Feasibility Analysis of Dispersion Curves in Calculating Equivalent Parameters of Honeycomb Pentamode Metamaterials

Abstract

Honeycomb material is one of the basic structures of two-dimensional pentamode materials. Dispersion curve, as a common method for analyzing crystal properties, is widely used in the study of pentamode materials. It is necessary to study the probability that using dispersion curves to calculate the equivalent parameters of honeycomb materials. In this paper, compared with the improved Gibson formula, the accuracy of the equivalent parameters calculated by dispersion curves of honeycomb pentamode materials with different structures is studied. The study found that the calculation error of dispersion curve for the homogeneous material equivalent parameters is lower than 1%; The error for anisopathic honeycomb pentamode materials is 10% to 20%, and it decreases with the ratio of wall thickness to edge length; Calculating anisotropic honeycomb pentamode material equivalent parameters by dispersion curves is inapplicable. But dispersion curves can be used to predict the degree of anisotropy of honeycomb materials, such as the ratio of volume modulus in the X and Y directions, with less than 5% errors.