Periodic composite function-based approach for designing architected materials with programmable Poisson's ratios

Advances in additive manufacturing enable fabrication of architected materials composed of microstructures with extreme mechanical properties. In the design of such architected materials, the parameterization of microstructures determines not just the computational cost, but also connectivity between adjacent microstructures. In this paper, we propose a periodic composite function(PCF)-based approach for designing microstructures. The shape of the microstructures is characterized by the value of the periodic composite functions. The proposed method can program microstructures with both positive and negative Poisson's ratios by a small number of parameters. Furthermore, due to its implicit representation, the proposed method allows for continuously tiling of microstructures with different mechanical properties. Explicit geometric features of the PCF-based microstructures are extracted, and the condition to maintain connectivity between adjacent microstructures is derived. Based on the proposed approach, multiple groups of 2D and 3D microstructures with Poisson's ratios ranging from negative to positive are presented. Combining with a deep neural network(DNN) based surrogate model to predict macroscopic material properties of the microstructures, the proposed method is applied to the design of architected materials for elastic deformation control. Numerical examples on both microstructure representation and architected materials design are presented to demonstrate the efficacy of the proposed approach.