The development of smart metamaterials has brought changes to human society, and various new products based on smart metamaterials are emerging endlessly. In recent years, smart electromagnetic metamaterials, smart acoustic metamaterials, smart mechanical metamaterials, smart thermal metamaterials and machine learning have attracted much attention in metamaterials. These fields share similar theories, such as multiphysics coupling fields, novel artificial cells and programmability. Through theoretical and technical research, smart metamaterials will show exquisite applications in many fields, such as antenna and optical communication systems, microwave imaging, acoustic stealth, thermal camouflage, etc. In particular, the characteristics of the personalized microstructure design of smart metamaterials perfectly match the characteristics of 3D printing. The combination of them leads the development of metamaterials, which are undoubtedly of great value. In this paper, focusing on the representative key technologies, we review the development history, main research directions and latest applications of smart metamaterials. Finally, the possible development direction of metamaterials is predicted.

Based on Mindlin’s theory and the plane wave expansion method, the formulas are proposed for the governing equations and dispersion relations of bending waves in piezoelectric phononic crystal plates. The shear correction factors can be obtained through transcendental equations based on forced vibrations of the plate. The plates are made of inclusions of different shapes and lattice types, finding that the inclusion shape dramatically affects the mid-to-high frequency band gaps. Piezoelectric materials exhibit distinct eigenfrequencies at the high-symmetry point Γ at low frequencies. Thickness affects the band gap width differently than in two-dimensional models, and cuts influence band gap width significantly.

The study uses complex variable functions and conformal mapping to investigate the scattering and dynamic stress concentration phenomena of SH waves in non-circular opening magnetic–elastic materials. Elastic dynamics and piezomagnetic equations are employed to derive expressions for the scattered wave intensity and dynamic stress concentration coefficient around non-circular openings. Special attention is devoted to elliptical openings, where different incident angles and dimensionless wave numbers exhibit varying effects on the dynamic stress concentration coefficients. The numerical results indicate a positive correlation between the dynamic stress concentration coefficient and the illumination region of elliptical openings, with low wave numbers exerting a more significant influence. These findings provide a valuable theoretical foundation for studying fatigue mechanics in piezomagnetic materials. Therefore, to enhance the performance and reliability of piezomagnetic materials, it is imperative to conduct elastic dynamic analysis of non-circular defects in low-frequency environments.

Based on the theory of magnetoacoustic coupled dynamics, the purpose of this paper is to evaluate the dynamic stress concentration near an elliptical opening in exponential-gradient piezomagnetic materials under the action of antiplane shear waves. By the wave function expansion, the solutions for the acoustic wave fields and magnetic fields can be obtained. Stress analysis is performed by the complex function method and the conformal mapping method, which are used to solve the boundary conditions problem, and is used to express the dynamic stress concentration coefficient (DSCC) theoretically. As cases, numerical results of DSCCs are plotted and discussed with different incident wave numbers and material parameters by numerical simulation. Compared with circular openings, elliptical openings are widely used in material processing techniques and are more difficult to solve. Numerical results show that the dynamic stress concentration coefficient at the elliptical opening is strongly dependent on various parameters, which indicates that the elliptical opening is more likely to cause crack and damage to exponential-gradient piezomagnetic materials.

The present study aims to investigate the transient response of stress concentration around a circular opening. The study focuses on the composition of the shockwave, which consists of SH waves of multiple frequencies. The wave equation, expressed by the displacement function, is transformed into the Helmholtz equation through the Fourier transform method. The spectral function can be obtained by employing analytic continuation and Fourier transform of the incident wave field. An analytical expression for the dynamic stress around the aperture can be derived using the wave function expansion method and by considering the boundary conditions. The influence of the aperture on the transient response is discussed based on the distribution of the dynamic stress concentration coefficient and stress peak coefficient under different aperture sizes. The results show that the peak of the dynamic stress concentration coefficient changes with the aperture. In contrast, the stress peak coefficient is primarily concentrated in the early stages of the transient response. Furthermore, it is observed that larger radii can induce alternating stress in the material, which may lead to fatigue failure. This strategy provides a solution for addressing similar challenges.

This paper investigated the reflection of plane waves at the interface of dipolar gradient elastic solids under the control of an external magnetic field. This study focused on the increasing influence of the microstructural effect as the incident wavelength approaches the characteristic length of the microstructure or at higher frequencies. Initially, the dispersion equation for the propagation of elastic waves was derived from the dipole strain gradient theory and Maxwell’s electromagnetic theory. Subsequently, the amplitude ratios of various reflected waves to incident P-waves and incident SV-waves were calculated based on the interface conditions. Finally, the numerical results were used to discuss the impact of the external magnetic field and microstructural characteristic length on the propagation of the reflected wave. It was observed that the microstructural effect generated new wave modes and introduced dispersion characteristics into the elastic waves. Conversely, the external magnetic field primarily influences the amplitude of the elastic wave propagation via the Lorentz force without creating new wave modes or affecting the dispersion properties of the elastic wave in the dipolar gradient elastic solid.