Maximum Value Distribution of Micromechanical Response Quantities
Publication: Journal of Engineering Mechanics
Volume 145, Issue 5
Abstract
The maximum value of a random field over a subdomain is a random variable whose probability distribution can be determined from the first-order marginal probability density function and autocorrelation function of the random field given that certain assumptions hold. It is shown in this work that this formulation, which traditionally has been applied to wind engineering problems, can express the probability distributions of the maximum values of mechanical response quantities of structures subjected to the boundary conditions applied in computational homogenization. Once the expression for the maximum value distribution is determined, the convergence of the maximum value to a deterministic value as a function of structure size can be easily computed. This may have implications in determining the representative volume element for mechanical properties driven by the extremes of the response quantities from which they are derived, such as in upscaling damage parameters. The concept is demonstrated by comparing the results using the maximum value formula to brute-force Monte Carlo simulation for a stochastic bar.
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Acknowledgments
This work has been partially supported by the AFOSR/RSL (Computational Mathematics Program, Manager Dr. A. Sayir) and AFRL/RX (Monitors Dr. C. Woodward and C. Przybyla) (Grant No. FA9550-12-1-0445) to the Center of Excellence on Integrated Materials Modeling (CEIMM) at Johns Hopkins University (partners JHU, UIUC, UCSB). Partial funding for this project was provided by the Office of Naval Research (ONR) through the Naval Research Laboratory’s Basic Research Program (No. N0001418WX00093).
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Published In
Journal of Engineering Mechanics
Volume 145 • Issue 5 • May 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Mar 22, 2018
Accepted: Nov 8, 2018
Published online: Mar 15, 2019
Published in print: May 1, 2019
Discussion open until: Aug 15, 2019
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