Auxetics and Other Systems with Unusual Characteristics

This is the sixteenth issue of Physica Status Solidi B focused on materials and models showing negative Poisson's ratio (PR), which are often called auxetics, and other systems of unusual, e.g., “negative”, characteristics [https://doi.org/10.1002/pssb.202200536]. Such issues started already in 2005 [https://doi.org/10.1002/pssb.200590008]. The present issue contains 12 papers which are grouped into three sections: macroscopic auxetics, microscopic auxetics, and other systems of unusual characteristics. The section starts with the paper by Roderic S. Lakes and Ballard Huey [https://doi.org/10.1002/pssb.202300411] in which the authors continue and extend their previous studies [https://doi.org/10.1002/pssb.202200336] on chiral isotropic elastic solids for which Poisson's ratio can be larger or smaller than in the classical thermodynamic bounds. In the second paper [https://doi.org/10.1002/pssb.202300410] Yikai Wang, Donald S. Stone, and Roderic S. Lakes Investigate cubic lattices based on tetrakaidecahedron cells with re-entrant ribs that are designed and fabricated via additive manufacturing. The authors show that Poisson's ratio decreases to a negative value as the re-entrant angle is made smaller. In such systems Poisson's ratio decreases also as ribs are made more slender. This is in contrast to convex tetrakaidecahedron (truncated octahedron) for which Poisson's ratio is close to 0.5 and rib slenderness has minimal effect on Poisson's ratio. The third paper, by Teik-Cheng Lim [https://doi.org/10.1002/pssb.202300413], reports the design of a metamaterial model—made from interconnected units of rotating parallelograms and triangles—in which its Poisson's ratio can range from positive to negative by changing the internal angles between the rotating units. This interesting paper can be thought of as an extension of earlier studies by the same author [https://doi.org/10.1002/pssb.202200385]. The next study is by Sławomir Czarnecki and Tomasz Łukasiak [https://doi.org/10.1002/pssb.202300495] who propose several semianalytical formulae for the optimal distribution of elastic moduli in 2D or 3D domains occupied by nonhomogeneous, least compliant bodies. The article emphasizes the fact that the stiffest, heterogeneous isotropic elastic material has almost always auxetic properties. Amine Harkati, Said Chouai, El-Haddi Harkati, Abderrezak Bezazi, Salah Ellagoune, and Fabrizio Scarpa study, by numerical and analytical methods, stress concentration factors in composite materials, with a specific focus on the influence of negative Poisson's ratio and out-of-plane modulus [https://doi.org/10.1002/pssb.202400115]. Through analytical and numerical simulations, they establish a robust correlation between the customized Poisson's ratio and modulus and the mitigation of stress concentration factors, particularly in epoxy/graphite-reinforced composites. This research offers innovative solutions for enhancing structural integrity and reducing susceptibility to stress-related issues. The following two articles are related to application of auxetics in rowing. In the first of them [https://doi.org/10.1002/pssb.202400289] Joseph N. Grima, Dario Cerasola, James N. Grima-Cornish, Michelle Vella Wood, Nadia Portelli, Darren Sillato, Marilyn Casha, Alfred Gatt, Tonio P. Agius, Cynthia Formosa, and Daphne Attard indicate that rowing handles could benefit from the use of mechanical metamaterials, auxetics in particular, owing to their anomalous manner in how they deform when subjected to mechanical deformations. In the second one [https://doi.org/10.1002/pssb.202400300], James N. Grima-Cornish, Daphne Attard, Alfred Gatt, Giovanni Ficarra, Dario Cerasola, Claire Saliba Thorne, Andrew Albanozzo, Paul Albanozzo, Ruben Gatt, Cynthia Formosa, and Joseph N Grima, inspired by the observations that auxetic materials and metamaterials behave differently compared to their conventional counterparts, describe results of their studies on how a handle prototype, specifically designed to incorporate the classic re-entrant motif, behaves and how end-users perceive it. Physical experiments conducted on such a prototype, as well as a survey amongst rowers using it, suggest its advantage with respect to a classical solution. In the article by Pierre-Sandre Farrugia, Ruben Gatt, and Joseph N. Grima, a three-dimensional (3D) auxetic system is described, designed by linking layers of rotating squares with torsion springs [https://doi.org/10.1002/pssb.202400212]. An analytical model derived for the Poisson's ratio is in good agreement with tests performed using a 3D-printed specimen of the proposed design. P. Sobieszczyk, M. Mroczek, D. Kuźma, and P. Zieliński consider ferroelastic textures, called star patterns, which are transformed into grilles [https://doi.org/10.1002/pssb.202400399]. Their rigid bars replace domain boundaries and are connected with hinges at their junctions. The grilles show several levels of self-similarity. The authors provide formulae for the scaling factors as functions of the shape and number N of the arms. At N = 4 the minimal model exhibits exactly one doubly degenerate mode of zero frequency. In some regions of the system parameters its reaction to stress is analogous to auxetics. In their article, Maria A. Cardona, Joseph N. Grima, Ken E. Evans, and Ruben Gatt indicate that theoretical studies have demonstrated the potential for various organic polymeric systems to exhibit auxetic behavior [https://doi.org/10.1002/pssb.202400213]. Most of such materials are, however, difficult to synthesize. This is in contrast to calix[4]arene which chemistry has advanced very much in recent years. Using force-field-based simulations, the authors obtain results which suggest that such materials can exhibit auxetic behavior when subjected to on-axis loading in the [001] direction. A model, based on purely geometric interactions, is studied by Jakub W. Narojczyk, Jerzy Smardzewski, Przemyslaw Kedziora, Konstantin V. Tretiakov, and Krzysztof W. Wojciechowski using Monte Carlo simulations with varying shape of the periodic box [https://doi.org/10.1002/pssb.202400529]. The study is focused on the influence of the spatial distribution of planar inclusions within the face centered cubic hard sphere crystal and its impact on the elastic properties of the crystal. Periodic systems containing two nanolayer inclusions (build of hard spheres of another diameter than the spheres forming the crystalline matrix) in the representative volume element, oriented orthogonally to [001]-direction and in various spatial ordering, indexed by nanolayer distance i, are considered. It is shown that the inclusions cause the deterioration of auxetic properties in the [110][1–10]-directions. However, the latter weakly depend on i and, it seems, the dependence is monotonic with i. The changes in the size of the inclusion particles, combined with different ordering of the inclusion layers, can be used to coarsely and/or finely tune the elastic properties of the model crystal. This section is represented by a single article. It concerns a negative thermal expansion (NTE) realized by an incomplete bi-material ring, i.e. a circular ring with a gap, which is the subject of the paper by Elena Pasternak and Arcady Dyskin [https://doi.org/10.1002/pssb.202400048]. The authors conclude that the ring exhibits NTE in the plane of the ring when the outer ring has higher thermal expansion coefficient than the inner one and it is the presence of the gap which is the basis of this thermal behavior. This is an interesting and valuable result which can find various applications. The authors claim that when the thermal expansion coefficients are equal, e.g. for a monomaterial incomplete ring, the effective (macroscopic) planar thermal expansion becomes zero. This result reflects the boundaries of the approximation. Simply, by definition, any mono-material should exhibit its characteristic thermal expansion. It is worth adding that the authors indicate that the NTE effect can be achieved also by spring or spiral structures where the role of the gap is played by the open ends. The authors indicate also that these structures will have higher stiffness than the incomplete bi-material ring. Some planar and 3D NTE structures are considered. I would like to thank all the Authors for submitting interesting and valuable papers, the Referees for their time and efforts spent in reviewing the papers, and the Editors of Physica Status Solidi B for processing the manuscript of my co-authorship and for helping me in solving various technical problems. Special thanks are due to Emeritus Professor Dr. William Graham Hoover (Elko, NV, USA) and to my co-workers from the Department of Auxetics, Functional Materials and Computer Simulations at the Institute of Molecular Physics of the Polish Academy of Sciences (Poznań, Poland) for their help. I am also grateful for the support and help received from the Authorities of the Poznań Supercomputing and Networking Center. This work was partially supported by the National Science Centre, Poland - grant 2017/27/B/ST3/02955.