Elastic pattern transformation in microstructure of cellular auxetic materials in compression test
By: Małgorzata Janus and Marian Marschalko
References
- Ameen, M.M., Rokoś, O., Peerlings, R.H., Geers, M.G.D. (2018). Size effects in nonlinear periodic materials exhibiting reversible pattern transformations. Mechanics of Materials, 124, 55–70. https://doi.org/10.1016/j.mechmat.2018.05.011
- Bertoldi, K., Reis, P.M., Willshaw, S., Mullin, T. (2010). Negative Poisson’s ratio behavior induced by an elastic instability. Advanced Materials, 22 (3), 361–366. https://doi.org/10.1002/adma.200901956
- Combescure, Ch., Henry, P., Elliot, R. (2016). Post-bifurcation and stability of finitely strained hexagonal honeycomb subjected to equi-biaxial in-plane loading. International Journal of Solids and Structures, 88-89, 296–318. https://doi.org/10.1016/j.ijsolstr.2016.02.016
- Dong, Z., Li, Ying, Zhao, T., Wu, W., Xiao, D., Liang, J. (2019). Experimental and numerical studies on the compressive mechanical properties of metallic metalic auxetic reentrant honeycomb. Materials and Design, 182. https://doi.org/10.1016/j.matdes.2019.108036
- Fu, M.H., Yu, Chen, Hu, L. (2017a). Bilinear elastic characteristic of enhanced auxetic honeycombs. Composite Structures, 175,191–110. https://doi.org/10.1016/j.ijimpeng.2020.103566
- Fu, M.H., Yu, Chen, Hu, L. (2017b). A novel auxetic honeycomb with enhanced in-plane stiffness and buckling strength. Composite Structures, 160, 547–585.
- Geymonat, G., Muller, S., Triantafyllidis, N. (1993). Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity, Archive for Rational Mechanics and Analysis, 122, 231–290.
- Gibson, L.J., Ashby, M.F. (1997). Cellular Solids: Structure and Properties. Cambridge: Cambridge University Press.
- Holmes Douglas, P. (2019). Elasticity and stability of shape-softing structures. Colloid and Interface Science, Elsevier, 40, 118–137.
- Jiang, Y., Rudra, B., Shim, J., Li, Y. (2019). Limiting strain for auxeticity under large compressive deformation: Chiral versus re-entrant cellular solids. International Journal of Solids and Structures, 162, 87–95.
- Janus-Michalska, M. (2009). Micromechanical Model of Auxetic Cellular Materials. Journal of Theoretical and Applied Mechanics, 4, 47, 5–22.
- Laroussi, M., Sab, K., Alaoui, A. (2002). Foam mechanics: nonlinear response of an elastic 3D-periodic microstructure. International Journal of Solids and Structures, 39, 3599–3623.
- Mitschke, H., Schury, F., Mecke, K., Wein, F., Stingl, M., Schröder-Turk, G.E. (2016). Geometry: The leading parameter for the Poisson’s ratio of bending--dominated cellular solids. International Journal of Solids and Structures, 100-101, 1–10.
- Muller, S. (1987). Homogenization of nonconvex integral functionals and cellular elastic materials. Archive for Rational Mechanics and Analysis, 99, 189–212.
- Nemat-Naser, S., Hori, M. (1999a). Micromechanics, 2nd edition, Elsevier.
- Nemat-Nasser, S., Hori, M. (1999b). On micromechanics theories for determining micro-macro relations in heterogeneous solids, Mechanics of Materials, 31, 667–682.
- Nguyen, C., Ho, D.T., Choi Seung, Chun Doo-Man, Kom, S.Y. (2019). Pattern transformation induced by elastic instability of metallic porous structures. Computational Materials Science, 157, 17–24.
- Okumura, D., Ohno, N., Noguchi, H. (2004). Elastoplastic microscopic bifurcation and post-bifurcation behavior of periodic cellular solids. Journal of Mechanics and Physics of Solids, 52, 641–666.
- Ohno, N., Okumura, D., Noguchi, H. (2002). Microscopic symmetric bifurcation condition of cellular solids based on a homogenization theory of finite deformation. Journal of Mechanics and Physics of Solids, 50, 1125–1153.
- Prawoto Y. (2012). Seeing auxetic materials from the mechanics point of view: A structural review on the negative Poisson’s ratio. Computational Materials Science, 58, 140–153.
- Papka, S.D., Kyriakides, S. (1994). In-plane compressive response and crushing of honeycomb. Journal of Mechanics and Physics of Solids, 42, 1499–1532.
- Papka, S.D., Kyriakides, S. (1999). Biaxial crushing of honeycombs – Part I: Experiments. 4367–4396. Part II: Analysis. 4397–4423. International Journal of Solids and Structures, 36.
- Ren, X., Shen, Ji., Tran, P., Ngo, T. (2018). Design and characterization of a tunable 3D buckling-induced auxetic material. Materials and Design, 336–342.
- Saiki, I., Terada, K., Ikeda, K., Hori, M. (2002). Appropriate number of unit cells in a representative volume element for micro-structural bifurcation encountered in multi-scale modeling. Computer Methods in Applied Mechanics and Engineering, 191, 2561–2585.
- Triantafyllidis, N., Schnaidt, W.C. (1993). Comparison of microscopic and macroscopic instabilities in a class of two-dimensional periodic composites. Journal of Mechanics and Physics of Solids, 41, 1533–1565.
DOI: https://doi.org/10.37705/TechTrans/e2026012 | Journal eISSN: 2353-737X | Journal ISSN: 0011-4561
Language: English
Submitted on: Nov 13, 2025
Accepted on: May 6, 2026
Published on: May 29, 2026
Published by: Cracow University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Related subjects:
© 2026 Małgorzata Janus, Marian Marschalko, published by Cracow University of Technology
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.