Analytical modeling and parametric study of equivalent stiffness for auxetic structures

Document Type : Research Paper


Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran.


Auxetic materials have a negative Poisson's ratio, which is different from most engineering materials. Auxetic materials are used in various fields such as medicine, sports science, sensors and actuators, etc. An auxetic structure is made of several cells in parallel and series. In this paper, the equivalent stiffness of an auxetic cell and structure are analytically extracted. The effect of the geometrical parameters, such as the angle and beam length of the auxetic cell, on auxetic cell and structure equivalent stiffness, are investigated. The extracted equations are verified using the simulation of the auxetic structure in the Abaqus software. In this study, numerical simulation is used in order to study the effect of the parameters of the auxetic cell on its equivalent mass. The results of this study show that changing the geometrical parameters of the auxetic cell, affect the vibration behavior of the auxetic structure. Also, the effect of geometrical parameters of the auxetic structure on the Poisson's ratio is investigated.


Main Subjects

[1]          M. Mir, M. N. Ali, J. Sami, U. Ansari, Review of mechanics and applications of auxetic structures, Advances in Materials Science and Engineering, Vol. 2014, 2014.
[2]          J. Schwerdtfeger, F. Wein, G. Leugering, R. Singer, C. Körner, M. Stingl, F. Schury, Design of auxetic structures via mathematical optimization, Advanced materials, Vol. 23, No. 22‐23, pp. 2650-2654, 2011.
[3]          K. E. Evans, A. Alderson, Auxetic materials: functional materials and structures from lateral thinking!, Advanced materials, Vol. 12, No. 9, pp. 617-628, 2000.
[4]          P. U. Kelkar, H. S. Kim, K.-H. Cho, J. Y. Kwak, C.-Y. Kang, H.-C. Song, Cellular auxetic structures for mechanical metamaterials: A review, Sensors, Vol. 20, No. 11, pp. 3132, 2020.
[5]          M. Choulaei, A.-H. Bouzid, Stress analysis of bolted flange joints with different shell connections, in Proceeding of, American Society of Mechanical Engineers, pp. V012T12A029.
[6]          M. Alizadeh, M. Choulaei, M. Roshanfar, J. Dargahi, Vibrational characteristic of heart stent using finite element model, International journal of health sciences, Vol. 6, No. S4, pp. 4095-4106, 06/15, 2022.
[7]          S. Iyer, M. Alkhader, T. Venkatesh, Electromechanical behavior of auxetic piezoelectric cellular solids, Scripta Materialia, Vol. 99, pp. 65-68, 2015.
[8]          X.-W. Zhang, D.-Q. Yang, Numerical and experimental studies of a light-weight auxetic cellular vibration isolation base, Shock and Vibration, Vol. 2016, 2016.
[9]          X. Zhang, D. Yang, Mechanical properties of auxetic cellular material consisting of re-entrant hexagonal honeycombs, Materials, Vol. 9, No. 11, pp. 900, 2016.
[10]        G. Imbalzano, P. Tran, T. D. Ngo, P. V. Lee, Three-dimensional modelling of auxetic sandwich panels for localised impact resistance, Journal of Sandwich Structures & Materials, Vol. 19, No. 3, pp. 291-316, 2017.
[11]        N. D. Duc, K. Seung-Eock, N. D. Tuan, P. Tran, N. D. Khoa, New approach to study nonlinear dynamic response and vibration of sandwich composite cylindrical panels with auxetic honeycomb core layer, Aerospace Science and Technology, Vol. 70, pp. 396-404, 2017.
[12]        F. Peng, Z. Yang, L. Jiang, Y. Ren, Research on shock responses of three types of honeycomb cores, in Proceeding of, IOP Publishing, pp. 012122.
[13]        W. Lee, Y. Jeong, J. Yoo, H. Huh, S.-J. Park, S. H. Park, J. Yoon, Effect of auxetic structures on crash behavior of cylindrical tube, Composite Structures, Vol. 208, pp. 836-846, 2019.
[14]        J. Zhang, X. Zhu, X. Yang, W. Zhang, Transient nonlinear responses of an auxetic honeycomb sandwich plate under impact loads, International Journal of Impact Engineering, Vol. 134, pp. 103383, 2019.
[15]        C. Li, H.-S. Shen, H. Wang, Nonlinear vibration of sandwich beams with functionally graded negative Poisson’s ratio honeycomb core, International Journal of Structural Stability and Dynamics, Vol. 19, No. 03, pp. 1950034, 2019.
[16]        H. Eipakchi, F. M. Nasrekani, Vibrational behavior of composite cylindrical shells with auxetic honeycombs core layer subjected to a moving pressure, Composite Structures, Vol. 254, pp. 112847, 2020.
[17]        S. Dutta, H. G. Menon, M. Hariprasad, A. Krishnan, B. Shankar, Study of auxetic beams under bending: A finite element approach, Materials Today: Proceedings, Vol. 46, pp. 9782-9787, 2021.
[18]        A. Kamthe, M. Walame, Determination of Energy Absorption Capacity of Auxetic Hexagon Structure with Different Geometrical Parameters by Simulation and Experimentation, 2021.
[19]        F. Ebrahimian, Z. Kabirian, D. Younesian, P. Eghbali, Auxetic clamped-clamped resonators for high-efficiency vibration energy harvesting at low-frequency excitation, Applied Energy, Vol. 295, pp. 117010, 2021.
[20]        Q.-H. Pham, P.-C. Nguyen, T. T. Tran, T. Nguyen-Thoi, Free vibration analysis of nanoplates with auxetic honeycomb core using a new third-order finite element method and nonlocal elasticity theory, Engineering with Computers, pp. 1-19, 2021.
[21]        H.-A. Pham, H.-Q. Tran, M.-T. Tran, V.-L. Nguyen, Q.-T. Huong, Free vibration analysis and optimization of doubly-curved stiffened sandwich shells with functionally graded skins and auxetic honeycomb core layer, Thin-Walled Structures, Vol. 179, pp. 109571, 2022.
[22]        S. Zhu, J. Li, Z. Qiao, J. Zhou, Multiple Periodic Vibrations of Auxetic Honeycomb Sandwich Plate with 1: 2 Internal Resonance, Journal of Nonlinear Mathematical Physics, Vol. 29, No. 2, pp. 423-444, 2022.
Volume 54, Issue 3
September 2023
Pages 336-346
  • Receive Date: 29 June 2023
  • Revise Date: 16 August 2023
  • Accept Date: 21 August 2023