Achieving directional propagation of elastic waves via topology optimization

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.

Automated discovery of reprogrammable nonlinear dynamic metamaterials

Harnessing the rich nonlinear dynamics of highly deformable materials has the potential to unlock the next generation of functional smart materials and devices. However, unlocking such potential requires effective strategies to spatially engineer material architectures within the nonlinear dynamic regime. Here we introduce an inverse-design framework to discover flexible mechanical metamaterials with a target nonlinear dynamic response. The desired dynamic task is encoded via optimal tuning of the full-scale metamaterial geometry through an inverse-design approach powered by a fully differentiable simulation environment. By deploying such a strategy, mechanical metamaterials are tailored for energy focusing, energy splitting, dynamic protection and nonlinear motion conversion. Furthermore, our design framework can be expanded to automatically discover reprogrammable architectures capable of switching between different dynamic tasks. For instance, we encode two strongly competing tasks-energy focusing and dynamic protection-within a single architecture, using static precompression to switch between these behaviours. The discovered designs are physically realized and experimentally tested, demonstrating the robustness of the engineered tasks. Our approach opens an untapped avenue towards designer materials with tailored robotic-like reprogrammable functionalities.

Optimal Designs of Phononic Crystal Microstructures Considering Point and Line Defects

In this paper, a two-stage optimization strategy for designing defective unit cells of phononic crystal (PnC) to explore the localization and waveguide states for target frequencies is proposed. In the optimization model, the PnC microstructures are parametrically described by a series of hyperelliptic curves, and the optimal designs can be obtained by systematically changing the designable parameters of hyperellipse. The optimization contains two individual processes. We obtain the configurations of a perfect unit cell for different orders of band gap maximization. Subsequently, by taking advantage of the supercell technique, the defective unit cells are designed based on the unit cell configuration for different orders of band gap maximization. The finite element models show the localization and waveguide phenomenon for target frequencies and validate the effectiveness of the optimal designs numerically.

Photonic crystal topological design for polarized and polarization-independent band gaps by gradient-free topology optimization

Photonic crystals can be adopted to control light propagation due to their superior band gap feature. It is well known the band gap feature of photonic crystals depends significantly on the topological design of the lattices, which is rather challenging due to the highly nonlinear objective function and multiple local minima feature of such design problems. To this end, this paper proposed a new band-gap topology optimization framework for photonic crystals considering different electromagnetic wave polarization modes. Based on the material-field series-expansion (MFSE) model and the dielectric permittivity interpolation scheme, the lattice topologies are represented by using a small number of design variables. Then, a sequential Kriging-based optimization algorithm, which shows strong global search capability and requires no sensitivity information, is employed to solve the band gap design problem as a series of sub-optimization problems with adaptive-adjusting design spaces. Numerical examples demonstrated the effectiveness of the proposed gradient-free method to maximize the band gap for transverse magnetic field (TM), transverse electric field (TE), and complete modes. Compared with previously reported designs, the present results exhibit less dependency on the guess of the initial design, larger band gaps and some interesting topology configurations.

Contact Nonlinear Acoustic Diode

Nonlinear implementations of acoustic diodes are inherently nonreciprocal and have received continuous attention from the beginning of the research boom for acoustic diodes. However, all the reported nonlinear schemes usually have the shortcomings such as low transmission ratio, action threshold, lack of stability and cumbersome setups. In the present design, we take advantage of extraordinarily large contact acoustic nonlinearity which is several orders of magnitude stronger than material nonlinearity. It is theoretically found that the spectra of the transmitted wave depend on the contact time. It is proven experimentally that the contact nonlinearity can be tamed by adjusting the driving amplitude, the static stress and the elastic constants of the materials. In order to build a compact acoustic diode, a sub-wavelength filter with a sandwich structure is designed. The total length of the acoustic diode is only three eighths of the incident wavelength. The amplitude-dependent behavior of the device exhibits similarities with electronic diodes. A more than 50% transmission ratio is obtained. A robust, stable, compact, highly efficient and solid-state acoustic diode is realized.

Asymmetric transmission of elastic shear vertical waves in solids

In this work, we propose an asymmetric transmission structure (ATS) for elastic shear vertical (SV) waves in solids, which has been relatively unexplored. The ATS is constituted by a metasurface and a phononic crystal (PC) possessing a directional band gap. While the metasurface aims to redirect the incident wave, the PC acts as a directional filter. The metasurface is composed of a stacked array of composite plates with two connecting parts made of different materials. To examine the performance of the designed ATS, full numerical simulations have been conducted. The numerical results indicate that the proposed ATS offered a relatively broad working frequency band and had a one order of magnitude difference in terms of transmission between the positive and negative incidences. Our study provides an alternative method to control elastic SV waves and could benefit applications in various fields, such as Micro-Electro-Mechanical System (MEMS), in which thin plates are frequently used components.

Thermally tunable topological edge states for in-plane bulk waves in solid phononic crystals

The remarkable properties of topological insulators have inspired numerous studies on topological transport for bulk waves, but the demonstrations of topological edge states with tunable frequency are few attempts. Here, we report on the active frequency tunability of topologically protected edge states for in-plane bulk waves by applying a thermal field. We find that the center frequency of topological band gap is shifted down and the band width is enlarged as the temperature increases. Meanwhile, the frequency range of topologically protected edge states is also shifted to low frequency region with the higher temperature. Furthermore, the robust propagation of in-plane bulk waves along a desired path is demonstrated within different frequency bands. The tunable frequency for both topological band gaps and topologically protected edge states achieves the active control of the transport for in-plane bulk waves, which may dramatically facilitate practical applications of novel phononic devices.