Modeling and Analysis of the Transient Behavior of an Elastic Metamaterial as a Generalized Cosserat Continuum

Abstract

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