Machine learning assisted approach to design lattice materials with prescribed band gap characteristics

Abstract

An artificial intelligence-assisted design framework for designing lattice materials with prescribed band gap characteristics in the range of 0–1000 kHz is proposed. The framework utilizes the double-walled hexagonal lattice which exhibits limited and narrow band gaps. The band gap characteristics of the double-walled hexagonal lattice are enhanced by increasing their number and width by imposing sinusoidal periodic perturbations on the lattice's cell walls. The imposed perturbations are controlled through their frequency and amplitude. A wide range of frequencies and amplitudes are considered to realize perturbed lattices with band gaps that cover the entire frequency range between 0 and 1000 kHz. The band gaps of each perturbed lattice over a range of porosities are obtained using finite element analysis. Machine learning, namely parallel multilayer neural networks, is used to model the relationship between porosity, perturbation amplitude and frequency on one side and band gap characteristics on the other. Results show that the proposed neural networks can predict the band gap characteristics with an average accuracy that exceeds 80%. The proposed neural networks are used to invert the topology-band gap relationship and determine the lattice parameters needed to provide a prescribed band gap characteristic. Based on the achieved accuracy of the proposed neural networks, the neural networks are used in the design framework to identify a few candidate solutions which are subsequently filtered using finite element analysis. The proposed framework promises to significantly minimize the time-consuming iterations associated with designing lattices with prescribed band gap behavior. Finally, a case study is used to demonstrate the application of the proposed framework to design a lattice material with a band gap between 575 and 625 kHz.