Automated lattice embedding and transitioning with application to multi-lattice topology optimization

Structures composed of spatially-varying architected materials have great potential for targeted mechanical and/or multifunctional behavior, but lack of structural integrity at the interfaces between different architecture geometries can degrade the expected performance. While smooth transitions between functionally-defined architected materials can be designed easily using mathematical interpolation, a robust transitioning scheme is less apparent for architectures without a simple mathematical description. Here we focus on periodic, strut-based lattices exhibiting cubic symmetry of their nodes and propose an algorithm that automates the design of smoothly-varying transitions between any finite set of these lattices embedded in a macroscale structure. The algorithm takes in lattice existence and relative density fields indicating which lattice and associated relative density exists at each point in the macroscale structure, and an ordered set of m key lattices to be embedded. We define a transitional skeleton (i.e., nodes and connectivity) that encapsulates all m key lattices via a continuous morphing between different nodal configurations, and use it to spatially transition between the different lattice geometries. Material is added after manipulating the skeletons according to the given relative density distribution. We explain details of the algorithm in 2D using a multi-lattice design obtained from topology optimization and show the flexibility and robustness of the algorithm by generating a lattice-embedded rendering of The Starry Night by Vincent Van Gogh. In 3D, we explore the effect of the transition radius and demonstrate manufacturability of the spatially-varying lattice-embedded structures by 3D printing a multi-lattice canopy obtained from topology optimization.