# Geometric construction of auxetic metamaterials

1 MAVERICK - Models and Algorithms for Visualization and Rendering
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
2 ANIMA - Authoring and directing story worlds
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : This paper is devoted to a category of metamaterials called auxetics, identified by their negative Poisson's ratio. Our work consists in exploring geometrical strategies to generate irregular auxetic structures. More precisely we seek to reduce the Poisson's ratio $\nu$, by pruning an irregular network based solely on geometric criteria. We introduce a strategy combining a pure geometric pruning algorithm followed by a physics-based testing phase to determine the resulting Poisson's ratio of our structures. We propose an algorithm that generates sets of irregular auxetic networks. Our contributions include geometrical characterization of auxetic networks, development of a pruning strategy, generation of auxetic networks with low Poisson's ratio, as well as validation of our approach. We provide statistical validation of our approach on large sets of irregular networks, and we additionally laser-cut auxetic networks in sheets of rubber. The findings reported here show that it is possible to reduce the Poisson's ratio by geometric pruning, and that we can generate irregular auxetic networks at lower processing times than a physics-based approach.
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Journal articles
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https://hal.inria.fr/hal-03145852
Contributor : Georges-Pierre Bonneau Connect in order to contact the contributor
Submitted on : Thursday, February 18, 2021 - 4:19:58 PM
Last modification on : Friday, November 5, 2021 - 2:58:02 PM

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### Citation

Georges-Pierre Bonneau, Stefanie Hahmann, Johana Marku. Geometric construction of auxetic metamaterials. Computer Graphics Forum, Wiley, 2021, (Eurographics 2021), 40 (2), pp.291-303. ⟨10.1111/cgf.142633⟩. ⟨hal-03145852⟩

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