Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben

2003 | Buch

Continuous Media Kapitel lesen Erstes Kapitel lesen

Numerical Modeling in Materials Science and Engineering

verfasst von: Michel Rappaz, Michel Bellet, Michel Deville

Verlag: Springer Berlin Heidelberg

Buchreihe : Springer Series in Computational Mathematics

Enthalten in: Professional Book Archive

Einloggen, um Zugang zu erhalten
insite
SUCHEN

Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Continuous Media
Abstract
Introduce the equations of conservation of mass, momentum, energy and solute. Introduce the principal equations for materials behavior, which will be developed in depth in chapters 5 through 7. Define the boundary conditions and initial conditions.
Michel Rappaz, Michel Bellet, Michel Deville
Chapter 2. The Finite Difference Method
Abstract
Illustrate the concept of the finite difference method for the simple one dimensional case of solute diffusion, with and without advective transport, for both stationary and non stationary cases. Generalize the concept of the finite difference method for two and three dimensional geometries. Show how the boundary and initial conditions are applied. Establish a link between the finite difference method and the similar finite volume and direct finite difference methods. Give an idea of the extension of the method to more complicated cases (non-Cartesian coordinate systems, alternating direction implicit method).
Michel Rappaz, Michel Bellet, Michel Deville
Chapter 3. The Finite Element Method
Abstract
Show the basic principles of the discretization of space using finite elements. Establish the means to obtain the integral forms of the conservation equations and to discretize them. Develop some aspects of the treatment of non stationary problems; non linear problems are dealt with in chapter 4.
Michel Rappaz, Michel Bellet, Michel Deville
Chapter 4. Elements of Numerical Algorithms
Abstract
Present the main algorithms for mesh generation. Introduce the basic methods for the solution of linear systems and the storage of matrices in memory. Describe the different techniques to treat non linear problems.
Michel Rappaz, Michel Bellet, Michel Deville
Chapter 5. Phase Transformations
Abstract
Review the concepts of phase diagrams and the equilibrium conditions that apply at an interface between two phases. Introduce the different scales of a process and the local transformation path concept. Derive the average continuity equations for two phases. Describe the convection and radiation contributions that intervene in hear transfer phenomena. Present the numerical methods for tracking an interface and those related to the average equations. Apply these methods to the modelling of processes and the calculation of microstructures.
Michel Rappaz, Michel Bellet, Michel Deville
Chapter 6. Deformation of Solids
Abstract
Introduce the concepts of irreversible deformations of continuous solid media: the plasticity criterion and the law of plastic flow. Review the constitutive equations for elastoplastic, elasto-viscoplastic and pure viscoplastic materials. Present the unilateral contact conditions and the main friction laws. Introduce the principal characteristics of the numerical treatment of the equilibrium equations.
Michel Rappaz, Michel Bellet, Michel Deville
Chapter 7. Incompressible Fluid Flow
Abstract
Establish the mathematical model of the problem being studied. In Particular, we will introduce the concept of the constitutive equation for a fluid, that is, the relation linking the stress tensor and the velocity gradients. The initial conditions for dynamic cases and the boundary conditions will also be discussed. Discuss the discretization methods for the numerical treatment of the mathematical model. Concentrating on the “velocity-pressure” formulation which is the most appropriate for the general treatment of three dimensional problems, we will present the finite difference and finite element discretization methods. As the advection terms are often dominant in these equations, we will be particularly interested in the upwind schemes. Propose a few applications as examples in order to illustrate the implementation of the proposed methods.
Michel Rappaz, Michel Bellet, Michel Deville
Chapter 8. Inverse Methods
Abstract
Describe the general principles of inverse methods with simple examples. Show the equivalence of inverse methods and the common least squares method. Extend the principle of the method to more complex situations.
Michel Rappaz, Michel Bellet, Michel Deville
Chapter 9. Stochastic Methods
Abstract
Introduce the concepts of distribution and generation of random numbers. Apply the method of random number generation to the integration of a function and the solution of a linear system of equations by Markov chains. Present the Monte Carlo method, the Ising and Potts models, and a few applications in materials science. Introduce the concept of random walkers for treating diffusion and aggregation problems. Give a general idea of deterministic and stochastic cellular automata methods.
Michel Rappaz, Michel Bellet, Michel Deville
Chapter 10. Appendices
Michel Rappaz, Michel Bellet, Michel Deville
Backmatter
Metadaten
Titel
Numerical Modeling in Materials Science and Engineering
verfasst von
Michel Rappaz
Michel Bellet
Michel Deville
Copyright-Jahr
2003
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-11821-0
Print ISBN
978-3-642-11820-3
DOI
https://doi.org/10.1007/978-3-642-11821-0