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Tables of Contents for Numerical Modeling in Materials Science and Engineering
Chapter/Section Title
Page #
Page Count
Preface
vii
 
Continuous Media
1
46
Objectives
1
1
Conservation and Continuity Equations
2
23
Constitutive Equations
25
10
Boundary and Initial conditions
35
9
Exercises
44
1
Bibliography
45
2
The Finite Difference Method
47
46
Objectives
47
1
One Dimensional Case
48
20
Two Dimensional Problems
68
13
Some Other Aspects of FDM
81
8
Example
89
2
Exercises
91
1
Bibliography
92
1
The Finite Element Method
93
56
Objectives
93
1
General Principles: Geometric Discretization and Integration
94
17
Obtaining and Discretizing the Integral Form for a Scalar Problem: a Chemical Diffusion Example
111
6
Solution of a Vector Problem: Mechanical Equilibrium Example
117
12
Implementation
129
10
Non Stationary Problems
139
7
Exercises
146
1
Bibliography
147
2
Elements of Numerical Algorithms
149
58
Objectives
149
1
Methods for Generating Meshes
150
23
Solution Methods for Linear Systems
173
16
Storage of Matrices in Memory
189
9
Non Linear Problems
198
6
Exercises
204
1
Bibliography
205
2
Phase Transformations
207
80
Objectives
207
1
State Equations
208
32
Initial and Boundary Conditions
240
13
Numerical Treatment
253
13
Examples
266
18
Exercises
284
1
Bibliography
285
2
Deformation of Solids
287
78
Objectives
287
1
Constitutive Equations
287
23
Boundary Conditions
310
8
Numerical Treatment
318
14
Examples
332
30
Exercises
362
1
Bibliography
363
2
Incompressible Fluid Flow
365
82
Objectives
365
1
Constitutive Equations
366
14
Boundary and Initial Conditions
380
7
Numerical Treatment of the Navier-Stokes Problem
387
36
Examples
423
19
Exercises
442
2
Bibliography
444
3
Inverse Methods
447
30
Objectives
447
1
A Simple Linear One Dimensional Problem
448
4
A Non Linear One Dimensional Problem
452
5
Inverse Method with Time Independent Parameters
457
7
Inverse Method with Time Dependent Parameters
464
4
Examples
468
5
Exercises
473
2
Bibliography
475
2
Stochastic Methods
477
40
Objectives
477
1
Generation of Random Numbers
478
7
Integration by Stochastic Methods
485
3
Solution of Systems of Equations
488
4
Monte Carlo Method
492
6
Random Walkers Method
498
8
Cellular Automata Method
506
4
Examples
510
4
Exercises
514
1
Bibliography
515
2
Appendices
517
18
Table of Symbols
517
4
Vector Calculus
521
4
Gauss Integration Method
525
6
Non Dimensional Numbers
531
1
Interpretation of the Terms of the Elementary Stiffness Matrix for a Diffusion Problem on a Triangular Linear Finite Element
532
3
Index
535