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纤维金属基复合材料（MMCs）均匀化中的概率相对熵

Probabilistic Relative Entropy in Homogenization of Fibrous Metal Matrix Composites (MMCs).

作者信息

Kamiński Marcin

机构信息

Research Head of Civil Engineering, Geodesy & Transportation, Department of Structural Mechanics, Lodz University of Technology, 93-590 Lodz, Poland.

出版信息

Materials (Basel). 2023 Sep 7;16(18):6112. doi: 10.3390/ma16186112.

DOI:10.3390/ma16186112
PMID:37763390
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10532673/
Abstract

The main aim of this work is to deliver uncertainty propagation analysis for the homogenization process of fibrous metal matrix composites (MMCs). The homogenization method applied here is based on the comparison of the deformation energy of the Representative Volume Element (RVE) for the original and for the homogenized material. This part is completed with the use of the Finite Element Method (FEM) plane strain analysis delivered in the ABAQUS system. The probabilistic goal is achieved by using the response function method, where computer recovery with a few FEM tests enables approximations of polynomial bases for the RVE displacements, and further-algebraic determination of all necessary uncertainty measures. Expected values, standard deviations, and relative entropies are derived in the symbolic algebra system MAPLE; a few different entropy models have been also contrasted including the most popular Kullback-Leibler measure. These characteristics are used to discuss the influence of the uncertainty propagation in the MMCs' effective material tensor components, but may serve in the reliability assessment by quantification of the distance between extreme responses and the corresponding admissible values.

摘要

这项工作的主要目的是对纤维金属基复合材料（MMC）的均匀化过程进行不确定性传播分析。这里应用的均匀化方法基于对原始材料和均匀化材料的代表性体积单元（RVE）的变形能进行比较。这部分工作通过使用ABAQUS系统中的有限元法（FEM）平面应变分析来完成。概率目标是通过响应函数法实现的，即通过几次有限元测试的计算机恢复能够近似RVE位移的多项式基，并进一步通过代数方法确定所有必要的不确定性度量。在符号代数系统MAPLE中导出期望值、标准差和相对熵；还对比了几种不同的熵模型，包括最常用的库尔贝克-莱布勒度量。这些特性用于讨论不确定性传播对MMC有效材料张量分量的影响，但也可通过量化极端响应与相应允许值之间的距离用于可靠性评估。

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