Shahbazian Behnam, Bautista Katsalukha Victor, Mirsayar Mirmilad
Department of Aerospace, Physics, and Space Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA.
Materials (Basel). 2024 Dec 12;17(24):6080. doi: 10.3390/ma17246080.
This study advances the state of the art by computing the macroscopic elastic properties of 2D periodic functionally graded microcellular materials, incorporating both isotropic and orthotropic solid phases, as seen in additively manufactured components. This is achieved through numerical homogenization and several novel MATLAB implementations (known in this study as , , , and ). The developed codes in the current work treat each cell as a material point, compute the corresponding cell elasticity tensor using numerical homogenization, and assign it to that specific point. This is conducted based on the principle of scale separation, which is a fundamental concept in homogenization theory. Then, by deriving a fit function that maps the entire material domain, the homogenized material properties are predicted at any desired point. It is shown that this method is very capable of capturing the effects of orthotropy during the solid phase of the material and that it effectively accounts for the influence of void geometry on the macroscopic anisotropies, since the obtained elasticity tensor has different E1 and E2 values. Also, it is revealed that the complexity of the void patterns and the intensity of the void size changes from one cell to another can significantly affect the overall error in terms of the predicted material properties. As the stochasticity in the void sizes increases, the error also tends to increase, since it becomes more challenging to interpolate the data accurately. Therefore, utilizing advanced computational techniques, such as more sophisticated fitting methods like the Fourier series, and implementing machine learning algorithms can significantly improve the overall accuracy of the results. Furthermore, the developed codes can easily be extended to accommodate the homogenization of composite materials incorporating multiple orthotropic phases. This implementation is limited to periodic void distributions and currently supports circular, rectangular, square, and hexagonal void shapes.
本研究通过计算二维周期性功能梯度微孔材料的宏观弹性特性，推动了技术发展，该材料包含各向同性和正交各向异性固相，如增材制造部件中所见。这是通过数值均匀化和几种新颖的MATLAB实现方式（在本研究中称为 、 、 和 ）实现的。当前工作中开发的代码将每个单元视为一个材料点，使用数值均匀化计算相应的单元弹性张量，并将其分配到该特定点。这是基于尺度分离原理进行的，尺度分离原理是均匀化理论中的一个基本概念。然后，通过推导一个映射整个材料域的拟合函数，在任何所需点预测均匀化材料特性。结果表明，该方法非常能够捕捉材料固相期间正交各向异性的影响，并且由于获得的弹性张量具有不同的E1和E2值，它有效地考虑了孔隙几何形状对宏观各向异性的影响。此外，还揭示了孔隙模式的复杂性以及孔隙尺寸从一个单元到另一个单元的变化强度会显著影响预测材料特性方面的总体误差。随着孔隙尺寸随机性的增加，误差也趋于增加，因为准确插值数据变得更具挑战性。因此，利用先进的计算技术，如更复杂的拟合方法（如傅里叶级数），并实施机器学习算法，可以显著提高结果的总体准确性。此外，开发的代码可以轻松扩展以适应包含多个正交各向异性相的复合材料的均匀化。此实现限于周期性孔隙分布，目前支持圆形、矩形、正方形和六边形孔隙形状。
