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Coupled thermomechanical response of gradient plasticity

INTERNATIONAL JOURNAL OF PLASTICITY 2017年 91卷 1-24页

作者： Aldakheel, Fadi Miehe, Christian Univ Stuttgart Inst Appl Mech Civil Engn Chair 1 Pfaffenwaldring 7 D-70569 Stuttgart Germany

The coupled thermo-mechanical strain gradient plasticity theory that accounts for microstructure based size effects is outlined within this work. This incorporates spatial gradients of selected micro-structural fields based on length-scales that describe the evolving dissipative mechanisms. In the mechanical part, the model problem of von Mises plasticity with gradient-extended hardening/softening response is considered as discussed in Miehe et al. (2013, 2014a). In the thermal part, we follow the investigations of Simo and Miehe (1992) that demonstrate the effect of temperature on the mechanical fields resulting in a thermal expansion. To this end, two classes of solution schemes for the coupled problem are considered: (i) Global product formula algorithm arising from operator split which leads to a two step solution procedure, and (ii) an implicit coupled algorithm which employs simultaneous solution of the coupled system of equations. In the product formula algorithm, the mechanical and thermal problems are solved separately, resulting in a symmetric problem. However, in the implicit coupled algorithm, a simultaneous solution of the coupled system of equations for gradient thermo-plasticity is employed. A noteworthy drawback of this solution scheme arises from the high computational efforts in comparison with the product formula algorithm. From the computational viewpoint, the standard Galerkin finite element method fails in the context of isochoric plastic flow due to the over constrained pressure field. To circumvent these difficulties, we extend the well-known Q1P0-type and MINI-type mixed finite elements design of gradient plasticity to account for thermal effects. The performance of the formulation is demonstrated by means of some representative examples. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Gradient-extended theory Thermomechanical processes Elastic-viscoplastic material numerical algorithms

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CLOSED-LOOP SOFT-CONSTRAINED TIME-OPTIMAL CONTROL OF FLEXIBLE SPACE STRUCTURES

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1992年第1期15卷 96-103页

作者： BIKDASH, M CLIFF, EM NAYFEH, AH VIRGINIA POLYTECH INST & STATE UNIV DEPT AEROSP & OCEAN ENGNBLACKSBURGVA 24061 VIRGINIA POLYTECH INST & STATE UNIV DEPT ENGN SCI & MECHBLACKSBURGVA 24061

We propose numerically efficient solutions for the open- and closed-loop time-optimal soft-constrained control of a linear system representing a large flexible space structure. The open-loop solution is expressed in terms of the controllability Grammian matrix, for which we have obtained a closed-form expression for the undamped system. The qualitative dependence of the control on the initial state and the existence of many solutions satisfying the necessary conditions are shown. A nominal closed-loop control policy is subsequently formulated, but it is shown to be numerically expensive due to the nonuniqueness of extremal solutions. A continuation-based algorithm is proposed to alleviate the computational problem. Finally, the open- and closed-loop controls are shown to exhibit a saturation property reminiscent of the hard-constrained problem.

关键词： Large Space Structures Linear Quadratic Regulator Time Optimal Control Feedback Control System Perturbation Analysis Vibration Suppression Kalman Filter Computing Boundary Value Problems numerical algorithms

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Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity. Part II: Computational issues

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2009年第1期46卷 92-124页

作者： Valoroso, Nunziante Rosati, Luciano Univ Napoli Parthenope Dipartimento Tecnol Ctr Direz Isola C4 I-80143 Naples Italy Univ Naples Federico II Dipartimento Ingn Strutturale I-80125 Naples Italy

The implementation of the projected algorithm and of the consistent tangent tensor for general isotropic three-invariant elastoplastic models under plane stress conditions discussed in Part I of this paper [Valoroso, N., Rosati, L., 2008. Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity. Part 1: Theoretical formulation. International journal of Solids and Structures, doi: 10.1016/***.2008.08.012.] is addressed. The connections between the general three-dimensional case and the plane stress problem are analyzed in detail and an algorithmic treatment taking full advantage of the isotropic properties of the model is presented. In particular, intrinsic (matrix-free) expressions are provided for all steps of the stress computation scheme that allow one to carry out the numerical implementation in a way that is completely independent from the matrix representations. The numerical performances of the present solution scheme are evaluated through representative numerical examples. (c) 2008 Elsevier Ltd. All rights reserved.

关键词： numerical algorithms Finite elements Plane stress elastoplasticity Return mapping Consistent tangent

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Compact reconstruction of orientation distributions using generalized spherical harmonics to advance large-scale crystal plasticity modeling: Verification using cubic, hexagonal, and orthorhombic polycrystals

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ACTA MATERIALIA 2018年 155卷 418-432页

作者： Eghtesad, Adnan Barrett, Timothy J. Knezevic, Marko Univ New Hampshire Dept Mech Engn 33 Acad WayKingsbury HallW119 Durham NH 03824 USA

Compaction of crystallographic texture data is highly desirable in crystal plasticity simulations because the computational time involved in such calculations scales linearly with the number of crystal orientations. In a recent publication, we have reported a rigorous procedure for reducing large datasets of crystal orientations for cubic-orthotropic and hexagonal-orthotropic polycrystalline metals using symmetrized generalized spherical harmonics (GSH) functions. The procedure relies on a quantitative description of crystallographic texture using an orientation distribution function (ODF) and its series representation using GSH. The core procedure consists of matching the spectral representation of a fullsize ODF containing any number of crystal orientations with that of an ODF containing a compact set of orientations. In this paper, we generalize the procedure to any crystal structure with no restrictions to sample symmetry. These major extensions are accompanied by dealing with significantly more dimensions as well as imaginary terms. Two approaches for generating an initial set of orientations in the compact ODF are explored, one based on binning of a given fundamental zone in the Bunge-Euler orientation space and another that takes advantage of MTEX to maximize the compaction. The overall procedure has been successfully applied to compaction of large ODFs for cubic, hexagonal, and orthorhombic polycrystalline metals with orthotropic and no sample symmetry. It is quantitatively demonstrated that texture evolution, twin volume fraction evolution, stress-strain response, and geometrical changes of samples can be accurately simulated to large plastic strains with compact ODFs using crystal plasticity finite element models. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

关键词： Orientation distribution function Microstructures Anisotropic material Crystal plasticity numerical algorithms

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Toward perfectly absorbing boundary conditions for Euler equations

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AIAA JOURNAL 1999年第8期37卷 912-918页

作者： Hayder, ME Hu, FQ Hussaini, MY Rice Univ Ctr Res Parallel Computat Houston TX 77005 USA Old Dominion Univ Dept Math & Stat Norfolk VA 23529 USA Florida State Univ Program Computat Sci & Engn Tallahassee FL 32306 USA

We examine the effectiveness of absorbing layers as nonreflecting computational boundaries for the Euler equations. The absorbing-layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation. This methodology is similar to that used by Berenger for the numerical solutions of Maxwell's equations. Specifically, we apply this methodology to three physical problems-shock-vortex interactions, a plane free shear how, and an axisymmetric jet-with emphasis on acoustic wave propagation. Our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered.

关键词： Euler Equations Maxwell Equation Vortices Shear Layers numerical Modeling Kelvin Helmholtz Instability Navier Stokes Equations Shock Wave Interaction numerical algorithms MacCormack Method

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Efficient computational algorithms for forward and backward analysis of a dynamic pavement system

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COMPUTERS & STRUCTURES 1998年第2期69卷 255-263页

作者： Liang, RY Zhu, JX Univ Akron Dept Civil Engn Ctr Infrastruct Mat & Rehabil Akron OH 44325 USA

A simple dynamic analysis algorithm is presented in this paper for both forward and backward calculations of a pavement system consisting of an asphalt concrete layer, underlain by a uniform subgrade to a depth H wherein the bedrock is located. The subgrade soil is represented by a higher-order continuum model-the modified Vlasov model. The asphalt concrete layer is represented by a three-parameter complex compliance function in a frequency domain. The governing equations of the dynamic pavement system, along with the solution algorithms for both forward and backward computations, are presented in detail. A numerical example is provided to illustrate the importance of considering dynamic effect in predicting pavement response under dynamic load. In addition, numerical examples are given to demonstrate the use of nondestructive testing data to back calculate the material properties, such as the modulus, damping, creep compliance and fatigue cracking speed for an asphalt concrete layer and the modulus damping for the subgrade layer. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： dynamic pavement forward backward numerical algorithms

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IMPACT OF COMPUTATIONAL FLUID-DYNAMICS ON DEVELOPMENT TEST FACILITIES

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JOURNAL OF AIRCRAFT 1985年第3期22卷 182-187页

作者： KORKEGI, RH National Research Council Washington D. C.

The impact of computational fluid dynamics (CFD) on the traditional role of aeronautical ground test facilities over the next 15 years is assessed via a National Research Council study. More powerful scientific computers and more efficient numerical algorithms should result in the ability to practically compute the flowfield about a complete aircraft with the Reynolds-averaged Navier-Stokes equations at a unit cost three orders of magnitude lower than at present. No dramatic change in the cost of testing in ground facilities is foreseen because more efficient computer-enhanced facility operation is partially offset by increased power and labor costs. From the user viewpoint, the risk in development of a new aircraft or engine is so great that use of proven methods of verification by means of test facilities will not change significantly. In the next 15 years CFD and ground test facilities will be utilized in a complementary rather than competitive mode of obtaining design data and the end result will be a better product. © 1985 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： CFD Transonic Wind Tunnel Reynolds Averaged Navier Stokes Aircraft Configurations Turbulence Models numerical algorithms Aeronautics Aircraft Engine Design Angle of Attack Supercomputers

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COMPUTATIONAL ASPECTS OF THE PENTIUM AFFAIR

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IEEE COMPUTATIONAL SCIENCE & ENGINEERING 1995年第1期2卷 18-30页

作者： COE, T MATHISEN, T MOLER, C PRATT, V STANFORD UNIV STANFORDCA 94305 NORSK HYDRO AS OSLONORWAY

This is the story of exactly how the Pentium floating-point division problem was discovered, and what you need to know about the mathematics and computer engineering involved before deciding whether to replace the chi... 详细信息

关键词： numerical algorithms

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Filter bank subdivisions of bounded domains

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APPLIED numerical MATHEMATICS 2000年第3期32卷 331-357页

作者： Waldén, J Yale Univ Dept Math New Haven CT 06520 USA

We construct filter bank transforms that are adapted to bounded domains. The transforms are constructed with the aim of solving PDEs together with finite difference methods, and the properties important for this kind of application are analyzed. As the filter banks do not need to correspond to wavelets, short filters can be used. The price paid is extra growth factors in the number of coefficients and in the error, compared to the multiresolution analysis approach. However, these factors are small. We give upper bounds of the growth factors, and show numerical examples for an interval, a three-dimensional box, and a triangle. We also show examples of fast differentiation and other operations on thresholded expansions. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.

关键词： wavelets adaptive PDE methods finite difference methods numerical algorithms

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Flow stress model for IN718 accounting for evolution of strengthening precipitates during thermal treatment

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COMPUTATIONAL MATERIALS SCIENCE 2014年 82卷 531-539页

作者： Fisk, M. Ion, J. C. Lindgren, L. -E. Malmo Univ Fac Technol & Soc SE-20506 Malmo Sweden Lulea Univ Technol Dept Sci & Engn SE-97187 Lulea Sweden

A flow stress model describing precipitate hardening in the nickel based alloy Inconel (R) 718 following thermal treatment is presented. The interactions between precipitates and dislocations are included in a dislocation density based material model. Compression tests have been performed using solution annealed, fully-aged and half-aged material. Models were calibrated using data for solution annealed and fully-aged material, and validated using data from half-aged material. Agreement between experimental data and model predictions is good. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Dislocations Strengthening mechanisms Metallic material Mechanical testing numerical algorithms Inconel 718 Gamma double prime

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