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Micro-, meso- to macroscopic modeling of deformation behavior of semi-crystalline polymer

INTERNATIONAL JOURNAL OF PLASTICITY 2013年 49卷 164-184页

作者： Uchida, Makoto Tada, Naoya Okayama Univ Grad Sch Nat Sci & Technol Kita Ku Okayama 7008530 Japan

To represent the elasto-viscoplastic deformation behavior of semi-crystalline polymer (SCP), which has a complicated hierarchical structure, a micro-, meso- to macroscopic computational model was developed. A laminar composite model and FE-based homogenization method were used to relate the mechanical behaviors in micro- to mesoscopic and meso- to macroscopic scales of the material. Using the proposed model, elasto-viscoplastic deformation behaviors of high density polyethylene under several macroscopic boundary conditions were computationally investigated. Material's parameters used in the constitutive equations for microstructure of SCP were defined by fitting the calculated stress-strain relation into the experimental data. Then, the effects of deformation mode and crystallinity on deformation behavior of SCP were investigated. Obtained stress-strain relations represented the experimentally observed characteristics such as an anisotropic strain hardening rate depending on the deformation mode and an increase in the Young's modulus and the flow stress with the crystallinity. Then, the neck propagation process in the uniaxial tension with different strain rate was investigated. The present model represented a development of macroscopic non-uniform deformation characterized by the mechanical response of micro- to mesoscopic deformation. (c) 2013 Elsevier Ltd. All rights reserved.

关键词： Polymeric material Layered material Finite element numerical algorithms

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A spectral method solution to crystal elasto-viscoplasticity at finite strains

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INTERNATIONAL JOURNAL OF PLASTICITY 2013年 46卷 37-53页

作者： Eisenlohr, P. Diehl, M. Lebensohn, R. A. Roters, F. Max Planck Inst Eisenforsch GmbH D-40237 Dusseldorf Germany Los Alamos Natl Lab Div Mat Sci & Technol Los Alamos NM 87545 USA

A significant improvement over existing models for the prediction of the macromechanical response of structural materials can be achieved by means of a more refined treatment of the underlying micromechanics. For this, achieving the highest possible spatial resolution is advantageous, in order to capture the intricate details of complex microstructures. Spectral methods, as an efficient alternative to the widely used finite element method (FEM), have been established during the last decade and their applicability to the case of polycrystalline materials has already been demonstrated. However, until now, the existing implementations were limited to infinitesimal strain and phenomenological crystal elasto-viscoplasticity. This work presents the extension of the existing spectral formulation for polycrystals to the case of finite strains, not limited to a particular constitutive law, by considering a general material model implementation. By interfacing the exact same material model to both, the new spectral implementation as well as a FEM-based solver, a direct comparison of both numerical strategies is possible. Carrying out this comparison, and using a phenomenological constitutive law as example, we demonstrate that the spectral method solution converges much faster with mesh/grid resolution, fulfills stress equilibrium and strain compatibility much better, and is able to solve the micromechanical problem for, e.g., a 256(3) grid in comparable times as required by a 64(3) mesh of linear finite elements. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Microstructures Crystal plasticity numerical algorithms Finite elements High-resolution periodic volume element

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Micromechanical modeling of coupled viscoelastic-viscoplastic composites based on an incrementally affine formulation

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2013年第10期50卷 1755-1769页

作者： Miled, B. Doghri, I. Brassart, L. Delannay, L. Catholic Univ Louvain IMMC B-1348 Louvain Belgium

This study proposes a micromechanical modeling of inclusion-reinforced viscoelastic-viscoplastic composites, based on mean-field approaches. For this, we have generalized the so-called incrementally affine linearization method which was proposed by Doghri et al. (2010a) for elasto-viscoplastic materials. The proposal provides an affine relation between stress and strain increments via an algorithmic tangent operator. In order to find the incrementally affine expression, we start by the linearization of evolution equations at the beginning of a time step around the end time of the step. Next, a numerical integration of the linearized equations is required using a fully implicit backward Euler scheme. The obtained algebraic equations lead to an incrementally affine formulation which is form-similar to linear thermoelasticity, therefore known homogenization models for linear thermoelastic composites can be applied. The proposed method can deal with general viscoelastic-viscoplastic constitutive models with an arbitrary number of internal variables. The semi-analytical predictions are validated against finite element simulations and experimental results. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Homogenization Viscoelasticity Viscoplasticity Linearization numerical algorithms Micromechanics

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Estimation of the full Nye's tensor and its gradients by micro-mechanical stereo-inference using EBSD dislocation microscopy

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INTERNATIONAL JOURNAL OF PLASTICITY 2013年 50卷 146-157页

作者： Hardin, Thomas J. Adams, Brent L. Fullwood, David T. Wagoner, Robert H. Homer, Eric R. Brigham Young Univ Dept Mech Engn Provo UT 84602 USA Ohio State Univ Dept Mat Sci & Engn Columbus OH 43210 USA

A novel method of micromechanical stereoinference is reported which yields components and gradients of Nye's GND tensor which are inaccessible by surface EBSD. In particular, it determines the Nye's tensor gradients going into the sample bulk. The method overcomes limitations imposed by metal's electron opacity by combining experimentally-accessible Nye's tensor components and measured infinitesimal elastic distortion tensors with a solution to the underlying stress equilibrium equations. The full Nye's tensor can be transformed into a crystal coordinate frame and interpreted in the context of slip systems, a more physical sense than in the sample or experimental frame. A demonstration of the method is given for a simulated microstructure. The method is largely robust to random experimental noise but may be sensitive to pattern-center errors. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Dislocations Elastic material Electron microscopy numerical algorithms

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Dislocation models of interfacial shearing induced by an approaching lattice glide dislocation

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INTERNATIONAL JOURNAL OF PLASTICITY 2013年 41卷 1-13页

作者： Chu, H. J. Wang, J. Beyerlein, I. J. Pan, E. Los Alamos Natl Lab Div Mat Sci & Technol Los Alamos NM 87545 USA Yanzhou Univ Coll Hydraul Sci & Engn Yangzhou 225009 Peoples R China Los Alamos Natl Lab Div Theoret Los Alamos NM 87545 USA Univ Akron Dept Civil Engn Akron OH 44325 USA

When a lattice glide dislocation approaches a bi-metal interface with relatively low shear strength, it causes the interface to shear. Interfacial shearing is accommodated by the nucleation and growth of interfacial dislocations, which have an attractive interaction with the incoming dislocation. Thus a critical length scale exists at which the net force on the incoming lattice glide dislocation can transition from being initially repulsive to attractive. In this paper, we develop dislocation-based interface shear models in order to represent this mechanism of interface/dislocation interaction at the continuum scale. Three versions are devised with different degrees of complexity and hence computational cost: the continuous shear model (CSM), simplified-CSM model (SCSM), and single dislocation shear model (SDSM). We simulate the interaction processes with these three models by means of a Green's function method for an anisotropic bimaterial. All three models find that the critical length scale at which the dislocation becomes attracted to the interface increases as the interfacial shear resistance decreases. While the most complex model of the three, the CSM, performs the best, the SCSM and SDSM are more advantageous for implementation into higher-length scale dislocation dynamics models. Published by Elsevier Ltd.

关键词： Dislocations numerical algorithms Anisotropic material Layered material

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A communication-efficient linear system solver for large eddy simulation of jet engine noise

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CLUSTER COMPUTING-THE JOURNAL OF NETWORKS SOFTWARE TOOLS AND APPLICATIONS 2013年第1期16卷 157-170页

作者： Situ, Yingchong Liu, Lixia Martha, Chandra S. Louis, Matthew E. Li, Zhiyuan Sameh, Ahmed H. Blasidell, Gregory A. Lyrintzis, Anatasios S. Purdue Univ Dept Comp Sci W Lafayette IN 47907 USA Google Inc Kirkland WA USA Purdue Univ Sch Aeronaut & Astronaut W Lafayette IN 47907 USA

High-fidelity computational fluid dynamics (CFD) tools, such as the large eddy simulation technique, have become feasible in aiding the field of computational aeroacoustics (CAA) to compute noise on petascale computing platforms. CAA poses significant challenges for researchers because the computational schemes used in the CFD tools should have high accuracy, good spectral resolution, and low dispersion and diffusion errors. A high-order compact finite difference scheme, which is implicit in space, can be used for such simulations because it fulfills the requirements for CAA. Usually, this method is parallelized using a transposition scheme;however, that approach has a high communication overhead. In this paper, we discuss the use of a parallel tridiagonal linear system solver based on the truncated SPIKE algorithm for reducing the communication overhead in our large eddy simulations. We present theoretical performance analysis and report experimental results collected on two parallel computing platforms.

关键词： Finite difference methods Iterative solution techniques Linear systems numerical algorithms Parallel algorithms

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Simple Solution to the Three Point Resection Problem

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JOURNAL OF SURVEYING ENGINEERING 2013年第3期139卷 120-125页

作者： Ligas, Marcin AGH Univ Sci & Technol Fac Min Surveying & Environm Engn Dept Geomat PL-30059 Krakow Poland

The paper presents a simple method of finding the solution to the planar three point resection problem. The main concept leading to the solution is based on an idea of two intersecting circles (which is not new in the literature). The points of intersection of two circles (of which one solves the problem) are obtained by solving a quadratic equation. As a result of the fact that one root of the quadratic equation is known, Vieta's formula is applied to find the other. When one of the measured angles is equal to 0 or 180 degrees, the problem reduces to the intersection of a straight line and a circle. This also leads to a quadratic equation which is solved by Vieta's formula. The derivation of the method is very simple (purely analytic) and free from any intermediate parameters, for example, angles, distances, or azimuths.

关键词： algorithms Surveys numerical algorithms Three point problem Surveying Vieta's formulas Intersecting circles

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Simplified approaches to viscoelastic rolling resistance

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2013年第6期50卷 853-862页

作者： Zehil, Gerard-Philippe Gavin, Henri P. Duke Univ Dept Civil & Environm Engn Durham NC 27708 USA

Modeling approaches yielding rolling resistance estimates for rigid spheres (and cylinders) on viscoelastic layers of finite thicknesses are introduced as lower-cost alternatives to more comprehensive solution-finding strategies. Detailed examples are provided to illustrate the capabilities of the different approaches over their respective ranges of validity. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Rolling resistance Cylinder Sphere Viscoelastic layer numerical algorithms Simplified approaches Approximate solutions

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Communication-Avoiding Krylov Techniques on Graphic Processing Units

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IEEE TRANSACTIONS ON MAGNETICS 2013年第5期49卷 1749-1752页

作者： MehriDehnavi, Maryam El-Kurdi, Yousef Demmel, James Giannacopoulos, Dennis McGill Univ ECE Dept Montreal PQ H3A 2A7 Canada Univ Calif Berkeley EECS & Math Dept Berkeley CA 94720 USA

Communicating data within the graphic processing unit (GPU) memory system and between the CPU and GPU are major bottlenecks in accelerating Krylov solvers on GPUs. Communication-avoiding techniques reduce the communication cost of Krylov subspace methods by computing several vectors of a Krylov subspace "at once," using a kernel called "matrix powers." The matrix powers kernel is implemented on a recent generation of NVIDIA GPUs and speedups of up to 5.7 times are reported for the communication-avoiding matrix powers kernel compared to the standards prase matrix vector multiplication (SpMV) implementation.

关键词： Graphic processors Krylov solvers numerical algorithms parallel algorithms

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numerical METHODS FOR UNCERTAINTY ANALYSIS IN DYNAMICAL SYSTEMS

NUMERICAL METHODS FOR UNCERTAINTY ANALYSIS IN DYNAMICAL SYST...

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作者： KYUNGEUN KIM Texas A&M University

学位级别：硕士

The current methods for uncertainty analysis in dynamical systems are restricted in terms of computational cost and evaluation domain since they either use grid points or work only along trajectories. To break through these problems we present a new method: the Rothe & maximum-entropy method which follows the steps below. A deterministic dynamical system with initial value uncertainties can be analyzed via the uncertainty propagation which is based on the Liouville equation in the form of the first-order linear partial differential equation. On this equation we conduct a semi-discretization in time via A-stable rational approximations of consistency order k and this yields the stationary spatial problem. This spatial problem now can be solved by the spatial discretization scheme: we propose the maximum-entropy approximation which provides unbiased interpolations even with fewer number of scattered points. Through these steps we finally obtain a system of linear equations for the evolution of the probability density function u t, which can be easily solved in several ways. This method can provide more efficiency in terms of computation time thanks to using fewer number of scattered points instead of grid points. Also, it enables the constant tracking of probability density functions in a specific fixed domain of interest and this is especially effective for switched systems.

关键词： Stochastic Systems Uncertainty Analysis Switched Systems numerical algorithms Thesis

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