Designing Structural Metamaterials

Abstract Designing Structural Metamaterials † João Cardoso 1, * , Patrícia Almeida 1 , Gonçalo Catatão 1 , Guilherme Cândida 1 , Frederico Páscoa 2 , Daniela Silva 1 , Carla Machado 2 , João P. Borges 1 and Alexandre Velhinho 1 1 2 * † CENIMAT/I3N, Materials Science Department, NOVA School of Science and Technology, Universidade NOVA de Lisboa, 2829-516 Caparica, Portugal; [email protected] (P.A.); [email protected] (G.C.); [email protected] (G.C.); [email protected] (D.S.); [email protected] (J.P.B.); [email protected] (A.V.) UNIDEMI, Mechanical and Industrial Engineering Department, NOVA School of Science and Technology, Universidade NOVA de Lisboa, 2829-516 Caparica, Portugal; [email protected] (F.P.); [email protected] (C.M.) Correspondence: [email protected]; Tel.: +351-932905117 Presented at the Materiais 2022, Marinha Grande, Portugal, 10–13 April 2022. Keywords: auxetics; negative thermal expansion; anepectic; composites; additive manufacturing Citation: Cardoso, J.; Almeida, P.; Catatão, G.; Cândida, G.; Páscoa, F.; Silva, D.; Machado, C.; Borges, J.P.; Velhinho, A. Designing Structural Metamaterials. Mater. Proc. 2022, 8, 55. https://doi.org/10.3390/ materproc2022008055 Academic Editors: Geoffrey Mitchell, Nuno Alves, Carla Moura and Joana Coutinho Published: 31 May 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Metamaterials are materials that exhibit properties that are opposite to those normally found in nature. For structural metamaterials, the most studied cases are those showing negative Poisson’s ratio (also known as auxetics), negative coefficient of thermal expansion (NTE), and/or negative linear compressibility (also known as negative bulk modulus). These properties can be found in nature only for very specific cases and conditions. Cork is known to have a Poisson’s ratio of zero while re-entrant polymer foams and some metallic crystals have a Poisson’s ratio below zero [1]. Water is known to have a negative thermal expansion coefficient between the temperatures of 0 and 4 ◦ C, while ZrW2O8 shows the same behavior between the temperatures of 0.3 and 1050 Kelvin [2]. Furthermore, there are very few materials that naturally present negative linear compressibility, as shown by most research carried out on man-made structures. Anepectic materials, on the other hand, which simultaneously present both negative Poisson’s ratio and negative thermal expansion, while being potentially advantageous in fields as diverse as those of medicine, defense, sports, automobile, and aeronautics, have only recently come to light, and as such still warrant in-depth studies. The anepectic behavior can be obtained by coupling two or more adequately chosen base materials with specific architectures. By observing the five categories of known auxetic materials (re-entrant, chiral, rotating, crumpled sheet, and perforated sheet), it is possible to choose which parts of a structure should be replaced with a second material of suitable stiffness and thermal expansion to transform an auxetic structure into an anepectic one. This approach was previously applied for 2D meshes [3], and current work has extended similar results into the third dimension. The current work reports a series of simulation and experimental results on rotating and re-entrant 3D metamaterials manufactured by the filament deposition method, as well as the underlying theories and state-of-the-art presentation [4]. Author Contributions: Conceptualization: A.V., J.P.B., C.M.; Methodology: A.V., J.P.B., C.M., J.C.; Software: F.P., J.C., C.M.; Validation: J.C., P.A., G.C. (Gonçalo Catatão), G.C. (Guilherme Cândida), D.S.; Formal analysis: J.C., P.A., G.C. (Gonçalo Catatão), G.C. (Guilherme Cândida), D.S.; Investigation: J.C., P.A., G.C. (Gonçalo Catatão), G.C. (Guilherme Cândida), D.S.; Resources: A.V., J.P.B., C.M.; Data curation: J.C.; Writing—Original draft preparation: J.C.; Writing—Review and editing: A.V., J.P.B.; Visualization: J.C., P.A., G.C. (Gonçalo Catatão), G.C. (Guilherme Cândida), D.S.; Supervision; A.V., J.P.B., C.M.; Project administration: A.V., J.P.B.; Funding acquisition: A.V.; J.P.B., C.M., J.C. All authors have read and agreed to the published version of the manuscript. Mater. Proc. 2022, 8, 55. https://doi.org/10.3390/materproc2022008055 https://www.mdpi.com/journal/materproc Mater. Proc. 2022, 8, 55 2 of 2 Funding: The authors acknowledge Fundação para a Ciência e a Tecnologia (FCT - MCTES) for its financial support via the project UIDB/00667/ 2020 (UNIDEMI) and UIDB/50025/2020-2023 (CENIMAT/I3N). João Cardoso acknowledges the funding by FCT – Fundação para a Ciência e Tecnologia under the research grant SFRH/BD/146227/2019. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: No data has been reported in this study. Conflicts of Interest: The authors declare no conflict of interest. References 1. 2. 3. 4. Ren, X.; Das, R.; Tran, P.; Ngo, T.D.; Xie, Y.M. Auxetic metamaterials and structures: A review. Smart Mater. Struct. 2018, 27, 23001. [CrossRef] Evans, J.S.O.; Mary, T.A.; Vogt, T.; Sleight, A.W. Negative thermal expansion from 0.3 to 1050 K in zirconium tungstate. Science 1996, 272, 90–92. [CrossRef] Raminhos, J.S.; Borges, J.P.; Velhinho, A. Development of polymeric anepectic meshes: Auxetic metamaterials with negative thermal expansion. Smart Mater. Struct. 2019, 28, 045010. [CrossRef] Cardoso, J.O.; Borges, J.P.; Velhinho, A. Structural metamaterials with negative mechanical/thermomechanical indices: A review. Prog. Nat. Sci. Mater. Int. 2021, 31, 801–808. [CrossRef]