Metamaterials are man-made materials engineered to possess certain desired and often counterintuitive properties. It is well-known that elastic metamaterials may exhibit unusual bulk elastic properties when subject to dynamic loads at certain frequencies, such as negative Poisson’s ratio, negative modulus, and/or negative mass density. This paper focuses on the modeling of a one-dimensional micropolar-type elastic metamaterial subject to transient dynamic loading. The metamaterial consists of unit cells that support both translational and rotational motion and can be modeled as a micropolar-type continuum. Interestingly, the equations governing the dynamics of the new micropolar-type continuum possess remarkable similitude with those governing the transient response of an elastic bar with elastic supports. The resulting governing equation is solved using the Fourier transform technique. The transient dynamic response of the metamaterial subject to an axial impact is then studied based on both the developed continuum model and the original discrete model. Finite element analysis of the equivalent bar model is also conducted. The results from the developed continuum model is compared with the discrete model and the finite element analysis to evaluate its suitability. This work presents a novel micropolar-type model for a specific metamaterial and investigates its transient response using both continuum modeling and discrete unit cell modeling. The results indicate that the micropolar-type model can accurately capture the transient behavior of the propagation of the strain pulse in the metamaterial
Elastic metamaterials are man-made materials engineered with the purpose of inducing atypical bulk elastic properties. To model a type of elastic metamaterial with local rotational effects, a new two-dimensional continuum model which incorporates local rotation as a scalar field superposed on the translational displacement fields is utilized. This paper provides a comprehensive study of surface wave propagation in this new continuous medium. Unlike the classical Rayleigh wave, the surface wave in this new medium is dispersive. An explicit dispersion relation is obtained, and a closed-form solution of the dispersion curve is derived. The dispersion relation is then used to evaluate the general behaviour of the surface wave. It is found that even for the cases where the effect of local rotation is relatively weak, the surface wave still clearly shows dispersion. The phase velocity of the surface wave falls mostly between the classical Rayleigh wave and the shear wave, especially for cases where the effect of local rotation is weak. In addition to the classical Rayleigh wave, there exists another surface wave which possesses a wavespeed depending only on local rotational parameters. It was also found that particles residing on the free surface of the material move in an elliptical fashion similar to that of classical Rayleigh wave propagation.
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