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Journal Articles Continuum Mechanics and Thermodynamics Year : 2019

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

1 Dipartimento di Ingegneria Strutturale e Geotecnica [Rome]
2 M&MoCS - International Research Centre on Mathematics & Mechanics of Complex Systems
3 DICEAA - Dipartimento di Ingegneria Civile, Edile-Architettura, Ambientale
4 Research Institute for Mechanics, National Research Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod Russia
5 IMATH - Institut de Mathématiques de Toulon - EA 2134
6 Institute of Mechanics and Printing
7 Department of Experimental Physiology and Pathophysiology Medical University of WarsawWarsaw Poland
8 Department of Mechanical Engineering [Berkeley]
9 UNISS - Università degli Studi di Sassari = University of Sassari [Sassari]
10 ROMA TRE - Università degli Studi Roma Tre = Roma Tre University
11 LGCB - Laboratoire Génie Civil et Bâtiment
12 Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland
13 SFEDU - Southern Federal University [Rostov-on-Don]
14 KU - University of Kansas [Lawrence]
15 International Telematic University Uninettuno
16 Unict - Università degli studi di Catania = University of Catania
17 Dipartimento di Ingegneria Civile, Ambientale e ArchitetturaUniversità degli studi di Cagliari, Cagliari, Italy
18 LaSIE - Laboratoire des Sciences de l'Ingénieur pour l'Environnement - UMR 7356
19 Research Institute for Mechanics, National Research Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod Russia
20 LEMTA - Laboratoire d'Energétique et Mécanique Théorique et Appliquée
21 Faculty of Mechanics, Berlin University of Technology, Berlin, Germany
22 Laboratoire des Sciences des Procédés et des Matériaux, Université Paris 13, Villetaneuse, France
23 Fraunhofer EMI - Fraunhofer Institute for High-Speed Dynamics - Ernst-Mach-Institut
24 LMT - Laboratoire de Mécanique et Technologie
Claude Boutin
Jan Neggers

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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Dates and versions

hal-01829943 , version 1 (22-07-2018)

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Cite

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, 2019, 31 (4), pp.851-884. ⟨10.1007/s00161-018-0689-8⟩. ⟨hal-01829943⟩
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