Elastic pattern transformation in microstructure of cellular auxetic materials in compression test

Małgorzata Janus; Marian Marschalko

doi:10.37705/TechTrans/e2026012

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Elastic pattern transformation in microstructure of cellular auxetic materials in compression test

Technical Transactions

Volume 123 (2026): Issue 1 (January 2026)

By: Małgorzata Janus and Marian Marschalko

Open Access

|May 2026

Abstract

The goal of this paper is to investigate the pattern transformation in auxetic material microstructure in compression loading. Nonlinear behavior resulting from large microstructural beams deflection and buckling is analysed. Deformation study in compression test is performed using ABAQUS by conducting finite element calculation. Timoshenko beam elements are used for material microstructure discretization. Calculations lead to obtaining nonlinear equilibrium paths. The analysis allow to asses values of critical stress and critical strains. Specimens of increasing size consisting of elemental segments are analyzed. Influence of geometric microstructural parameters on the type of pattern transformation and response of material as equivalent continuum is studied.

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
Search in Google Scholar Back to article
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
Search in Google Scholar Back to article
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
Search in Google Scholar Back to article
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
Search in Google Scholar Back to article
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
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
Gibson, L.J., Ashby, M.F. (1997). Cellular Solids: Structure and Properties. Cambridge: Cambridge University Press.
Search in Google Scholar Back to article
Holmes Douglas, P. (2019). Elasticity and stability of shape-softing structures. Colloid and Interface Science, Elsevier, 40, 118–137.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
Janus-Michalska, M. (2009). Micromechanical Model of Auxetic Cellular Materials. Journal of Theoretical and Applied Mechanics, 4, 47, 5–22.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
Muller, S. (1987). Homogenization of nonconvex integral functionals and cellular elastic materials. Archive for Rational Mechanics and Analysis, 99, 189–212.
Search in Google Scholar Back to article
Nemat-Naser, S., Hori, M. (1999a). Micromechanics, 2nd edition, Elsevier.
Search in Google Scholar Back to article
Nemat-Nasser, S., Hori, M. (1999b). On micromechanics theories for determining micro-macro relations in heterogeneous solids, Mechanics of Materials, 31, 667–682.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
Papka, S.D., Kyriakides, S. (1994). In-plane compressive response and crushing of honeycomb. Journal of Mechanics and Physics of Solids, 42, 1499–1532.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.37705/TechTrans/e2026012 | Journal eISSN: 2353-737X | Journal ISSN: 0011-4561

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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

Keywords:

auxetic cellulars,

pattern transformation,

microstructural instability,

critical load

Related subjects:

Architecture and design,

Architecture,

Architects, buildings,

Engineering,

Mechanical engineering,

Mechanics,

Industrial chemistry,

Chemical engineering,

Materials sciences,

Materials sciences, other

© 2026 Małgorzata Janus, Marian Marschalko, published by Cracow University of Technology
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 123 (2026): Issue 1 (January 2026)