On the data-driven description of lattice materials mechanics

• Published in: Results in engineering Vol. 22; p. 102235
• Main Authors: Ben-Yelun, Ismael, Irastorza-Valera, Luis, Saucedo-Mora, Luis, Montáns, Francisco Javier, Chinesta, Francisco
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2024; Elsevier
• Subjects: Graph neural networks; Lattice materials; Mechanical metamaterials; Mechanical metamaterials; Graph neural networks; Lattice materials
• ISSN: 2590-1230; 2590-1230
• DOI: 10.1016/j.rineng.2024.102235

In the emerging field of mechanical metamaterials, using periodic lattice structures as a primary ingredient is relatively frequent. However, the choice of aperiodic lattices in these structures presents unique advantages regarding failure, e.g., buckling or fracture, because avoiding repeated patterns prevents global failures, with local failures occurring in turn that can beneficially delay structural collapse. Therefore, it is expedient to develop models for computing efficiently the effective mechanical properties in lattices from different general features while addressing the challenge of presenting topologies (or graphs) of different sizes. In this paper, we develop a deep learning model to predict energetically-equivalent mechanical properties of linear elastic lattices effectively. Considering the lattice as a graph and defining material and geometrical features on such, we show that Graph Neural Networks provide more accurate predictions than a dense, fully connected strategy, thanks to the geometrically induced bias through graph representation, closer to the underlying equilibrium laws from mechanics solved in the direct problem. Leveraging the efficient forward-evaluation of a vast number of lattices using this surrogate enables the inverse problem, i.e., to obtain a structure having prescribed specific behavior, which is ultimately suitable for multiscale structural optimization problems. •We develop surrogate models to predict effective behavior in lattice materials.•Dense neural network derivation with inverse effective area of sliced lattices.•Graph neural networks are accurate given only geometrical and material data.•Fast evaluations of numerous lattices via surrogate ease the inverse problem.•Pareto front selection of the lightest structure given a prescribed behavior.