Numerical modeling in materials science and engineering / Michel Rappaz, Michel Bellet, Michel Deville ; translated by Ray Snyder.

Format:

Book

Author/Creator:

Rappaz, Michel.

Contributor:

Rappaz, Michel.

Bellet, Michel, 1960-

Deville, M. O. (Michel O.)

Series:

Springer series in computational mathematics ; 32.

Springer series in computational mathematics ; 32

Standardized Title:

Modélisation numérique en science et génie des matériaux. English

Language:

English

French

Subjects (All):

Materials science--Mathematical models.

Materials science.

Engineering--Mathematical models.

Engineering.

Mathematical models.

Physical Description:

xi, 540 pages : illustrations ; 24 cm.

Place of Publication:

Berlin ; New York : Springer-Verlag, [2003]

Language Note:

Translated from the French.

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.

Contents:

Chapter 1 Continuous Media 1

1.2 Conservation and Continuity Equations 2

1.3 Constitutive Equations 25

1.4 Boundary and Initial conditions 35

Chapter 2 The Finite Difference Method 47

2.2 One Dimensional Case 48

2.3 Two Dimensional Problems 68

2.4 Some Other Aspects of FDM 81

Chapter 3 The Finite Element Method 93

3.2 General Principles: Geometric Discretization and Integration 94

3.3 Obtaining and Discretizing the Integral Form for a Scalar Problem: a Chemical Diffusion Example 111

3.4 Solution of a Vector Problem: Mechanical Equilibrium Example 117

3.5 Implementation 129

3.6 Non Stationary Problems 139

Chapter 4 Elements of Numerical Algorithms 149

4.2 Methods for Generating Meshes 150

4.3 Solution Methods for Linear Systems 173

4.4 Storage of Matrices in Memory 189

4.5 Non Linear Problems 198

Chapter 5 Phase Transformations 207

5.2 State Equations 208

5.3 Initial and Boundary Conditions 240

5.4 Numerical Treatment 253

Chapter 6 Deformation of Solids 287

6.2 Constitutive Equations 287

6.3 Boundary Conditions 310

6.4 Numerical Treatment 318

Chapter 7 Incompressible Fluid Flow 365

7.2 Constitutive Equations 366

7.3 Boundary and Initial Conditions 380

7.4 Numerical Treatment of the Navier-Stokes Problem 387

Chapter 8 Inverse Methods 447

8.2 A Simple Linear One Dimensional Problem 448

8.3 A Non Linear One Dimensional Problem 452

8.4 Inverse Method with Time Independent Parameters 457

8.5 Inverse Method with Time Dependent Parameters 464

Chapter 9 Stochastic Methods 477

9.2 Generation of Random Numbers 478

9.3 Integration by Stochastic Methods 485

9.4 Solution of Systems of Equations 488

9.5 Monte Carlo Method 492

9.6 Random Walkers Method 498

9.7 Cellular Automata Method 506

10.2 Vector Calculus 521

10.3 Gauss Integration Method 525

10.4 Non Dimensional Numbers 531

10.5 Interpretation of the Terms of the Elementary Stiffness Matrix for a Diffusion Problem on a Triangular Linear Finite Element 532.

Notes:

Includes bibliographical references and index.

ISBN:

3540426760

OCLC:

50684704