Normal mode analysis of mechanical metamaterials

Abstract

Mechanical meta-materials are the materials or structures which do not exist in nature but are artificially created to generate novel mechanical properties, such as negative Poisson’s ratio, large specific strength, negative elastic modulus, etc. On the other hand, the normal mode analysis is the method to identify the vibration modes and to understand the dynamical properties of materials. In this study, we applied the normal mode analysis to mechanical metamaterials exhibiting negative or positive Poisson’s ratio by using numerical diagonalization. As a result, we found that there exists one floppy (zero frequency) mode as well as conventional acoustic modes at smaller frequencies and optical modes at large frequencies. We also found that self-collapse behavior occurs when the uni-axial stretching is applied onto the material.