均质化(气候)
不确定度量化
有限元法
蒙特卡罗方法
多边形网格
背景(考古学)
数学优化
计算机科学
算法
应用数学
结构工程
数学
工程类
机器学习
地质学
统计
生物多样性
生态学
古生物学
计算机图形学(图像)
生物
作者
Anh Tran,Pieterjan Robbe,Theron Rodgers,Hojun Lim
出处
期刊:JOM
[Springer Nature]
日期:2023-10-25
被引量:1
标识
DOI:10.1007/s11837-023-06182-x
摘要
Crystal plasticity finite element method (CPFEM) has been an integrated computational materials engineering (ICME) workhorse to study materials behaviors and structure-property relationships for the last few decades. These relations are mappings from the microstructure space to the materials properties space. Due to the stochastic and random nature of microstructures, there is always some uncertainty associated with materials properties, for example, in homogenized stress-strain curves. For critical applications with strong reliability needs, it is often desirable to quantify the microstructure-induced uncertainty in the context of structure-property relationships. However, this uncertainty quantification (UQ) problem often incurs a large computational cost because many statistically equivalent representative volume elements (SERVEs) are needed. In this article, we apply a multi-level Monte Carlo (MLMC) method to CPFEM to study the uncertainty in stress-strain curves, given an ensemble of SERVEs at multiple mesh resolutions. By using the information at coarse meshes, we show that it is possible to approximate the response at fine meshes with a much reduced computational cost. We focus on problems where the model output is multi-dimensional, which requires us to track multiple quantities of interest (QoIs) at the same time. Our numerical results show that MLMC can accelerate UQ tasks around 2.23 $$\times $$ , compared to the classical Monte Carlo (MC) method, which is widely known as ensemble average in the CPFEM literature.
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