Additive manufacturing has revolutionized structural optimization by enhancing component strength and reducing material requirements. One approach used to achieve these improvements is the application of multi-lattice structures, where the macro-scale performance relies on the detailed design of mesostructural lattice elements. Many current approaches to designing such structures use data-driven design to generate multi-lattice transition regions, making use of machine learning models that are informed solely by the geometry of the mesostructures. However, it remains unclear if the integration of mechanical properties into the dataset used to train such machine learning models would be beneficial beyond using geometric data alone. To address this issue, this work implements and evaluates a hybrid geometry/property Variational Autoencoder (VAE) for generating multi-lattice transition regions. In our study, we found that hybrid VAEs demonstrate enhanced performance in maintaining stiffness continuity through transition regions, indicating their suitability for design tasks requiring smooth mechanical properties.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modeling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc. A relatively new class of materials, architected (meta-)materials, emerged in the last century. As a subclass of architected materials, lattices are a collection of struts (edges) which are connected at nodes. See Figure 1a below and Figure 5 in the Appendix. Lattices are especially mechanically efficient, offering a very high specific stiffness (stiffness divided by density). For instance, it is possible to make materials with the density of water and the strength of steel.

For natural frequency optimization of engineering structures, cellular composites have been shown to possess an edge over solid. However, existing multiscale design methods for cellular composites are either computationally exhaustive or confined to a single class of microstructures. In this paper, we propose a data-driven topology optimization (TO) approach to enable the multiscale design of cellular structures with various choices of microstructure classes. The key component is a newly proposed latent-variable Gaussian process (LVGP) model through which different classes of microstructures are mapped into a low-dimensional continuous latent space. It provides an interpretable distance metric between classes and captures their effects on the homogenized stiffness tensors. By introducing latent vectors as design variables, a differentiable transition of stiffness matrix between classes can be easily achieved with an analytical gradient. After integrating LVGP with the density-based TO, an efficient data-driven cellular composite optimization process is developed to enable concurrent exploration of microstructure concepts and the associated volume fractions for natural frequency optimization. Examples reveal that the proposed cellular designs with multiclass microstructures achieve higher natural frequencies than both single-scale and single-class designs. This framework can be easily extended to other multi-scale TO problems, such as thermal compliance and dynamic response optimization.