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

Francesco Dell'Isola 1, 2, 3, 4 Pierre Seppecher 2, 5 Jean-Jacques Alibert 5 Tomasz Lekszycki 2, 6, 7 Roman Grygoruk 6 Marek Pawlikowski 6 David Steigmann 8 Ivan Giorgio 2, 4 Ugo Andreaus 9 Emilio Turco 2, 10 Maciej Golaszewski 6 Nicola Rizzi 11 Claude Boutin 12 Victor A. Eremeyev 2, 13, 14 Anil Misra 2, 15 Luca Placidi 2, 4, 16 Emilio Barchiesi 17, 2, 4 Leopoldo Greco 2, 18 Massimo Cuomo 2, 18 Antonio Cazzani 19 Alessandro Della Corte 2, 3, 4 Antonio Battista 2, 4, 20 Daria Scerrato 2, 21 Inna Zurba Eremeeva 2 Yosra Rahali 22 Jean-François Ganghoffer 2, 22 Wolfang Müller 23 Gregor Ganzosch 23 Mario Spagnuolo 4, 24 Aron Pfaff 25 Katarzyna Barcz 6 Klaus Hoschke 25 Jan Neggers 26 François Hild 26
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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Francesco Dell'Isola, Pierre Seppecher, Jean-Jacques Alibert, Tomasz Lekszycki, Roman Grygoruk, et al.. Pantographic metamaterials: an example of mathematically driven design and of its technological challenges. Continuum Mechanics and Thermodynamics, Springer Verlag, 2018, pp.1-34. ⟨hal-01829943⟩

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