Data-driven inverse design of the perforated auxetic phononic crystals for elastic wave manipulation

In addition to the distinctive features of tunable Poisson’s ratio from positive to negative and low stress concentration, the perforated auxetic metamaterials by peanut-shaped cuts have exhibited excellent phononic crystal (PNC) behavior as well for elastic wave manipulation. Thus they have attracted much attention in vibration suppression for dynamic applications. However, traditional structural designs of the auxetic PNCs considerably depend on designers’ experience or inspiration to fulfill the desired multi-objective bandgap properties through extensive trial and error. Hence, developing a more efficient and robust inverse design method remains challenging to accelerate the creation of auxetic PNCs and improve their performance. To shorten this gap, a new machine learning (ML) framework consisting of double back propagation neural network (BPNN) modules is developed in this work to produce desired configurations of the auxetic PNCs matching the customized bandgap. The first inverse BPNN module is trained to establish a logical mapping from the bandgap properties to the structural parameters, and then the second forward BPNN module is introduced to give the new property prediction by using the design configurations generated from the former. The error between the new predictions and the desired target properties is minimized through a limited number of iterations to produce the final optimal objective configurations. The results indicate that the perforated auxetic metamaterials behave relatively wide complete bandgap and the present ML model is effective in designing them with specific bandgaps within or beyond the given dataset. The study provides a powerful tool for designing and optimizing the perforated auxetic metamaterials in dynamic environment.