Graph Neural Networks for Arbitrary Auxetic Metamaterials
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ABSTRACT Metamaterials are materials and structures designed to have specific properties, such as better energy absorption or dissipation, low density or high thermal insulation. Within this family, auxetic metamaterials have a negative Poisson’s ratio: they laterally expand when subjected to longitudinal tension. This property does not only affect to the mechanical behaviour of the metamaterial, it can also have consequences on thermal or magnetic response [1]. Traditionally, auxetic metamaterials have been designed based on theoretical models of unit cells and personal experience. To create new auxetic metamaterials with specific properties, inverse engineering can also be used [2]. In both cases, it is necessary to calculate the behaviour of the designed metamaterial, either analytically or through simulation. This research presents a methodology that allows the properties of a metamaterial with arbitrary geometry to be calculated quickly and accurately. To do this, Graph Neural Networks are used which, due to their versatility, can be adapted to different designs, such as re-entrant models, chiral models or completely unstructured structures. The GNN is capable of calculating displacement, strain and stress distributions in the metamaterial and, when subjected to a tensile test, calculating the value of Young's modulus and Poisson's ratio of the sample. REFERENCES [1] Y. Zhang, W. Z. Jiang, J. Dong, X. Ren, “Recent Advances of Auxetic Metamaterials in Smart Materials and Structural Systems”, Adv. Funct. Mater, 35 (2025), 2421746 [2] J.H. Bastek, D.M. Kochmann. “Inverse design of nonlinear mechanical metamaterials via video denoising diffusion models”. Nat Mach Intell 5, 1466–1475 (2023). https://doi.org/10.1038/s42256-023-00762-x
