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.

翻译：在机械超材料这一新兴领域中，使用周期性晶格结构作为主要构成要素相对常见。然而，在这些结构中选择非周期性晶格在失效（例如屈曲或断裂）方面具有独特优势，因为避免重复图案可防止整体失效，转而发生局部失效，从而有利于延迟结构坍塌。因此，有必要开发能够根据不同一般特征高效计算晶格等效力学性能的模型，同时应对呈现不同尺寸拓扑（或图）的挑战。本文中，我们开发了一种深度学习模型，以有效预测线弹性晶格的能量等效力学性能。通过将晶格视为图并在其上定义材料与几何特征，我们证明图神经网络相比密集全连接策略能提供更准确的预测，这得益于通过图表示引入的几何诱导偏差，更贴近直接问题中求解的力学基本平衡定律。利用该代理模型对大量晶格进行高效正向评估，可实现逆向问题求解，即获得具有特定规定行为的结构，这最终适用于多尺度结构优化问题。