Investigation On The Feasibility Of The Analysis Of Wave Characteristics Of Gradient Matrix Materials By Homogeneous Effective Material Parameters

As a new non-homogeneous lattice material, functionally gradient lattice material, compared to homogeneous lattice material, has better mechanical properties. Functionally gradient lattice material can be developed for lightweight, high strength, impact resistance and versatility structure, which have wide and promising applications in fields of aviation, aerospace, automotive and shipbuilding, etc. Therefore, the investigation on dynamic mechanical properties of the material is critical for the development and application of new material.Generally, the dynamic parameters of lattice materials in the low frequency range are determined or calculated by using the quasi-static analysis method, which application conditions in non-homogeneous matrix materials not only involve in the frequency and amplitude of propagating waves in materials but also the gradient index of materials. Aiming at the problem, functional gradient honeycomb materials are taken as examples to investigate the impact of gradient index of materials on the errors of the gradient material dynamic parameters, which are calculated by using the quasi-static analysis method. The main work of this paper is as follows.Firstly, the two methods, the representative volume element method and the asymptotic homogenization method, are introduced to calculate the equivalent properties of the composites. And the finite element implementation program of the two methods was compiled respectively. 2-D and 3-D numerical examples are used to test the validity of the two methods and verify the superiority of the asymptotic homogenization method. Secondly, the design methods for honeycomb materials with gradient macroscopic properties are investigated by changing the material composition or the structure size in the unit cells. And the relationship charts between the effective parameters of the unit cell, calculated by asymptotic homogenization method, and its material composition or structure size are obtained.Thirdly, on the basis of these data, the computing models of gradient honeycomb materials are constructed, and the macro effective mechanical parameters of the materials are evaluated by applying the asymptotic homogenization method, then according to these effective material parameters, the mean velocity and the transmission coefficient of the elastic wave propagating in a slab of gradient honeycomb materials is solved. Furthermore, the mean velocity and the transmission coefficient are compared with the resulted data obtained by means of the full displacement field analysis with FEM The comparative studies show, the errors between the dynamic material parameters predicted by quasi-static analysis method and those gotten by the full field dynamic analysis method do not exceed 5% if the gradient index of gradient matrix materials belongs to a certain range.Finally, several examples of gradient honeycomb materials are constructed within the scope of the argument gradient index, and their elastic wave velocity in different directions are analyzed by using the quasi-static analysis method and the full field dynamic analysis method, separately. The numerical results further verify that it is feasible to analyze the wave characteristics of gradient matrix materials by homogeneous effective material parameters under the application condition of the gradient index of materials.