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E-raamat: Numerical Modeling in Materials Science and Engineering

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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.

Arvustused

From the reviews:





"The book offers an impressive and excellent overview of a large variety of important aspects in the broad field of numerical modelling in material science and engineering. The authors included many meaningful and scientifically interesting examples. These are very valuable not only for students but also for the advanced computationally-oriented reader interested looking into new areas of research. To conclude, the book is highly recommendable to advanced students as well as scientists in the fields of engineering and material science." (Technische Mechanik, Vol. 24 (3-4), 2004)

"The book under review is devoted to the numerical simulation and modeling in (especially) materials science and engineering. It aims at familiarizing the materials scientists and engineers with the numerical methods and techniques that are state-of-the-art in this subject. this is a well written and well-organized reference book that will hopefully prove to be indispensable, especially for those materials scientists and engineers whose investigations make use of the various numerical methods and techniques developed in this book." (HM Srivastava, Applied Mechanics Reviews, Vol. 56 (6), November, 2003)

"This book is essentially devoted to numerical simulation and modeling in engineering and materials science. this book is written to meet the needs of a textbook at the undergraduate and graduate levels in materials science and engineering. It may also be useful for researchers and engineering professionals who are interested in numerical methods, numerical simulation and modeling in engineering and materials science. Summarizing, this book is an important addition to the literature on material science." (L. Debnath, Zentralblatt MATH, Vol. 1024, 2003)

"This book is devoted to numerical simulation and modeling in materials science and engineering. The aim of the monograph is to acquaint the materials science student orthe engineer with the numerical methods which are state-of-the-art in this subject . The book is written at an introductory level and goes directly to the point. It should be recommended to students in material science and engineers who are either new in this field or want to get acquainted with numerical methods." (Jean-Luc Guermond, Mathematical Reviews, 2003 h)

This is a carefully constructed introduction to the techniques and applications of numerical modelling in materials science and engineering. The layout of the text is clear and the order of presentation of material is logical. The advantage, of course, is that the book will survive changes in programming languages and fashions, and hold its value both as a textbook for undergraduates and graduates and as a reference. (A. H. Harker, Contemporary Physics, February, 2012)

Muu info

Springer Book Archives
Preface VII
Chapter 1 Continuous Media 1(46)
1.1 Objectives
1(1)
1.2 Conservation and Continuity Equations
2(23)
1.3 Constitutive Equations
25(10)
1.4 Boundary and Initial conditions
35(9)
1.5 Exercises
44(1)
1.6 Bibliography
45(2)
Chapter 2 The Finite Difference Method 47(46)
2.1 Objectives
47(1)
2.2 One Dimensional Case
48(20)
2.3 Two Dimensional Problems
68(13)
2.4 Some Other Aspects of FDM
81(8)
2.5 Example
89(2)
2.6 Exercises
91(1)
2.7 Bibliography
92(1)
Chapter 3 The Finite Element Method 93(56)
3.1 Objectives
93(1)
3.2 General Principles: Geometric Discretization and Integration
94(17)
3.3 Obtaining and Discretizing the Integral Form for a Scalar Problem: a Chemical Diffusion Example
111(6)
3.4 Solution of a Vector Problem: Mechanical Equilibrium Example
117(12)
3.5 Implementation
129(10)
3.6 Non Stationary Problems
139(7)
3.7 Exercises
146(1)
3.8 Bibliography
147(2)
Chapter 4 Elements Of Numerical Algorithms 149(58)
4.1 Objectives
149(1)
4.2 Methods for Generating Meshes
150(23)
4.3 Solution Methods for Linear Systems
173(16)
4.4 Storage of Matrices in Memory
189(9)
4.5 Non Linear Problems
198(6)
4.6 Exercises
204(1)
4.7 Bibliography
205(2)
Chapter 5 Phase Transformations 207(80)
5.1 Objectives
207(1)
5.2 State Equations
208(32)
5.3 Initial and Boundary Conditions
240(13)
5.4 Numerical Treatment
253(13)
5.5 Examples
266(18)
5.6 Exercises
284(1)
5.7 Bibliography
285(2)
Chapter 6 Deformation Of Solids 287(78)
6.1 Objectives
287(1)
6.2 Constitutive Equations
287(23)
6.3 Boundary Conditions
310(8)
6.4 Numerical Treatment
318(14)
6.5 Examples
332(30)
6.6 Exercises
362(1)
6.7 Bibliography
363(2)
Chapter 7 Incompressible Fluid Flow 365(82)
7.1 Objectives
365(1)
7.2 Constitutive Equations
366(14)
7.3 Boundary and Initial Conditions
380(7)
7.4 Numerical Treatment of the Navier-Stokes Problem
387(36)
7.6 Examples
423(19)
7.7 Exercises
442(2)
7.8 Bibliography
444(3)
Chapter 8 Inverse Methods 447(30)
8.1 Objectives
447(1)
8.2 A Simple Linear One Dimensional Problem
448(4)
8.3 A Non Linear One Dimensional Problem
452(5)
8.4 Inverse Method with Time Independent Parameters
457(7)
8.5 Inverse Method with Time Dependent Parameters
464(4)
8.6 Examples
468(5)
8.7 Exercises
473(2)
8.8 Bibliography
475(2)
Chapter 9 Stochastic Methods 477(40)
9.1 Objectives
477(1)
9.2 Generation of Random Numbers
478(7)
9.3 Integration by Stochastic Methods
485(3)
9.4 Solution of Systems of Equations
488(4)
9.5 Monte Carlo Method
492(6)
9.6 Random Walkers Method
498(8)
9.7 Cellular Automata Method
506(4)
9.8 Examples
510(4)
9.9 Exercises
514(1)
9.10 Bibliography
515(2)
Chapter 10 Appendices 517(18)
10.1 Table of Symbols
517(4)
10.2 Vector Calculus
521(4)
10.3 Gauss Integration Method
525(6)
10.4 Non Dimensional Numbers
531(1)
10.5 Interpretation of the Terms of the Elementary Stiffness Matrix for a Diffusion Problem on a Triangular Linear Finite Element
532(3)
Index 535