BDH-NN: Bi-Directional Homogenization method using Neural Networks for the mechanical metamaterial design

Metamaterials are artificial composites with periodically arranged microstructural units, engineered to manifest material properties not typically found in nature. This paper presents the Bi-Directional Homogenization method using Neural Networks (BDH-NN) for mechanical metamaterial design. The BDH-NN framework encompasses a homogenization process from the microscale to the mesoscale and an inverse homogenization (IH) process from the macroscale to the mesoscale. Utilizing the level set method, the BDH-NN framework implicitly represents microstructure prototypes and generates diverse heterogeneous microstructures by blending multiple prototype compositions. Subsequently, a dataset is created, and a precise surrogate model is established using neural networks to link the control parameters of microstructures with their mechanical properties, significantly reducing the computational burden for microstructural property analysis. Furthermore, BDH-NN employs neural networks for reparameterization as optimizers, performs sensitivity analysis through automatic differentiation (AD) techniques, and optimizes neural network parameters using backpropagation, thereby streamlining the sensitivity analysis process. Finally, the effectiveness and stability of the BDH-NN method in metamaterial design are demonstrated through the design of various negative Poisson's ratio (NPR) metamaterials.