Department of Mechanics: Seminar: Schwarz and Felsch 2023

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9 May 2023, 15:00-16:00 CET, Room B-366 @ Thákurova 7, 166 29 Prague 6

Mechanical metamaterials switch auxeticity during compression

David Schwarz (Cluster of Excellence livMatS @ FIT – Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, D-79110 Freiburg, Germany)



Auxetic metamaterials exhibit a fascinating trait under mechanical load. While conventional materials expand, auxetics shrink laterally during compression. Such behavior associated with negative Poisson’s ratio is achieved thanks to the rational geometrical and topological organization of the metamaterial and can therefore be tuned depending on a specific application. Traditional auxetic metamaterials continuously shrink in all directions with an increase in compressive load. Here we propose to analyze the sinusoidal lattice capable of both shrinking and expanding amid mechanical loading, depending on the applied force value. The geometrical change from straight connections (e.g., as in reentrant lattices) to curvy beams (sinusoidal lattice) results in a strain and load-dependent sign of the Poisson’s ratio. Meaning, under compression, negative transverse strain occurs only before the point of self-contact in the metamaterial. Thereafter the observed Poisson’s ratio is positive, thus creating a toggle point for the metamaterial auxeticity. The unit cell geometry determines the critical compressive strain for such a switch. Here we use finite element simulations to characterize this not yet studied phenomenon. We perform mechanical testing on additively manufactured specimens to back numerical predictions. Ultimately, this observed phenomenon can be harnessed in the design of mechanical switches or as an if-then condition for minimum exerted compressive force. With the developed framework, similar metamaterials can be designed with their mechanical behavior tailored to novel use cases.

Generative design of curved beam metamaterials

Gerrit Felsch (Cluster of Excellence livMatS @ FIT – Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, D-79110 Freiburg, Germany)



Materials whose properties are determined by their internal architecture in addition to composition — so-called metamaterials — have emerged as a growing field of study over the past decades [1]. These materials are usually assembled from periodically arranged unit cells. While the mechanical properties of these materials can be predicted though finite element simulations, many applications also require to identify architectures with specific target properties [2]. To solve this inverse problem, we introduce a deep-learning framework for generating metamaterials with desired properties. By supplying the generative model with a guide structure in addition to the target properties, we are not only able to generate a large number of alternative architectures with the same properties, but also to express preference for a specific shape. To demonstrate the capabilities of this approach we applied it to generate unit cells for a new class of reentrant-hexagonal metamaterials based on curved beams. Reentrant-hexagonal metamaterials are well known to be able to exhibit a wide range of different material properties based on their architecture. This includes properties tied to unusual behavior such as a negative Poisson’s ratio [3], which can be tuned by adjusting the angles between beams. However, changing the angles also influences the overall dimensions of the unit cells. By replacing straight beams with curved ones, it is possible to control the Poisson’s ratio of reentrant-hexagonal metamaterials without affecting the overall dimensions. We show that our deep-learning framework is able to accurately generate unit cells fitting specific properties for curved beam metamaterials.


[1] K. Bertoldi, V. Vitelli, J. Christensen, and M. van Hecke, “Flexible mechanical metamaterials”, Nature Reviews Materials, vol. 2, p. 17066, 2017.

[2] J. U. Surjadi, L. Gao, H. Du, X. Li, X. Xiong, N. X. Fang, and Y. Lu, “Mechanical metamaterials and their engineering applications, ”Advanced Engineering Materials, vol. 21, no. 3, p. 1800864, 2019.

[3] L. J. Gibson and M. F. Ashby. Cellular solids: Structure & properties. Pergamon Press, 1988.

Acknowledgements: This activity was supported by the Ministry of Education, Youth, and Sports, program Operational Programme Research, Development, and Education, Project OPVVV CAAS CZ.02.1.01/0.0/0.0/16_019/0000778.