Hybrid intelligent framework for designing band gap-rich 2D metamaterials

An artificial intelligence machine learning-based design framework is proposed to design lattice-based metamaterials with hexagonal symmetry that deliver wide band gaps at user-desired frequency ranges between 0 and 1000 kHz. The design approach starts by selecting a traditional, easy-to-manufacture parent lattice-based material that does not necessarily exhibit wide or functional band gaps. Subsequently, the parent lattice is transformed into a band-gap-rich lattice by superposing periodic triangular-shaped perturbations (i.e., zigzag-sine-based curvatures) with controllable frequencies and magnitudes on its ligaments. Finally, the frequency and magnitude parameters needed to deliver a specific band gap between 0 and 1000 kHz are determined using a hybrid intelligent framework, developed based on an Adaptive Neuro-Fuzzy Inference Systems (ANFIS). The ANFIS network integrates fuzzy logic expert models and artificial neural networks’ machine learning capabilities. Such a hybrid network is known for its ability to model strongly nonlinear and complex data. The data used in training the ANFIS models is generated using parametric finite element-based simulations where band gaps corresponding to a wide range of perturbation frequencies and magnitudes are computationally determined. The parametric study showed a nonlinear and complex topology-band gap characteristic relation; however, the Adaptive Neuro-Fuzzy Inference System (ANFIS) proved capable of modeling the observed complex topology-band gap behavior efficiently. The accuracy of the ANFIS models exceeded 99 % in several design ranges (i.e., perturbation parameters ranges). These were designated as high-accuracy design regions and were highlighted in the proposed design approach. Using multiple case studies with different band gap requirements, the ANFIS-based design framework proved effective in delivering customized lattice-based metamaterials with user-defined band gap frequencies.