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Probabilistic modeling of microstructure evolution using finite element representation of statistical correlation functions

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INTERNATIONAL JOURNAL OF PLASTICITY 2012年 30-31卷 62-80页

作者： Sundararaghavan, V. Kumar, A. Univ Michigan Ann Arbor MI 48109 USA

A probabilistic finite element scheme is presented for simulating evolution of polycrystalline microstructures during deformation. The microstructure is described using conditional orientation correlation function (COCF), defined as the probability density of occurrence of a crystal orientation g' at a distance r from a given orientation g. The COCF is represented using three interconnected layers of finite element meshes in the g' r and g spaces. As the microstructure evolves, the reoriented neighborhood and strain fields close to an orientation (g) are captured by updating probability fields in these finite element meshes. For this purpose, a novel total Lagrangian approach has been developed that allows evolution of probability densities while satisfying normalization constraints, probability interdependencies and symmetries. The improvement in prediction of texture and strains achieved by the COCF approach over ODF-based methods is quantified through deformation analysis of a planar polycrystalline microstructure. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Microstructural descriptors numerical algorithms Crystal plasticity Microstructures Probability and Statistics

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A novel approach to study dislocation density tensors and lattice rotation patterns in atomistic simulations

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2012年第4期60卷 711-722页

作者： Begau, C. Hua, J. Hartmaier, A. Ruhr Univ Bochum ICAMS D-44801 Bochum Germany Xian Univ Architecture & Technol Dept Mech Sch Sci Xian 710055 Shaanxi Peoples R China

Crystal plasticity caused by the nucleation and interaction of dislocations is an important aspect in crystal deformation. Recent nanoindentation experiments in single crystals of copper or aluminum revealed large deviations in the lattice rotation and an inhomogeneous distribution of the dislocation density in the plastic zone under the indenter tip. Molecular dynamics simulations offer the possibility to study the origin of these phenomena on an atomistic scale, but require sophisticated analysis routines in order to deal with the massive amount of generated data. Here a new efficient approach to analyze atomistic data on the fly during the simulation is introduced. This approach allows us to identify the dislocation network including Burgers vectors on the timescale of picoseconds and below. This data does not only reveal the evolution of dislocation structures, but it offers the possibility to quantify local dislocation density tensors calculated on an atomic level. The numerical results are compared with experimental data from the literature. The presented approach provides useful insight into the active deformation mechanisms during plastic deformation that will help us to bridge simulations on atomic scales and continuum descriptions. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Dislocations Indentation and hardness numerical algorithms

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Identification of plastic constitutive parameters at large deformations from three dimensional displacement fields

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COMPUTATIONAL MECHANICS 2012年第1期49卷 53-71页

作者： Rossi, Marco Pierron, Fabrice LMPF Arts & Metiers ParisTech F-51006 Chalons Sur Marne France

The aim of this paper is to provide a general procedure to extract the constitutive parameters of a plasticity model starting from displacement measurements and using the Virtual Fields Method. This is a classical inverse problem which has been already investigated in the literature, however several new features are developed here. First of all the procedure applies to a general three-dimensional displacement field which leads to large plastic deformations, no assumptions are made such as plane stress or plane strain although only pressure-independent plasticity is considered. Moreover the equilibrium equation is written in terms of the deviatoric stress tensor that can be directly computed from the strain field without iterations. Thanks to this, the identification routine is much faster compared to other inverse methods such as finite element updating. The proposed method can be a valid tool to study complex phenomena which involve severe plastic deformation and where the state of stress is completely triaxial, e.g. strain localization or necking occurrence. The procedure has been validated using a three dimensional displacement field obtained from a simulated experiment. The main potentialities as well as a first sensitivity study on the influence of measurement errors are illustrated.

关键词： Constitutive modelling Inelastic and finite deformation Inverse methods numerical algorithms

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Designing linear distributed algorithms with memory for fast convergence

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2012年第15期22卷 1691-1702页

作者： Roy, Sandip Wan, Yan Saberi, Ali Xue, Mengran Washington State Univ Dept Elect Engn Pullman WA 99164 USA Univ N Texas Dept Elect Engn Denton TX 76203 USA

Motivated by both distributed computation and decentralized control applications, we studied the distributed linear iterative algorithms with memory. Specifically, we showed that the system of linear equations Gx = b b can be solved through a distributed linear iteration for arbitrary invertible G using only a single memory element at each processor. Further, we demonstrated that the memoried distributed algorithm can be designed to achieve much faster convergence than a memoryless distributed algorithm. Two small simulation examples were included to illustrate the results. Copyright (c) 2011 John Wiley & Sons, Ltd.

关键词： distributed algorithms large-scale networks decentralized control theory numerical algorithms

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Tangent Orbit Technique in Three Dimensions

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2012年第6期35卷 1907-1911页

作者： Zhang, Gang Zhou, Di Harbin Inst Technol Sch Astronaut Harbin 150001 Peoples R China

The tangent orbit technique in three dimensions (3D) is studied. Based on a new definition of tangent orbits in 3D, three orbit transfer problems are solved, including tangent to initial orbit, tangent to final orbit, and cotangent transfer. By solving the flight-direction angle, the tangent to initial/final orbit problem is analytically solved. However, the cotangent transfer problem in 3D is solved by a numerical iterative algorithm. Unlike the tangent orbit technique in two dimensions (2D), the flight-direction angles of two tangent orbits in 3D are not equal. The single solution of the cotangent transfer in 2D can be solved in closed form, whereas in 3D there may exist several solutions which can only be solved by a numerical iterative algorithm. For the tangent to initial/final orbit problem the conditions are solved only by a numerical iterative algorithm, whereas for the cotangent transfer problem the conditions cannot even be directly obtained.

关键词： Transfer Orbit Earth Centered Inertial Iterative Algorithm Secant Method Attitude Control System Boundary Value Problems Flight Path Angle Orbital Rendezvous Yaw numerical algorithms

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Application of the companion factorization to linear non-autonomous area-preserving maps

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LINEAR & MULTILINEAR ALGEBRA 2012年第2期60卷 201-217页

作者： Abderraman Marrero, J. Rachidi, M. Tech Univ Madrid Telecommun Engn Sch Dept Math Appl Informat Technol ETSIT UPM Madrid 28040 Spain Univ Moulay Ismail Fac Sci Grp Difference Equat Fibonacci Sequences & Applic Dept Math & Informat Beni Mhamed Meknes Morocco

For a large class of discrete matrix difference equations many qualitative problems remain unsolved. The companion matrix factorization is applied here to the shift matrices associated to linear non-autonomous area-preserving maps. It permits us to introduce second order linear difference equations, which provide a faster computation of the transition matrices with respect to numerical algorithms based on the standard product of matrices. In addition, compact representations for the main elements of these discrete planar systems can be provided when using the well-known solutions of linear difference equations. Some properties and applications of current interest are presented.

关键词： companion matrix factorization difference equations nested sums numerical algorithms stability transition matrix

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A Possibility Model in the Problems of Morphological Image Analysis

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MOSCOW UNIVERSITY PHYSICS BULLETIN 2012年第6期67卷 512-519页

作者： Zubyuk, A. V. Moscow MV Lomonosov State Univ Fac Phys Moscow 119991 Russia

The possibility models of mathematical methods of morphological image analysis are considered. In particular, a solution of the possibility-theoretical image classification problem is obtained. The solution can be used for acoustic signal analysis in geophysics [1], satellite images interpretation [2], etc. Methods for the empirical reconstruction of fuzzy shapes are developed.

关键词： morphological image analysis fuzzy morphology possibility theory numerical algorithms

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A comparative study of SQP-type algorithms for nonlinear and nonconvex mixed-integer optimization

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MATHEMATICAL PROGRAMMING COMPUTATION 2012年第4期4卷 383-412页

作者： Exler, Oliver Lehmann, Thomas Schittkowski, Klaus Univ Bayreuth Dept Comp Sci D-95440 Bayreuth Germany Konrad Zuse Zentrum ZIB D-14195 Berlin Germany

We present numerical results of a comparative study of codes for nonlinear and nonconvex mixed-integer optimization. The underlying algorithms are based on sequential quadratic programming (SQP) with stabilization by trust-regions, linear outer approximations, and branch-and-bound techniques. The mixed-integer quadratic programming subproblems are solved by a branch-and-cut algorithm. Second order information is updated by a quasi-Newton update formula (BFGS) applied to the Lagrange function for continuous, but also for integer variables. We do not require that the model functions can be evaluated at fractional values of the integer variables. Thus, partial derivatives with respect to integer variables are replaced by descent directions obtained from function values at neighboring grid points, and the number of simulations or function evaluations, respectively, is our main performance criterion to measure the efficiency of a code. numerical results are presented for a set of 100 academic mixed-integer test problems. Since not all of our test examples are convex, we reach the best-known solutions in about 90 % of the test runs, but at least feasible solutions in the other cases. The average number of function evaluations of the new mixed-integer SQP code is between 240 and 500 including those needed for one-or two-sided approximations of partial derivatives or descent directions, respectively. In addition, we present numerical results for a set of 55 test problems with some practical background in petroleum engineering.

关键词： MINLP Mixed-integer nonlinear programming SQP Sequential quadratic programming Trust region method Linear outer approximation MIQP Mixed-integer quadratic programming numerical algorithms Performance evaluation Mixed-integer test problems Engineering optimization

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Computational issues in rate-dependent plasticity models

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International Conference on Machine Design and Manufacturing Engineering (ICMDME 2012)

作者： De Angelis, Fabio Univ Naples Federico II Dept Struct Engn I-80125 Naples Italy

ISBN: (纸本)9783037854709

In the present paper computational issues and numerical integration algorithms are illustrated with reference to the evolutive process in rate-dependent plasticity problems. The adopted methodology conveniently relates the rate-dependent consistency parameter of the plasticity model with the flow function of the constitutive model in use. A fully implicit integration scheme is applied which correctly reduces to the inviscid limit for null viscosity parameter. numerical examples and computational results are reported which illustrate the effectiveness of the procedure.

关键词： Computational procedures numerical algorithms Rate-dependent plasticity

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Robust and Efficient algorithms for ℒ ∞ -Norm Computation for Descriptor Systems

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IFAC Proceedings Volumes 2012年第13期45卷 195-200页

作者： P. Benner V. Sima M. Voigt Max Planck Institute for Dynamics of Complex Technical Systems 39106 Magdeburg Germany National Institute for Research and Development in Informatics 011455 Bucharest Romania

In this paper we discuss algorithms for the computation of the ℒ ∞ -norm of transfer functions related to descriptor systems, both in the continuous- and discrete-time context. We show how one can achieve this goal by computing the eigenvalues of certain structured matrix pencils. These pencils can be transformed to skew-Hamiltonian/Hamiltonian matrix pencils which are constructed by only using the original data. Furthermore, we apply a structure-preserving algorithm to compute the desired eigenvalues. In this way we increase robustness and efficiency of the method. Finally, we present numerical results in order to illustrate the advantages of our approach.

关键词： Computer-aided control systems design descriptor systems eigenvalue problems ℋ ∞ control linear control systems norms numerical algorithms robust control

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