Numerical evaluation of the thermomechanical effective properties of a functionally graded material using the homogenization method
Numerical evaluation of the thermomechanical effective properties of a functionally graded material using the homogenization method
复制标题
DOI：
10.1016/j.ijsolstr.2008.02.012
复制
发表时间：
2008-06
影响因子：
3.6
通讯作者：
Y. Shabana;N. Noda
中科院分区：
文献类型：
--
作者：
Y. Shabana;N. Noda
在讨论功能梯度材料在热载荷和机械载荷作用下的应力时，需要考虑不同的热-机械等效性能。对于稳态热分析，这些性质包括杨氏模量、泊松比、热膨胀系数和热导率。另一方面，对于热传导问题的瞬态分析，应将密度和热容添加到上述性质中。基于有限元法（FEM）的均匀化方法（HM）被用于估计具有给定周期性纤维分布和复杂几何形状的复合材料的有效性能。对于周期性复合材料结构，不需要研究整个结构，而只需研究一个代表性体积元（RVE）或一个单胞（UC）。由于复合材料的整体性能取决于增强体的排列方式，因此分析了两种不同纤维排列方式的相应UC;即正方形和六边形排列。结果发现，正方形的安排预测较高的值的杨氏模量比六边形的，但有很小的差异。为了验证计算值的性质，结果与以前的实验测量和结果的解析和数值方法进行了比较，并取得了良好的一致性。
When the stresses of the functionally graded materials (FGMs) are discussed under thermal and/or mechanical loading conditions, the different thermomechanical effective properties are needed. For the steady state thermal analyses, these properties include the Young’s modulus, Poisson’s ratio, thermal expansion coefficient and thermal conductivity. For the transient analyses of the heat conduction problem, on the other hand, the density and heat capacity should be added to the aforementioned properties. The homogenization method (HM) based on the finite element method (FEM) is used as it has advantages, such as it is appropriate for estimating the effective properties of composites with a given periodic fiber distribution and complicated geometries. For a periodic composite structure, it is not necessary to study the whole structure but only a representative volume element (RVE) or a unit cell (UC). As the overall behavior of composites depends on the arrangement of the reinforcements, the corresponding UCs of two different arrangements of the fibers are analyzed; namely the square and hexagonal arrangements. It is found that the square arrangement predicts higher values of the Young’s modulus than the hexagonal one but with small difference. In order to verify the computed values of the properties, the results are compared with previous experimental measurements and results of analytical and numerical methods, and good agreement is achieved.