Topology Design of Soft Phononic Crystals for Tunable Band Gaps: A Deep Learning Approach

The phononic crystals composed of soft materials have received extensive attention owing to the extraordinary behavior when undergoing large deformations, making it possible to provide tunable band gaps actively. However, the inverse designs of them mainly rely on the gradient-driven or gradient-free optimization schemes, which require sensitivity analysis or cause time-consuming, lacking intelligence and flexibility. To this end, a deep learning-based framework composed of a conditional variational autoencoder and multilayer perceptron is proposed to discover the mapping relation from the band gaps to the topology layout applied with prestress. The nonlinear superelastic neo-Hookean model is employed to describe the constitutive characteristics, based on which the band structures are obtained via the transfer matrix method accompanied with Bloch theory. The results show that the proposed data-driven approach can efficiently and rapidly generate multiple candidates applied with predicted prestress. The band gaps are in accord with each other and also consistent with the prescribed targets, verifying the accuracy and flexibility simultaneously. Furthermore, based on the generalization performance, the design space is deeply exploited to obtain desired soft structures whose stop bands are characterized by wider bandwidth, lower location, and enhanced wave attenuation performance.