The Novel Implementation Of Asymptotic Homogenization To Predict The Effective Properties Of Periodic Materials Based On Commercial FEA Software

Periodic composite materials have the advantages of adjustable property and could realize the function of high specific strength, high specific gravity, zero thermal expansion, negative passion's ratio, etc. Which could not be realized by none of the component materials. Composite materials usually been used in extremely working condition, such as the thermal protection systems of hypersonic vehicles, the working space near the engine combustors. While the accurate prediction of the effective properties (thermal conductivity, thermal expansion coefficient) for the periodic materials are the foundation of its application. For simple model, analytical formula has been used to describe the behavior of the materials. For complicated model, numerical methods are usually been used to solve the problem, such as representative volume element (RVE) method, asymptotic homogenization (AH) method. RVE method is the most popular method for its simplicity, while the result of RVE method is not persuasive because it is not based on rigorous mathematical theory. The AH method is based on rigorous mathematical theory and the results are accuracy. While the AH method could not be implied by general finite element analysis (FEA) software, and the code was just been used by small group. This paper developed new method which could predict the effective thermal conductivity, coefficient of thermal expansion, the thermal temperature field of periodic materials considering radiation based on commercial FEA software. The new method is as simple as RVE method while the results are as accuracy as traditional AH method. The content and conclusions of this paper are listed as follows:(1) A novel implementation algorithm of AH method for predicting effective thermal conductivity (ETC) of periodic composite materials. Thermal conductivity is the key parameter to quantify the thermal behavior of materials, and it's significant to predict the ETC of periodic composite materials accurately. This paper developed a new method to predict the ETC periodic composite materials based on the commercial FEA software, and the process of calculation was listed in detail. Several numerical examples have been presented to illustrate the effectiveness of the proposed approach. The results proved that the new method could be used for unit cell with arbitrary complex geometry and materials. Meanwhile, the new method could use all element types provided by the FEA software and reduce the amount of computation by using reasonable element type.(2) A novel implementation algorithm of AH method for predicting the temperature field of heat transfer considering radiation. The influence of radiation must be considered with the high temperature environment, while the second-order AH method could predict the temperature field of hollow material considering radiation of internal boundary. This paper developed a new method to predict the temperature field of hollow material considering radiation of internal boundary based on commercial FEA software. The effectiveness of the new method has been proved by comparing with the results of FEA method. The results indicate that the first-order temperature field without radiation calculated by new method are as accuracy as the FEA. While the second-order temperature field considering radiation has the error of 2.9% compared with the FEA results. The theory of the new method needs further correction.(3) A novel implementation algorithm of asymptotic homogenization for predicting effective coefficient of thermal expansion (CTE) of periodic composite materials. For those composite materials which working in thermal surrounding, the accurate prediction of CTE of periodic composite materials could help in alleviating the thermal stress and the optimization of the structural design. This paper developed a new method to predict the CTE of periodic composite materials based on the commercial FEA software, and the process of calculation was listed in detail. The new algorithm can be executed easily using commercial FEA software as black box. We can use all kinds of element types available and their combinations in FEA software to discretize a unit cell of arbitrarily complicated structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.