Data-Driven Multi-Scale Modeling and Optimization for Elastic Properties of Cubic Microstructures
Data-Driven Multi-Scale Modeling and Optimization for Elastic Properties of Cubic Microstructures
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DOI：
10.1007/s40192-022-00258-3
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发表时间：
2022-04-06
影响因子：
3.3
通讯作者：
Acar, P.
中科院分区：
文献类型：
--
作者：
Hasan, M.;Mao, Y.;Acar, P.
本研究探讨了基于梯度和机器学习（ML）驱动的设计优化方法，以提升立方微结构的均匀化线性和非线性特性。该研究通过关联原子尺度和细观尺度模型，将均匀化特性作为底层微结构的函数进行计算。在此，微结构由取向分布函数表示，该函数决定晶体学取向的体积密度。细观尺度下的均匀化特性矩阵是利用通过密度泛函理论计算得到的单晶特性值来计算的。优化后的微结构设计通过文献中的现有数据进行了验证。正如预期，单晶设计能提供线性特性的极值，而非线性特性的最优值则可由单晶或多晶微结构提供。然而，就更好的可制造性而言，多晶设计相较于单晶更具优势。考虑到这一点，本文提出了一种基于机器学习的采样算法，用于在不降低最优特性值的前提下，确定线性和非线性特性的顶级多晶最优解。此外，还提出了一种逆向优化策略，用于针对诸如刚度常数（C - 11）和面内杨氏模量（E - 11）等规定的均匀化特性值来设计微结构。本文给出了该方法在铝（Al）、镍（Ni）和硅（Si）微结构方面的应用。
The present work addresses gradient-based and machine learning (ML)-driven design optimization methods to enhance homogenized linear and nonlinear properties of cubic microstructures. The study computes the homogenized properties as a function of underlying microstructures by linking atomistic-scale and meso-scale models. Here, the microstructure is represented by the orientation distribution function that determines the volume densities of crystallographic orientations. The homogenized property matrix in meso-scale is computed using the single-crystal property values that are obtained by density functional theory calculations. The optimum microstructure designs are validated with the available data in the literature. The single-crystal designs, as expected, are found to provide the extreme values of the linear properties, while the optimum values of the nonlinear properties could be provided by single or polycrystalline microstructures. However, polycrystalline designs are advantageous over single crystals in terms of better manufacturability. With this in mind, an ML-based sampling algorithm is presented to identify top optimum polycrystal solutions for both linear and nonlinear properties without compromising the optimum property values. Moreover, an inverse optimization strategy is presented to design microstructures for prescribed values of homogenized properties, such as the stiffness constant (C-11) and in-plane Young's modulus (E-11). The applications are presented for aluminum (Al), nickel (Ni), and silicon (Si) microstructures.