Validation of a numerical method based on Fast Fourier Transforms for heterogeneous thermoelastic materials by comparison with analytical solutions
Validation of a numerical method based on Fast Fourier Transforms for heterogeneous thermoelastic materials by comparison with analytical solutions
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DOI：
10.1016/j.commatsci.2014.02.027
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发表时间：
2014-05
影响因子：
3.3
通讯作者：
B. Anglin;R. Lebensohn;A. Rollett
中科院分区：
文献类型：
--
作者：
B. Anglin;R. Lebensohn;A. Rollett
提出了一种基于快速傅立叶变换的非均质材料热弹性响应的数值计算方法，并与EShelby夹杂问题的解析解进行了比较，验证了该方法的有效性。用球形和圆柱形、均匀和非均匀夹杂组态验证了所提出的谱方法的结果。文中还探讨了数值解对齐性、几何形状和分辨率的依赖关系，并量化和讨论了与已知解析解的差异。对于均匀夹杂的情况，所提出的数值方法是直接的，即不需要迭代。在分辨率足够高的情况下，对这些简单几何形状的微观力学场的预测与分析结果吻合得很好。文中还探讨了夹杂物体素化的具体方法，并评估了它对界面附近局域场的影响。
A numerical method based on Fast Fourier Transforms to compute the thermoelastic response of heterogeneous materials is presented and validated by comparison with analytical solutions of the Eshelby inclusion problem. Spherical and cylindrical, homogeneous and inhomogeneous inclusion configurations are used to validate the results of the proposed spectral method. Dependencies of the numerical solutions on homogeneity, geometry and resolution are also explored, and the differences with respect to known analytical solutions are quantified and discussed. In the case of homogeneous inclusions, the proposed numerical method is direct, i.e. does not require iteration. Using enough resolution, the micromechanical fields predicted for these simple geometries are shown to be in good agreement with the analytical results. The specific way in which inclusions are voxelized is also explored, and its effect on local fields near interfaces is assessed.