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E-raamat: Practical Multiscaling

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(Columbia University)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 03-Sep-2013
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118534854
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Practical MultiscalingSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 03-Sep-2013
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118534854
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Practical Multiscaling covers fundamental modelling techniques aimed at bridging diverse temporal and spatial scales ranging from the atomic level to a full-scale product level. It focuses on practical multiscale methods that account for fine-scale (material) details but do not require their precise resolution. The text material evolved from over 20 years of teaching experience at Rensselaer and Columbia University, as well as from practical experience gained in the application of multiscale software.

This book comprehensively covers theory and implementation, providing a detailed exposition of the state-of-the-art multiscale theories and their insertion into conventional (single-scale) finite element code architecture. The robustness and design aspects of multiscale methods are also emphasised, which is accomplished via four building blocks: upscaling of information, systematic reduction of information, characterization of information utilizing experimental data, and material optimization. To ensure the reader gains hands-on experience, a companion website hosting a lite version of the multiscale design software (MDS-Lite) is available.

Key features:





Combines fundamental theory and practical methods of multiscale modelling Covers the state-of-the-art multiscale theories and examines their practical usability in design Covers applications of multiscale methods Accompanied by a continuously updated website hosting the multiscale design software Illustrated with colour images

Practical Multiscaling is an ideal textbook for graduate students studying multiscale science and engineering. It is also a must-have reference for government laboratories, researchers and practitioners in civil, aerospace, pharmaceutical, electronics, and automotive industries, and commercial software vendors.
Preface xi
Acknowledgments xv
1 Introduction to Multiscale Methods
1(12)
1.1 The Rationale for Multiscale Computations
1(1)
1.2 The Hype and the Reality
2(1)
1.3 Examples and Qualification of Multiscale Methods
3(2)
1.4 Nomenclature and Definitions
5(1)
1.5 Notation
6(7)
1.5.1 Index and Matrix Notation
6(2)
1.5.2 Multiple Spatial Scale Coordinates
8(1)
1.5.3 Domains and Boundaries
9(1)
1.5.4 Spatial and Temporal Derivatives
9(1)
1.5.5 Special Symbols
10(1)
References
11(2)
2 Upscaling/Downscaling of Continua
13(82)
2.1 Introduction
13(3)
2.2 Homogenizaton of Linear Heterogeneous Media
16(31)
2.2.1 Two-Scale Formulation
16(7)
2.2.2 Two-Scale Formulation -- Variational Form
23(2)
2.2.3 Hill--Mandel Macrohomogeneity Condition and Hill--Reuss--Voigt Bounds
25(2)
2.2.4 Numerical Implementation
27(11)
2.2.5 Boundary Layers
38(3)
2.2.6 Convergence Estimates
41(6)
2.3 Upscaling Based on Enhanced Kinematics
47(3)
2.3.1 Multiscale Finite Element Method
48(1)
2.3.2 Variational Multiscale Method
48(1)
2.3.3 Multiscale Enrichment Based on Partition of Unity
49(1)
2.4 Homogenization of Nonlinear Heterogeneous Media
50(14)
2.4.1 Asymptotic Expansion for Nonlinear Problems
50(4)
2.4.2 Formulation of the Coarse-Scale Problem
54(4)
2.4.3 Formulation of the Unit Cell Problem
58(3)
2.4.4 Example Problems
61(3)
2.5 Higher Order Homogenization
64(5)
2.5.1 Introduction
64(1)
2.5.2 Formulation
65(4)
2.6 Multiple-Scale Homogenization
69(2)
2.7 Going Beyond Upscaling -- Homogenization-Based Multigrid
71(24)
2.7.1 Relaxation
73(4)
2.7.2 Coarse-grid Correction
77(2)
2.7.3 Two-grid Convergence for a Model Problem in a Periodic Heterogeneous Medium
79(2)
2.7.4 Upscaling-Based Prolongation and Restriction Operators
81(2)
2.7.5 Homogenization-based Multigrid and Multigrid Acceleration
83(1)
2.7.6 Nonlinear Multigrid
84(2)
2.7.7 Multigrid for Indefinite Systems
86(1)
Problems
87(4)
References
91(4)
3 Upscaling/Downscaling of Atomistic/Continuum Media
95(42)
3.1 Introduction
95(1)
3.2 Governing Equations
96(4)
3.2.1 Molecular Dynamics Equation of Motion
96(2)
3.2.2 Multiple Spatial and Temporal Scales and Rescaling of the MD Equations
98(2)
3.3 Generalized Mathematical Homogenization
100(13)
3.3.1 Multiple-Scale Asymptotic Analysis
100(2)
3.3.2 The Dynamic Atomistic Unit Cell Problem
102(1)
3.3.3 The Coarse-Scale Equations of Motion
103(3)
3.3.4 Continuum Description of Equation of Motion
106(1)
3.3.5 The Thermal Equation
107(5)
3.3.6 Extension to Multi-Body Potentials
112(1)
3.4 Finite Element Implementation and Numerical Verification
113(5)
3.4.1 Weak Forms and Semidiscretization of Coarse-Scale Equations
113(2)
3.4.2 The Fine-Scale (Atomistic) Problem
115(3)
3.5 Statistical Ensemble
118(2)
3.6 Verification
120(6)
3.7 Going Beyond Upscaling
126(11)
3.7.1 Spatial Multilevel Method Versus Space-Time Multilevel Method
127(2)
3.7.2 The WR Scheme
129(1)
3.7.3 Space--Time FAS
130(1)
Problems
131(2)
References
133(4)
4 Reduced Order Homogenization
137(112)
4.1 Introduction
137(2)
4.2 Reduced Order Homogenization for Two-Scale Problems
139(17)
4.2.1 Governing Equations
139(2)
4.2.2 Residual-Free Fields and Model Reduction
141(7)
4.2.3 Reduced Order System of Equations
148(2)
4.2.4 One-Dimensional Model Problem
150(4)
4.2.5 Computational Aspects
154(2)
4.3 Lower Order Approximation of Eigenstrains
156(28)
4.3.1 The Pitfalls of a Piecewise Constant One-Partition-Per-Phase Model
157(2)
4.3.2 Impotent Eigenstrain
159(4)
4.3.3 Hybrid Impotent-Incompatible Eigenstrain Mode Estimators
163(1)
4.3.4 Chaboche Modification
164(1)
4.3.5 Analytical Relations for Various Approximations of Eigenstrain Influence Functions
165(7)
4.3.6 Eigenstrain Upwinding
172(3)
4.3.7 Enhancing Constitutive Laws of Phases
175(5)
4.3.8 Validation of the Hybrid Impotent-Incompatible Reduced Order Model with Eigenstrain Upwinding and Enhanced Constitutive Model of Phases
180(4)
4.4 Extension to Nonlocal Heterogeneous Media
184(13)
4.4.1 Staggered Nonlocal Model for Homogeneous Materials
186(2)
4.4.2 Staggered Nonlocal Multiscale Model
188(1)
4.4.3 Validation of the Nonlocal Model
189(4)
4.4.4 Rescaling Constitutive Equations
193(4)
4.5 Extension to Dispersive Heterogeneous Media
197(12)
4.5.1 Dispersive Coarse-Scale Problem
199(2)
4.5.2 The Quasi-Dynamic Unit Cell Problem
201(3)
4.5.3 Linear Model Problem
204(1)
4.5.4 Nonlinear Model Problem
205(3)
4.5.5 Implicit and Explicit Formulations
208(1)
4.6 Extension to Multiple Spatial Scales
209(5)
4.6.1 Residual-Free Governing Equations at Multiple Scales
210(1)
4.6.2 Multiple-Scale Reduced Order Model
211(3)
4.7 Extension to Large Deformations
214(5)
4.8 Extension to Multiple Temporal Scales with Application to Fatigue
219(8)
4.8.1 Temporal Homogenization
220(4)
4.8.2 Multiple Temporal and Spatial Scales
224(1)
4.8.3 Fatigue Constitutive Equation
225(1)
4.8.4 Verfication of the Multiscale Fatigue Model
226(1)
4.9 Extension to Multiphysics Problems
227(12)
4.9.1 Reduced Order Coupled Vector-Scalar Field Model at Multiple Scales
228(4)
4.9.2 Environmental Degradation of PMC
232(3)
4.9.3 Validation of the Multiphysics Model
235(4)
4.10 Multiscale Characterization
239(10)
4.10.1 Formulation of the Inverse Problem
239(2)
4.10.2 Characterization of Model Parameters in ROH
241(1)
Problems
241(2)
References
243(6)
5 Scale-separation-free Upscaling/Downscaling of Continua
249(56)
5.1 Introduction
249(2)
5.2 Computational Continua (C2)
251(14)
5.2.1 Nonlocal Quadrature
251(3)
5.2.2 Coarse-Scale Problem
254(3)
5.2.3 Computational Unit Cell Problem
257(3)
5.2.4 One-Dimensional Model Problem
260(5)
5.3 Reduced Order Computational Continua (RC2)
265(13)
5.3.1 Residual-Free Computational Unit Cell Problem
266(8)
5.3.2 The Coarse-Scale Weak Form
274(1)
5.3.3 Coarse-Scale Consistent Tangent Stiffness Matrix
275(3)
5.4 Nonlocal Quadrature in Multidimensions
278(19)
5.4.1 Tetrahedral Elements
278(9)
5.4.2 Triangular Elements
287(5)
5.4.3 Quadrilateral and Hexahedral Elements
292(5)
5.5 Model Verification
297(8)
5.5.1 The Beam Problem
300(2)
Problems
302(1)
References
303(2)
6 Multiscale Design Software
305(90)
6.1 Introduction
305(3)
6.2 Microanalysis with MDS-Lite
308(32)
6.2.1 Familiarity with the GUI
309(3)
6.2.2 Labeling Data Files
312(1)
6.2.3 The First Walkthrough MDS-Micro Example
312(6)
6.2.4 The Second Walkthrough MDS-Micro Example
318(13)
6.2.5 Parametric Library of Unit Cell Models
331(9)
6.3 Macroanalysis with MDS-Lite
340(55)
6.3.1 First Walkthrough MDS-Macro Example
341(21)
6.3.2 Second Walkthrough MDS-Macro Example
362(11)
6.3.3 Third Walkthrough Example
373(6)
6.3.4 Fourth Walkthrough Example
379(12)
Problems
391(2)
References
393(2)
Index 395
Jacob Fish, Columbia University, USA Jacob Fish is the Robert A. W. and Christine S. Carleton Professor in Civil Engineering at Columbia University. He is the Founder and Editor-in-Chief of the International Journal of Multiscale Computational Engineering and serves as an Associate Editor of the International Journal for Numerical Methods in Engineering. He is also on the editorial board of the Computer Methods in Applied Mechanics and Engineering, the International Journal of Computational Methods and the International Journal of Computational Engineering Science. He has has written over 160 journal articles, book chapters and has authored two previous books. Dr. Fish specializes in Multiscale Science and Engineering with applications to aerospace, automotive industry, civil engineering, biological and material sciences.
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