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The role of elastic anisotropy on the macroscopic constitutive response and yield onset of cubic oligo- and polycrystals

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INTERNATIONAL JOURNAL OF PLASTICITY 2019年 121卷 153-200页

作者： Vieira, R. R. Tenreiro de Bortoli, D. de Carvalho, M. Vieira Pires, F. M. Andrade Univ Porto Dept Mech Engn Porto Portugal Inst Sci & Innovat Mech & Ind Engn INEGI Porto Portugal

The single crystal elastic anisotropy is one of the most important properties affecting the macroscopic response of polycrystalline materials, both in the elastic regime and the early stages of plastic deformation. In this work, the impact of monocrystalline parameters on the mechanical behaviour of cubic polycrystals is studied in detail. The analysis is conducted with an RVE-based computational homogenisation framework which includes several original strategies and criteria developed to enable the efficient statistical analysis of virtual micro-structures. In particular, these developments include a stress-driven adaptation to the usually employed strain-driven homogenisation approach, used to study the plastic polycrystalline response in stress space. The effects of number of grains and realisations considered, finite element mesh discretisation level, and algorithms used to generate both the grain morphology and orientation distribution are also assessed. Considering a number of materials with cubic symmetry, expressions for the number of grains required for an elastically isotropic response are deduced, along with bounds for the homogenised elastic stiffness components of oligocrystals, in both cases as a function of the monocrystalline elastic anisotropy. In the plastic domain, multiple microscopic and macroscopic criteria to describe the yield onset of such polycrystals are evaluated and compared. This is done for both elastically isotropic and anisotropic polycrystals, where once again the effect of different levels of monocrystalline elastic anisotropy are evaluated. The numerically derived yield surface of isotropic polycrystals is fitted to both Tresca and von Mises yield functions, and for anisotropic oligocrystals, the statistical bounds for the expected distribution of micro-yield stresses are deduced, in terms of both the number of grains and of the level of single crystal elastic anisotropy. The results obtained are thus a step towards clarifying the

关键词： Yield condition Crystal plasticity Anisotropic material probability and statistics Multi-scale modelling

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A stochastic study of the collective effect of random distributions of dislocations

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2019年 124卷 10-34页

作者： Gurrutxaga-Lerma, B. Trinity Coll Cambridge Cambridge CB2 1TQ England Univ Cambridge Dept Engn Trumpington St Cambridge CB2 1PZ England

The effect that random populations of dislocations have on a material is examined through stochastic integration of a random cloud of dislocations lying at some distance away from a material point. The problem is studied in one, two, and three dimensions. In 1D, the cloud consists of individual edge dislocations placed along the real line;in 2D, of edge dislocations and edge dipoles on the plane;in 3D, of dislocation loops, In all cases, the dislocation cloud is randomly distributed in space, associated to which several relevant physical parameters, including the material's slip geometry, the dislocation's sign, and its relative orientation, are also stochastically treated. A fully disordered population, i.e., one where the dislocation's signatures and orientations are entirely random, is first studied. It is shown that such disordered systems entail a strong indeterminacy in the collective stress fields, which here is solved by enforcing mass conservation locally. In 2D, this is achieved by modelling a cloud of edge dipoles instead of individual dislocations;in 3D, this is naturally guaranteed by the modelling of closed dislocation loops. The long-range fields of the dipoles in 2D and of the loops in 3D is modelled via their multipolar force expansions, which greatly simplifies the analytical treatment of the problem. The cloud's effect is then studied by performing the stochastic integration of the multipolar fields via Campbell's theorem. The local order, but not the magnitude of the dislocation density, is shown to be critical in contributing to the plastic relaxation of the material: fully disordered systems are shown to self-attenuate, leading to plastic neutrality;ordered and partially ordered systems, achieved when dislocation signatures are aligned, display a direct relationship between the dislocation density and the average stress shielding the material. We establish and generalise the conditions that a system of dislocations must fulfil to display Taylor

关键词： Dislocations Plasticity probability and statistics Point process Scaling laws

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Integration with an adaptive harmonic mean algorithm

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INTERNATIONAL JOURNAL OF MODERN PHYSICS A 2020年第24期35卷

作者： Caldwell, Allen Eller, Philipp Hafych, Vasyl Schick, Rafael Schulz, Oliver Szalay, Marco Max Planck Inst Phys & Astrophys D-80805 Munich Germany Tech Univ Munich D-80333 Munich Germany Google LLC Santa Barbara CA 93101 USA

Numerically estimating the integral of functions in high dimensional spaces is a nontrivial task. A oft-encountered example is the calculation of the marginal likelihood in Bayesian inference, in a context where a sampling algorithm such as a Markov Chain Monte Carlo provides samples of the function. We present an Adaptive Harmonic Mean Integration (AHMI) algorithm. Given samples drawn according to a probability distribution proportional to the function, the algorithm will estimate the integral of the function and the uncertainty of the estimate by applying a harmonic mean estimator to adaptively chosen regions of the parameter space. We describe the algorithm and its mathematical properties, and report the results using it on multiple test cases.

关键词： probability and statistics integral estimation evidence MCMC

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A stochastic equation for predicting tensile fractures in ductile polymer solids

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2018年 490卷 1076-1086页

作者： Nitta, Koh-hei Li, Chun-yao Kanazawa Univ Inst Sci & Engn Kakuma Campus Kanazawa Ishikawa 9201192 Japan

The statistical fracture behavior of isotactic polypropylene solids under different tensile speeds at room temperature was investigated. Tensile tests were performed more than one hundred times at different tensile speeds, and the statistical data, such as the time to break, the ultimate stress, and the tensile toughness were examined as a function of crosshead speed. All probability distribution curves of fracture time, ultimate stress, and tensile toughness followed Gaussian statistics approximately. With increasing tensile speed, the fracture time tended to decrease and the mean ultimate strength increased, whereas the toughness was independent of the tensile speed. We found an analogy in the mathematical mechanism between the ductile fracture of polymer solids and particle Brownian diffusion. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Fracture Polymeric material Mechanical response probability and statistics

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A Sparse Regression Method for Group-Wise Feature Selection with False Discovery Rate Control

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2018年第4期15卷 1066-1078页

作者： Gossmann, Alexej Cao, Shaolong Brzyski, Damian Zhao, Lan-Juan Deng, Hong-Wen Wang, Yu-Ping Tulane Univ Bioinnovat PhD Program New Orleans LA 70118 USA Tulane Univ Ctr Bioinformat & Genom New Orleans LA 70118 USA Univ Texas MD Anderson Canc Ctr Dept Bioinformat & Computat Biol Houston TX 77004 USA Indiana Univ Dept Epidemiol & Biostat Bloomington IN USA Jagiellonian Univ Inst Math PL-31007 Krakow Poland Tulane Univ Dept Global Biostat & Data Sci New Orleans LA 70118 USA Tulane Univ Dept Biomed Engn New Orleans LA 70118 USA

The method of Sorted L-One Penalized Estimation, or SLOPE, is a sparse regression method recently introduced by Bogdan et. al. [1]. It can be used to identify significant predictor variables in a linear model that may have more unknown parameters than observations. When the correlations between predictor variables are small, the SLOPE method is shown to successfully control the false discovery rate (the expected proportion of the irrelevant among all selected predictors) at a user specified level. However, the requirement for nearly uncorrelated predictors is too restrictive for genomic data, as demonstrated in our recent study [2] by an application of SLOPE to realistic simulated DNA sequence data. A possible solution is to divide the predictor variables into nearly uncorrelated groups, and to modify the procedure to select entire groups with an overall significant group effect, rather than individual predictors. Following this motivation, we extend SLOPE in the spirit of Group LASSO to Group SLOPE, a method that can handle group structures between the predictor variables, which are ubiquitous in real genomic data. Our theoretical results show that Group SLOPE controls the group-wise false discovery rate (gFDR), when groups are orthogonal to each other. For use in non-orthogonal settings, we propose two types of Monte Carlo based heuristics, which lead to gFDR control with Group SLOPE in simulations based on real SNP data. As an illustration of the merits of this method, an application of Group SLOPE to a dataset from the Framingham Heart Study results in the identification of some known DNA sequence regions associated with bone health, as well as some new candidate regions.

关键词： probability and statistics correlation and regression analysis statistical computing machine learning mathematics and statistics biology and genetics

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Modification of Mohr's criterion in order to consider the effect of the intermediate principal stress

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INTERNATIONAL JOURNAL OF PLASTICITY 2018年 108卷 40-54页

作者： Comanici, Ana Maria Barsanescu, Paul Doru Gheorghe Asachi Tech Univ Iasi Romania Dept Mech Engn Mechatron & Robot Blvd Mangeron 63 Iasi 700050 Romania

Mohr-Coulomb (M-C) criterion is widely used for isotropic brittle materials, although it has some disadvantages which limit its wider application. One important disadvantage of this theory is that it ignores the effect of the intermediate principal stress, although it has an important influence on materials behaviour. Therefore, Mohr-Coulomb theory is actually used only for materials in biaxial state of stress. In this paper, a modified form of Mohr's criterion has been suggested, in order to overcome this limitation. The modified criterion takes into account the influence of intermediate principal stress in the case of materials under triaxial loading conditions. On the basis of two new hypotheses, a real triaxial state of stress is replaced by a virtual biaxial state of stress. The above mentioned stress states are considered to be equivalent for a material when the failure is imminent in both cases. Both Mohr's theory and the concept of equivalence of stress states are combined in order to obtain the virtual biaxial state of stress, which is determined using all three principal stresses. The modified Mohr's theory can be used only for triaxial state of stress. For biaxial and uniaxial state of stress it is reduced to the classical one. The proposed hypotheses have an important advantage because does not require additional material coefficients. The calculated values using the virtual biaxial state of stress and the linear M-C criterion are in good agreement with experimental data for grey cast iron. The article also presents a compact statistical analysis for both stresses and errors, in order to objectively assess the effectiveness of the formulated hypotheses.

关键词： Yield condition Metallic material Analytic functions probability and statistics Virtual Mohr circle Intermediate principal stress

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United Nations Education Program in Space Science and Technology 1988-2018

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Creative Education 2019年 10卷 2219-2231页

作者： Lewis Pyenson Arak M. Mathai Hans J. Haubold Department of History Western Michigan University Kalamazoo MI USA Department of Mathematics and Statistics McGill University Montreal Canada Office for Outer Space Affairs United Nations Vienna International Centre Vienna Austria

Based on resolutions of the United Nations General Assembly, UN-affiliated Regional Centres for Space Science and Technology Education were established in China, India, Morocco, Nigeria, Brazil/Mexico, and Jordan. Simultaneously, education curricula at the university level were developed for the core disciplines of remote sensing, satellite communications, satellite meteorology, space and atmospheric science, and global navigation satellite systems. In 2017 , these education curricula were supplemented by the publication of two open access books covering full university courses in linear algebra and probability & statistics.

关键词： Regional Education Centres Education Curricula Space and Atmospheric Science Remote Sensing and Geographic Information System Satellite Communications Satellite Meteorology and Global Climate Global Navigation Satellite Systems Linear Algebra probability and statistics

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Thinking and Discussion on the Teaching of the "probability and statistics"

Thinking and Discussion on the Teaching of the "Probability ...

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Lecture Notes in Information Technology—2012 International Conference on Education Technology and Management Engineering(ETME 2012)

作者： Li Chen,Yanling Pan Department of Mathematics,Zhengzhou Normal University,Zhengzhou,Henan 450044

In this paper,the authors carry out an analysis on the problems that exist in the teaching of the course probability and statistics now,and take advantage of the teaching cases of the course probability and statistics in the real word to guide the students to implement thinking,association,comparison and conclusion with a higher *** purpose of this paper is promoting the students to obtain a deeper understanding of some concepts,making an enhancement to the students' awareness in mathematics,and training the students to possess the ability to make use of the mathematical knowledge to resolve the practical problems with a gradual step.

关键词： probability and statistics Educational Reform Teaching Cases

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Martingale und Prozesse 1

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丛书名： De Gruyter Studium Ser.

2018年

作者： René L. Schilling

ISBN: (数字)9783110350685

ISBN: (纸本)9783110350678

Dieser Band ist der dritte Teil der ,,Modernen Stochastik". Als Fortsetzung der ,,Wahrscheinlichkeit" werden nun dynamische stochastische Phänomene anhand stochastischer Prozesse in diskreter Zeit betrachtet. Die erste Hälfte des Buchs gibt eine Einführung in die Theorie der diskreten Martingale - ihr Konvergenzverhalten, optional sampling & stopping, gleichgradige Integrierbarkeit und Martingalungleichungen. Die Stärke der Martingaltechniken wird in den Kapiteln über Anwendungen in der klassischen Wahrscheinlichkeitsrechnung und über die Burkholder-Davis-Gundy-Ungleichungen illustriert. Die zweite Hälfte des Buchs beschäftigt sich mit Irrfahrten auf dem Gitter ℤd und auf ℝd, ihrem Fluktuationsverhalten, Rekurrenz und Transienz. Die letzten beiden Kapitel geben einen Einblick in die probabilistische Potentialtheorie sowie einen Ausblick auf die Brownsche Bewegung: Donskers Invarianzprinzip. 　 Contents Fair Play Bedingte Erwartung Martingale Stoppen und Lokalisieren Konvergenz von Martingalen L2-Martingale Gleichgradig integrierbare Martingale Einige klassische Resultate der W-Theorie Elementare Ungleichungen für Martingale Die Burkholder-Davis-Gundy Ungleichungen Zufällige Irrfahrten auf ℤd - erste Schritte Fluktuationen einer einfachen Irrfahrt auf ℤ Rekurrenz und Transienz allgemeiner Irrfahrten Irrfahrten und Analysis Donskers Invarianzprinzip und die Brownsche Bewegung

关键词： Mathematics probability and statistics

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Studies on passive flexible protection to resist landslides caused by the May 12, 2008, Wenchuan earthquake

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STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGS 2017年第11期26卷

作者： Liu, Chengqing Wei, Xiaodan Lu, Zheng Wu, Handan Yang, Yuling Chen, Linya Southwest JiaoTong Univ Sch Civil Engn Chengdu Peoples R China Tongji Univ Res Inst Struct Engn & Disaster Reduct 1239 Siping Rd Shanghai 200092 Peoples R China

The landslides caused by the 5.12 Wenchuan earthquake resulted in enormous casualties and property losses. Since the earthquake, more than 3,600 landslides have occurred, and 17 of them were catastrophic, each of which has killed more than 30 people. Meanwhile, passive flexible protection has gradually been introduced to resist landslides due to its significant advantages of economy, safety, and environmental protection. To resist landslides effectively, it is necessary to study the load path and design method of passive flexible protection under the action of landslides. In the design of passive flexible protection against landslides, determination of the landslide load is the primary task. In this paper, the formulas of the probability density function and distribution function of the landslide pressure are developed to obtain the value of the accumulated landslide pressure acting on the passive flexible protection, which can be used as the load input parameter in the design of passive flexible protection to resist landslides. Based on the case of the "Shiziliang" potential landslide for the 5.12 earthquake, the pressure data of the landslide are collected, the calculation formulas of the volume, and the pressure of the intercepted landslide are established, and the statistical parameters of the landslide pressure-loading sample are obtained. According to the Kolmogorov-Smirnov test method, the loading sample of the landslide pressure obeys an extreme-value type-I distribution, and then the load model of the landslide pressure is determined. Based on the reliability analysis method, the standard value of the landslide pressure with an over-95% assurance rate is obtained. These results can provide references for load confirmation to design the passive flexible protection to resist landslides.

关键词： force transmission path landslide pressure loads confirmation passive flexible protection probability and statistics reliability anaxlysis

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