Multi-scale multi-material topology optimization for lattice structures with interface connective microstructures

This article presents a novel concurrent multi-scale multi-material topology optimization method for designing lattice structures composed of solid microstructure and multiple lattice microstructures while the connectivity of dissimilar lattice microstructures is assured. At the macroscale, microstructures with different predefined volume fractions are treated as different materials. Lattice microstructure can be well connected with solid microstructure. However, the disconnection between different lattice microstructures would lead to load transition problems, impeding the practical applications of lattice structures. To address this issue, a new controllable interface identification method based on the pseudo-cost domain method is proposed. Identified interface domains between different lattice microstructures are filled with solid microstructures. A modified material interpolation framework is developed with the discrete material optimization method to achieve optimal topology of the macrostructure and the distribution of microstructures. This methodology is formulated as a compliance minimization problem. Numerical examples are provided to demonstrate the effectiveness of the proposed method.