Numerical modeling in materials science and engineering

Title:

Personal Author:

Rappaz, Michel

Publication Information:

Berlin, Germany : Springer-Verlag, 2003

ISBN:

9783540426769

Subject Term:

Materials science -- Mathematics

Engineering -- Mathematical models

Added Author:

Bellet, Michel

Deville, Michel

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010029180	TA403 R36 2003	Open Access Book	Book	Searching... Unknown

This book introduces the concepts and methodologies related to the modelling of the complex phenomena occurring in materials processing. After a short reminder of conservation laws and constitutive relationships, the authors introduce the main numerical methods: finite differences, finite volumes and finite elements. These techniques are developed in three main chapters of the book that tackle more specific problems: phase transformation, solid mechanics and fluid flow. The two last chapters treat inverse methods to obtain the boundary conditions or the material properties and stochastic methods for microstructural simulation. This book is intended for undergraduate and graduate students in materials science and engineering, mechanical engineering and physics and for engineering professionals or researchers who want to get acquainted with numerical simulation to model and compute materials processing.

Preface	p. VII
Chapter 1 Continuous Media	p. 1
1.1 Objectives	p. 1
1.2 Conservation and Continuity Equations	p. 2
1.3 Constitutive Equations	p. 25
1.4 Boundary and Initial conditions	p. 35
1.5 Exercises	p. 44
1.6 Bibliography	p. 45
Chapter 2 The Finite Difference Method	p. 47
2.1 Objectives	p. 47
2.2 One Dimensional Case	p. 48
2.3 Two Dimensional Problems	p. 68
2.4 Some Other Aspects of FDM	p. 81
2.5 Example	p. 89
2.6 Exercises	p. 91
2.7 Bibliography	p. 92
Chapter 3 The Finite Element Method	p. 93
3.1 Objectives	p. 93
3.2 General Principles: Geometric Discretization and Integration	p. 94
3.3 Obtaining and Discretizing the Integral Form for a Scalar Problem: a Chemical Diffusion Example	p. 111
3.4 Solution of a Vector Problem: Mechanical Equilibrium Example	p. 117
3.5 Implementation	p. 129
3.6 Non Stationary Problems	p. 139
3.7 Exercises	p. 146
3.8 Bibliography	p. 147
Chapter 4 Elements of Numerical Algorithms	p. 149
4.1 Objectives	p. 149
4.2 Methods for Generating Meshes	p. 150
4.3 Solution Methods for Linear Systems	p. 173
4.4 Storage of Matrices in Memory	p. 189
4.5 Non Linear Problems	p. 198
4.6 Exercises	p. 204
4.7 Bibliography	p. 205
Chapter 5 Phase Transformations	p. 207
5.1 Objectives	p. 207
5.2 State Equations	p. 208
5.3 Initial and Boundary Conditions	p. 240
5.4 Numerical Treatment	p. 253
5.5 Examples	p. 266
5.6 Exercises	p. 284
5.7 Bibliography	p. 285
Chapter 6 Deformation of Solids	p. 287
6.1 Objectives	p. 287
6.2 Constitutive Equations	p. 287
6.3 Boundary Conditions	p. 310
6.4 Numerical Treatment	p. 318
6.5 Examples	p. 332
6.6 Exercises	p. 362
6.7 Bibliography	p. 363
Chapter 7 Incompressible Fluid Flow	p. 365
7.1 Objectives	p. 365
7.2 Constitutive Equations	p. 366
7.3 Boundary and Initial Conditions	p. 380
7.4 Numerical Treatment of the Navier-Stokes Problem	p. 387
7.6 Examples	p. 423
7.7 Exercises	p. 442
7.8 Bibliography	p. 444
Chapter 8 Inverse Methods	p. 447
8.1 Objectives	p. 447
8.2 A Simple Linear One Dimensional Problem	p. 448
8.3 A Non Linear One Dimensional Problem	p. 452
8.4 Inverse Method with Time Independent Parameters	p. 457
8.5 Inverse Method with Time Dependent Parameters	p. 464
8.6 Examples	p. 468
8.7 Exercises	p. 473
8.8 Bibliography	p. 475
Chapter 9 Stochastic Methods	p. 477
9.1 Objectives	p. 477
9.2 Generation of Random Numbers	p. 478
9.3 Integration by Stochastic Methods	p. 485
9.4 Solution of Systems of Equations	p. 488
9.5 Monte Carlo Method	p. 492
9.6 Random Walkers Method	p. 498
9.7 Cellular Automata Method	p. 506
9.8 Examples	p. 510
9.9 Exercises	p. 514
9.10 Bibliography	p. 515
Chapter 10 Appendices	p. 517
10.1 Table of Symbols	p. 517
10.2 Vector Calculus	p. 521
10.3 Gauss Integration Method	p. 525
10.4 Non Dimensional Numbers	p. 531
10.5 Interpretation of the Terms of the Elementary Stiffness Matrix for a Diffusion Problem on a Triangular Linear Finite Element	p. 532
Index	p. 535

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