029959919040015

11. Prall D., Lakes R. S. Properties of a chiral honeycomb with a Poisson’s ratio of −1. Int. J. Mech. Sci. 39 (3), 305–314 (1997).

12. Pendry J.B. A Chiral Route to Negative Refraction. Science 306 (5700), 1353–1355 (2004). https://doi.org/10.1126/science.1104467

13. Gansel J.K., Thiel M., Rill M. S., Decker M., Bade K., Saile V., Freymann G. Gold helix photonic metamaterial as broadband circular polarizer. Science 325 (5947), 1513–1515 (2009). https://doi.org/10.1126/science.1177031

14. Frenzel T., Kadic M., Wegener M. Three-dimensional mechanical metamaterials with a twist. Science 358 (6366), 1072–1074 (2017). https://doi.org/10.1126/science.aao4640

15. Fu M.-H., Zheng B.B., Li W.-H. A novel chiral three-dimensional material with negative Poisson’s ratio and the equivalent elastic parameters. Composite Structures 176, 442–448 (2017). https://doi.org/10.1016/j.compstruct.2017.05.027

16. Alderson A., Alderson K. L., Attard D., Evans K.E., Gatt R., Grima N., MillerW., Ravirala N., Smith C.W., Zied K. Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading. Composites Science and Technology 70 (7), 1042–1048 (2010). https://doi.org/10.1016/j.compscitech.2009.07.009

References

1. Kweun J.M., Lee H. J., Oh J.H., Seung H.M., Kim Y.Y. Transmodal Fabry-P´erot resonance: Theory and realization with elastic metamaterials. Phys. Rev. Lett. 118, 205901-1–205901-6 (2017). https://doi.org/10.1103/PhysRevLett.118.205901

2. Evans K.E., Nkansah M.A., Hutchinson I. J., Rogers S.C. Molecular network design. Nature 353 (6340), 124–125 (1991). https://doi.org/10.1038/353124a0

3. Lesieutre G., Browne J.A., Frecker M. Scaling of performance, weight, and actuation of a 2-D compliant cellular frame structure for a morphing wing. Journal of Intelligent Material Systems and Structures 22 (10), 979–986 (2011). https://doi.org/10.1177/1045389X11412641

4. Olympio K.R., Gandhi F. Flexible Skins for Morphing Aircraft Using Cellular Honeycomb Cores. Journal of Intelligent Material Systems and Structures 21 (17), 1719–1735 (2010). https://doi.org/10.1177/1045389X09350331

5. Bubert E.A., Woods B.K., Lee K., Kothera C. S., Wereley N.M. Design and fabrication of a passive 1D morphing aircraft skin. Journal of Intelligent Material Systems and Structures 21 (17), 1699–1717 (2010). https://doi.org/10.1177/1045389X10378777

6. Heo H., Ju J., Kim D.-M., Jeon C.-S. Passive Morphing Airfoil with Honeycombs. Proceedings of the ASME 2011 International Mechanical Engineering Congress and Exposition. Volume 1: Advances in Aerospace Technology; Energy Water Nexus; Globalization of Engineering; Posters. Denver, Colorado, USA, 263–271 (2011). https://doi.org/10.1115/IMECE2011-64350

7. Ju J., Ananthasayanam J., Summers J.D., Joseph P. Design of cellular shear bands of a nonpneumatic tire-Investigation of contact pressure. SAE International Journal of Passenger Cars - Mechanical Systems 3 (1), 598–606 (2010). https://doi.org/10.4271/2010-01-0768

8. Ju J., Kim D.-M., Kim K. Flexible cellular solid spokes of a non-pneumatic tire. Composite Structures 94 (8), 2285–2295 (2012). https://doi.org/10.1016/j.compstruct.2011.12.022

9. Goldstein R.V., Gorodtsov V.A., Lisovenko D. S., Volkov M.A. Negative Poisson’s ratio for cubic crystals and nano/microtubes. Phys. Mesomech. 17 (2), 97–115 (2014). https://doi.org/10.1134/S102995991402002

10. Goldstein R.V., Gorodtsov V.A., Lisovenko D. S., Volkov M.A. Thin Homogeneous TwoLayered Plates of Cubic Crystals with Different Layer Orientation. Phys. Mesomech. 22 (4), 261–268 (2019). https://doi.org/10.1134/S1029959919040015

11. Prall D., Lakes R. S. Properties of a chiral honeycomb with a Poisson’s ratio of −1. Int. J. Mech. Sci. 39 (3), 305–314 (1997).

12. Pendry J.B. A Chiral Route to Negative Refraction. Science 306 (5700), 1353–1355 (2004). https://doi.org/10.1126/science.1104467

13. Gansel J.K., Thiel M., Rill M. S., Decker M., Bade K., Saile V., Freymann G. Gold helix photonic metamaterial as broadband circular polarizer. Science 325 (5947), 1513–1515 (2009). https://doi.org/10.1126/science.1177031

14. Frenzel T., Kadic M., Wegener M. Three-dimensional mechanical metamaterials with a twist. Science 358 (6366), 1072–1074 (2017). https://doi.org/10.1126/science.aao4640

15. Fu M.-H., Zheng B.B., Li W.-H. A novel chiral three-dimensional material with negative Poisson’s ratio and the equivalent elastic parameters. Composite Structures 176, 442–448 (2017). https://doi.org/10.1016/j.compstruct.2017.05.027

16. Alderson A., Alderson K. L., Attard D., Evans K.E., Gatt R., Grima N., MillerW., Ravirala N., Smith C.W., Zied K. Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading. Composites Science and Technology 70 (7), 1042–1048 (2010). https://doi.org/10.1016/j.compscitech.2009.07.009

Downloads

Published

2021-05-29

How to Cite

Akhmetshin, L. R., & Smolin, I. Y. (2021). Influence of unit cell parameters of tetrachiral mechanical metamaterial on its effective properties. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8(1), 150–157. https://doi.org/10.21638/spbu01.2021.113

Issue

Vol. 8 No. 1 (2021)

Section

Mechanics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.