Data-driven statistical reduced-order modeling and quantification of polycrystal mechanics leading to porosity-based ductile damage
Data-driven statistical reduced-order modeling and quantification of polycrystal mechanics leading to porosity-based ductile damage
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数据驱动的统计降阶建模和多晶力学的量化导致基于孔隙度的延性损伤
DOI：
10.1016/j.jmps.2023.105386
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发表时间：
2023
影响因子：
5.3
通讯作者：
Argus, Robert
中科院分区：
文献类型：
--
作者：
Zhang, Yinling;Chen, Nan;Bronkhorst, Curt A.;Cho, Hansohl;Argus, Robert
预测多晶金属材料基于孔隙率的延性损伤过程是一个重要的实用课题。韧性损伤及其前兆由应力和材料状态量的极值来表示，其空间概率密度函数(PDF)是具有强肥尾的高度非高斯的。使用复杂的基于连续介质的物理模型的传统确定性预测通常缺乏对材料变形过程中结构演化的统计数据的描述。确实代表复杂结构演变的计算工具通常都很昂贵。不可避免的模型错误和缺乏不确定性量化也可能导致严重的预测偏差，特别是在预测与延性损伤相关的极端事件时。本文提出了一种数据驱动的统计降阶建模框架，用于对导致基于孔隙率的延性损伤的多晶团聚体的变形过程进行不确定量化的概率预测。该框架首先从全场多晶模拟的时空解开始计算特定状态变量的前几个时刻的时间演化。然后利用一种基于因果熵的稀疏模型辨识算法来发现这些矩的控制方程，该算法包含了基本物理约束。利用最大熵原理，从预测矩中得到了概率密度函数时间演化的近似解。基于具有代表性的体心立方(BCC)Ta的多晶实现的数值实验表明，一个巧妙的降阶模型可以描述冯·米塞斯应力的非高斯PDF的时间演化，并量化极端事件的概率。学习过程还表明，平均应力不是简单的加性强迫，以驱动更高阶矩和极端事件。相反，它以一种强烈的非线性和乘性方式与后者相互作用。此外，当应用于训练数据集之外的实现时，校准的矩方程提供了相当准确的预测，表明了模型的稳健性和外推技巧。最后，使用基于信息的测量来定量地证明前四个矩足以表征整个变形历史中的关键的高度非高斯特征。
Predicting the process of porosity-based ductile damage in polycrystalline metallic materials is an essential practical topic. Ductile damage and its precursors are represented by extreme values in stress and material state quantities, the spatial probability density function (PDF) of which are highly non-Gaussian with strong fat tails. Traditional deterministic forecasts utilizing sophisticated continuum-based physical models generally lack in representing the statistics of structural evolution during material deformation. Computational tools which do represent complex structural evolution are typically expensive. The inevitable model error and the lack of uncertainty quantification may also induce significant forecast biases, especially in predicting the extreme events associated with ductile damage. In this paper, a data-driven statistical reduced-order modeling framework is developed to provide a probabilistic forecast of the deformation process of a polycrystal aggregate leading to porosity-based ductile damage with uncertainty quantification. The framework starts with computing the time evolution of the leading few moments of specific state variables from the spatiotemporal solution of full-field polycrystal simulations. Then a sparse model identification algorithm based on causation entropy, including essential physical constraints, is utilized to discover the governing equations of these moments. An approximate solution of the time evolution of the PDF is obtained from the predicted moments exploiting the maximum entropy principle. Numerical experiments based on polycrystal realizations of a representative body-centered cubic (BCC) tantalum illustrate a skillful reduced-order model in characterizing the time evolution of the non-Gaussian PDF of the von Mises stress and quantifying the probability of extreme events. The learning process also reveals that the mean stress is not simply an additive forcing to drive the higher-order moments and extreme events. Instead, it interacts with the latter in a strongly nonlinear and multiplicative fashion. In addition, the calibrated moment equations provide a reasonably accurate forecast when applied to the realizations outside the training data set, indicating the robustness of the model and the skill for extrapolation. Finally, an information-based measurement is employed to quantitatively justify that the leading four moments are sufficient to characterize the crucial highly non-Gaussian features throughout the entire deformation history considered.
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DOI：
--
发表时间：
2017
期刊：
影响因子：
--
作者：
Hansohl Cho;C. Bronkhorst;H. Mourad;J. Mayeur;D. Luscher
通讯作者：
D. Luscher
DOI：
--
发表时间：
2020-12
期刊：
ArXiv
影响因子：
--
作者：
Jiayu Zhai;M. Dobson;Yao Li-
通讯作者：
Jiayu Zhai;M. Dobson;Yao Li-
DOI：
--
发表时间：
2013
期刊：
影响因子：
--
作者：
J. Escobedo;C. Trujillo;D. Dennis;E. Cerreta;C. Bronkhorst
通讯作者：
C. Bronkhorst
DOI：
10.1073/pnas.1517384113
发表时间：
2016-04-12
影响因子：
11.1
作者：
Brunton, Steven L.;Proctor, Joshua L.;Kutz, J. Nathan
通讯作者：
Kutz, J. Nathan
影响因子：
5.3
作者：
V. Berdichevsky
通讯作者：
V. Berdichevsky