Title:On Power-Law Tail of Strength Distribution of Brittle and Quasi-brittle Structures
Speaker:Dr. Jia-Liang Le (University of Minnesota)
Time:Thursday,Jun 28, 2018, 10:00- 11:30
Venue:Lecture Hall 604 , Traffic building, Wushan Campus
Welcome all the teachers and students to attend this lecture!
Abstract:
Understanding the tail behavior of the probability distribution of structural strength is of para- mount importance for reliability-based design of engineering structures. For brittle and quasi- brittle structures, the tail distribution not only determines the design strength at a low failure probability, but also governs the functional form of the strength distribution of large-size structures. There exists clear evidence that the Weibull distribution is applicable to brittle structures. Based on the theory of extreme value statistics, the applicability of Weibull distribution suggests that the tail distribution must follow a power law. The justification of the power-law tail distribution was first proposed by Freudenthal based on an assumed type of flaw statistics and linear elastic fracture mechanics of non-interacting flaws. A series of recent studies suggested that the power-law tail can be explained by the transition rate theory governing the statistics of material failure at the nano-scale. In this study, we investigate the tail distribution by considering the randomness in both material strength and applied stress field. The present analysis adopts a nonlocal strength-based failure criterion, in which the spatial variability of the material strength is represented by an autocorrelated random field. The failure statistics of the structure is calculated as a first passage probability. We analyze this problem in 1D, 2D and 3D settings, and the results indicate that in all cases the tail distribution of the nominal structural strength follows a power law. It is shown that the power-law tail behavior of strength distribution stems from the tail distribution of material strength. The flaw statistics introduces additional randomness to the nominal structural strength but does not dictate the power-law form of its tail distribution.
Introduction of the speaker:
Dr. Jia-Liang Le is currently an associate professor of Civil, Environmental, and Geo- Engineering at the University of Minnesota. He earned his Bachelor of Engineering (First Class Honors) and Master of Engineering from the National University of Singapore, and a Ph.D. in structural mechanics from Northwestern University. He is a registered professional engineer. His research interests include fracture mechanics, probabilisticmechanics, scaling, computational mechanics and structuralreliability. He received the Best Paper Award of the 48th U.S. Rock Mechanics/Geomechanics Symposium, the Young Investigator Award from the U.S. Army Research Office, and the 2017 EMI Leonardo da Vinci Award from the American Society of Civil Engineers. He is currently serving on the editorial boards of Journal of Engineering Mechanics ASCE, and Science China: Technological Sciences. He has authored one research monograph (Probabilistic Mechanics of Quasibrittle Structures published by Cambridge University Press) and over 50 journal papers.
