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Pantographic metamaterials: an example of mathematically driven design and of its technological challenges

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Abstract

In this paper, we account for the research efforts that have been started, for some among us, already since 2003, and aimed to the design of a class of exotic architectured, optimized (meta) materials. At the first stage of these efforts, as it often happens, the research was based on the results of mathematical investigations. The problem to be solved was stated as follows: determine the material (micro)structure governed by those equations that specify a desired behavior. Addressing this problem has led to the synthesis of second gradient materials. In the second stage, it has been necessary to develop numerical integration schemes and the corresponding codes for solving, in physically relevant cases, the chosen equations. Finally, it has been necessary to physically construct the theoretically synthesized microstructures. This has been possible by means of the recent developments in rapid prototyping technologies, which allow for the fabrication of some complex (micro)structures considered, up to now, to be simply some mathematical dreams. We show here a panorama of the results of our efforts (1) in designing pantographic metamaterials, (2) in exploiting the modern technology of rapid prototyping, and (3) in the mechanical testing of many real prototypes. Among the key findings that have been obtained, there are the following ones: pantographic metamaterials (1) undergo very large deformations while remaining in the elastic regime, (2) are very tough in resisting to damage phenomena, (3) exhibit robust macroscopic mechanical behavior with respect to minor changes in their microstructure and micromechanical properties, (4) have superior strength to weight ratio, (5) have predictable damage behavior, and (6) possess physical properties that are critically dictated by their geometry at the microlevel.

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Acknowledgements

This work was supported by a grant from the Government of the Russian Federation (contract No. 14.Y26.31.0031).

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Authors and Affiliations

  1. Dipartimento di Ingegneria Strutturale e Geotecnica, Università degli Studi di Roma “La Sapienza.”, Via Eudossiana 18, 00184, Rome, Italy

    Francesco dell’Isola, Ugo Andreaus & Emilio Barchiesi

  2. International Research Center M&MoCS, Università degli Studi dell’Aquila, Via Giovanni Gronchi 18 - Zona industriale di Pile, 67100, L’Aquila, Italy

    Francesco dell’Isola, Pierre Seppecher, Tomasz Lekszycki, Ivan Giorgio, Emilio Turco, Victor A. Eremeyev, Anil Misra, Luca Placidi, Emilio Barchiesi, Leopoldo Greco, Massimo Cuomo, Alessandro Della Corte, Antonio Battista, Daria Scerrato, Inna Zurba Eremeeva & Jean-François Ganghoffer

  3. Dipartimento di Ingegneria Civile, Edile-Architettura e Ambientale, Università degli Studi dell’Aquila, Via Giovanni Gronchi 18 - Zona industriale di Pile, 67100, L’Aquila, Italy

    Francesco dell’Isola & Alessandro Della Corte

  4. Research Institute for Mechanics, National Research Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

    Francesco dell’Isola, Ivan Giorgio, Luca Placidi, Emilio Barchiesi, Alessandro Della Corte, Antonio Battista, Daria Scerrato & Mario Spagnuolo

  5. Institut de Mathématiques de Toulon, Université de Toulon et du Var, Avenue de l’ Université, BP 132, 83957, La Garde Cedex, France

    Pierre Seppecher & Jean Jacques Alibert

  6. Institute of Mechanics and Printing, Warsaw University of Technology, 85 Narbutta Street, 02-524, Warsaw, Poland

    Tomasz Lekszycki, Roman Grygoruk, Marek Pawlikowski, Maciej Gołaszewski & Katarzyna Barcz

  7. Department of Experimental Physiology and Pathophysiology, Medical University of Warsaw, 1b Banacha Street, 02-097, Warsaw, Poland

    Tomasz Lekszycki

  8. Department of Mechanical Engineering, University of California at Berkeley, 6133 Etcheverry Hall, Mailstop 1740, Berkeley, CA, USA

    David Steigmann

  9. Dipartimento di Architettura, Design, Urbanistica, Università degli Studi di Sassari, Asilo Sella, Via Garibaldi 35 (I piano), 07041, Alghero, SS, Italy

    Emilio Turco

  10. Dipartimento di Architettura, Università degli studi Roma Tre, Via della Madonna dei Monti 40, 00184, Rome, Italy

    Nicola Rizzi

  11. Ecole Nationale des Travaux Publics de l’Etat, LGCB CNRS 5513 - CeLyA, Université de Lyon, 69518, Vaulx-en-Velin Cedex, France

    Claude Boutin

  12. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, ul. Gabriela Narutowicza 11/12, 80-233, Gdańsk, Poland

    Victor A. Eremeyev

  13. Mathematics, Mechanics and Computer Science Department, South Federal University, Milchakova, str., 8a, Rostov-on-Don, Russia, 344090

    Victor A. Eremeyev

  14. Civil, Environmental and Architectural Engineering Department, The University of Kansas, 1530 W. 15th Street, Lawrence, KS, 66045-7609, USA

    Anil Misra

  15. Engineering Faculty, International Telematic University Uninettuno, C.so Vittorio Emanuele II 39, 00186, Rome, Italy

    Luca Placidi

  16. Dipartimento di Ingegneria Civile ed Ambientale (sezione di Ingegneria Strutturale), Università di Catania, Edificio Polifunzionale, IV piano, Viale Andrea Doria, 6 I, 95125, Catania, Italy

    Leopoldo Greco & Massimo Cuomo

  17. Dipartimento di Ingegneria Civile, Ambientale e Architettura, Università degli studi di Cagliari, Via Marengo 2, Cagliari, Italy

    Antonio Cazzani

  18. Laboratoire des Sciences de l’Ingénieur pour l’ Environnement, Université de La Rochelle, 23 avenue Albert Einstein, BP 33060, 17031, La Rochelle, Italy

    Antonio Battista

  19. Laboratoire d’Energétique et de Mécanique Théorique et Appliquée, University of Lorraine, 2 Avenue de la Foret de Haye, BP 90161, 54505, Vandoeuvre-lés-Nancy cedex, France

    Yosra Rahali & Jean-François Ganghoffer

  20. Faculty of Mechanics, Berlin University of Technology, Einsteinufer 5, 10587, Berlin, Germany

    Wolfgang Müller & Gregor Ganzosch

  21. Laboratoire des Sciences des Procédés et des Matériaux, Université Paris 13, Campus de Villetaneuse 99 avenue Jean-baptiste Clément, 93430, Villetaneuse, France

    Mario Spagnuolo

  22. Fraunhofer Institute for High-Speed Dynamics, Ernst-Mach-Institut, Eckerstraße 4, 79104, Freiburg, Germany

    Aron Pfaff & Klaus Hoschke

  23. Laboratoire de Mécanique et Technologie (LMT), ENS Paris-Saclay/CNRS/Université Paris-Saclay, 61 avenue du Président Wilson, 94235, Cachan Cedex, France

    Jan Neggers & François Hild

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  1. Francesco dell’Isola
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  14. Victor A. Eremeyev
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Correspondence to Emilio Barchiesi.

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Communicated by Andreas Öchsner.

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dell’Isola, F., Seppecher, P., Alibert, J.J. et al. Pantographic metamaterials: an example of mathematically driven design and of its technological challenges. Continuum Mech. Thermodyn. 31, 851–884 (2019). https://doi.org/10.1007/s00161-018-0689-8

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