五种五零能模式材料单胞构型及其性能分析
发布时间：2018-09-11 14:43
【摘要】：随着航天事业与电子工业的快速发展,复合材料及其结构在现实生活的方方面面均有应用,超常材料作为材料科学的新兴领域吸引了大量学者的关注,这类材料拥有自然材料不具备的性质,如负折射率、超吸收、负泊松比等超凡特性。五零能模式材料就是一种新型的人工超材料,虽属于弹性材料,但组成其单胞的特殊构型使其宏观静态表现为仅能承载一种受力状态,动态表现为仅能传播一种弹性波,等效弹性模量矩阵六个特征值中仅一个不为零。针对上述新兴材料,对材料本身力学性能的准确预测更是该材料能成功应用的关键。典型预测周期性材料等效性能的方法有渐近均匀化方法和代表体元法。代表体元法力学模型清晰,操作容易,但因缺乏严格数学理论,对材料的性质不能精确预测,仅可作为近似估计使用。与之相反的是渐近均匀化方法,它基于数学理论基础严谨的摄动理论,在复合材料等效性质方面算法成熟。但复杂的计算过程阻碍了该方法的应用。本文基于ANSYS平台实现代表体元法与渐近均匀化方法的有限元求解,编制两种方法的APDL程序,实现复合材料等效性能的预测。本文给出多种单胞构型,针对这些单胞桁架构型计算得到等效弹性模量矩阵特征值,从而得到五种五零能模式材料的单胞构型。计算材料单胞等效弹性性能,得到等效弹性矩阵及特征值,通过比较可知,这五种单胞构型可分成两类不同的弹性特性,其中一类材料可传递弹性膨胀波,另一类可传递弹性剪切波。计算单胞的等效弹性性能时,分别采用代表体元法和渐近均匀化法两种计算方式。研究表明对于这种低密度弹性材料的分析,从计算时间及计算精度方面考虑,代表体元法更适合。五零能模式材料的分析分为两步更直观,开始从单胞桁架模型入手,检验单胞构型是否满足五零能模式的定义,然后分析单胞实体模型,比较单胞构型参数与材料等效弹性模量的关系。
[Abstract]:With the rapid development of space industry and electronics industry, composite materials and their structures have been applied in all aspects of real life. As a new field of material science, supernormal materials have attracted a lot of scholars'attention. These materials have some special properties that natural materials do not have, such as negative refractive index, superabsorption, negative Poisson's ratio and so on. Zero-energy mode material is a new type of artificial metamaterial. Although it belongs to elastic material, the special configuration of its cell makes it show that it can only bear one stress state in macro-static state and only one elastic wave can be transmitted in dynamic state. Only one of the six eigenvalues of the equivalent elastic modulus matrix is not zero. Accurate prediction of the mechanical properties of the material itself is the key to its successful application. The typical methods for predicting the equivalent properties of periodic materials are asymptotic homogenization method and representative voxel method. On the contrary, the asymptotic homogenization method, which is based on the perturbation theory with rigorous mathematical theory, is mature in the equivalent properties of composite materials. But the complex calculation process hinders the application of this method. In this paper, the equivalent modulus matrix eigenvalues are calculated for these single cell truss structures, and then the cell configurations of five kinds of 50-energy mode materials are obtained. By comparing the eigenvalues, we can see that the five cell configurations can be divided into two kinds of different elastic properties, one kind of material can transmit elastic expansion wave, the other kind can transmit elastic shear wave. The representative voxel method is more suitable for the analysis of elastic materials in terms of calculation time and accuracy. The analysis of 50-energy mode materials is divided into two steps, which are more intuitive. Starting with the cell truss model, we examine whether the cell configuration meets the definition of 50-energy mode, then analyze the cell solid model, compare the cell configuration parameters and materials, etc. The relationship between effective elastic modulus.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB33
本文编号：2236989
[Abstract]:With the rapid development of space industry and electronics industry, composite materials and their structures have been applied in all aspects of real life. As a new field of material science, supernormal materials have attracted a lot of scholars'attention. These materials have some special properties that natural materials do not have, such as negative refractive index, superabsorption, negative Poisson's ratio and so on. Zero-energy mode material is a new type of artificial metamaterial. Although it belongs to elastic material, the special configuration of its cell makes it show that it can only bear one stress state in macro-static state and only one elastic wave can be transmitted in dynamic state. Only one of the six eigenvalues of the equivalent elastic modulus matrix is not zero. Accurate prediction of the mechanical properties of the material itself is the key to its successful application. The typical methods for predicting the equivalent properties of periodic materials are asymptotic homogenization method and representative voxel method. On the contrary, the asymptotic homogenization method, which is based on the perturbation theory with rigorous mathematical theory, is mature in the equivalent properties of composite materials. But the complex calculation process hinders the application of this method. In this paper, the equivalent modulus matrix eigenvalues are calculated for these single cell truss structures, and then the cell configurations of five kinds of 50-energy mode materials are obtained. By comparing the eigenvalues, we can see that the five cell configurations can be divided into two kinds of different elastic properties, one kind of material can transmit elastic expansion wave, the other kind can transmit elastic shear wave. The representative voxel method is more suitable for the analysis of elastic materials in terms of calculation time and accuracy. The analysis of 50-energy mode materials is divided into two steps, which are more intuitive. Starting with the cell truss model, we examine whether the cell configuration meets the definition of 50-energy mode, then analyze the cell solid model, compare the cell configuration parameters and materials, etc. The relationship between effective elastic modulus.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB33
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