Paper Info
Title
Microstructure Models and Material Response by Extreme Value Theory.
Abstract
We develop (1) probabilistic models for the compliance tensor A(x) of linear elastic random microstructures and (2) a method for estimating the distributions of large material responses from relatively small sets of response samples by using concepts of the extreme value theory (EVT). Two models are considered for the compliance tensor A(x). The first constructs the compliance tensor from random fields defining its eigenvalues and eigenvectors. The second represents A(x) by products of triangular matrices and their transposes. Numerical examples are presented to illustrate the implementation of the models of A(x). The EVT-based method for estimating properties of large material responses constitutes an efficient and accurate alternative to classical Monte Carlo simulation. It is applied to estimate the distribution of the largest stress Sigma(max) in a rectangular plate with random properties under uniform tension. The proposed estimates of the distribution of Smax are robust even if based on relatively small sets of response samples and can be used to extend empirical distributions of Sigma(max) beyond data.
Year
DOI
Venue
2016
10.1137/15M1006453
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
Keywords
DocType
Volume
compliance tensor,extreme value theory,material response,microstructure,Gaussian field,translation field
Journal
4
Issue
ISSN
Citations 
1
2166-2525
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Mircea Grigoriu143.83