Numerical Modeling in Materials Science and Engineering

by Rappaz, Michel; Bellet, M.; Deville, M.; Snyder, Ray

• ISBN13: 9783540426769
• ISBN10: 3540426760
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: Springer Nature

Summary

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.

Table of Contents

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