Five Kinds Of Micro-structures Of Pentamode Metamaterials And Their Performance Analysis

With the rapid development of the aerospace and electronics industry, composite materials and their structures are widely applied. As a new field of materials science, metamaterials have attracted a lot of attention due to the fact that the material behavior such as negative refractive index, super-absorbent and negative poisson’s ratio etc., cannot be found in natural world. In essence pentamode materials are new artificial metamaterials simply called as PM materials. Although PM materials belong to elastic materials, the features of possessing only one load-carrying mode under static forces situation, transmiting only one kind of elastic waves under dynamic excitation because of their special micro-structures, which means their matrix eigenvalues of equivalent elastic modulus only have one non-zero value, makes them different.For all these new materials, the material behaviors determine whether they can be widely applied. The representative volume element (RVE) method and the asymptotic homogenization (AH) method are employed to predict equivalent properties of the periodic materials. The RVE method is easy to carry out because of clear physical model; however, it can only provide approximate prediction of effective properties without rigorous mathematical foundation. In the contrast, based on the rigorous mathematical foundation of perturbation theory, the AH method has mature algorithm on forecasting effective properties of periodic materials with microstructures. The only weakness is the complex calculation process affect the extensive application of the method. Based on ANSYS, this thesis accomplishes the finite element solutions of the RVE and AH method respectively by APDL programing in order to predict the equivalent properties of materials.A variety of micro-structures are put forward in this thesis. Five kinds of PM materials are found by calculating their matrix eigenvalues of the truss model. The calculation results of the simulation comparison show that these five kinds of PM materials can be classified into two groups:one of them transmits elastic expansion waves while the other one transmits elastic shear waves. The RVE method and the AH method are employed to calculate the equivalent elastic properties respectively. Considering time and calculation accuracy, the RVE method is more suitable for analyzing the effective elastic moduli of PM materials. In general, it is proper to analyze the PM materials by two steps, the truss model to judge whether the effective elastic modulus satisfy the definition of PM materials should be analyzed firstly; and then the single entity truss model should be analyzed to find the relation between parameters of the micro-structures and equivalent elastic modulus and to complete material design.