Thermomechanics of Evolving Phase Boundaries in the Plane

Erscheinungsjahr 1993
ISBN: 978-0-19-853694-9
Verlag: OUP Oxford

Buch, Englisch, 160 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 417 g

This book is one of the very first on the subject of mathematical materials science and presents a view different from that prevalent in the physical literature. Issues foundational in nature are stressed with the emphasis on the interplay between mathematics and physics. It discusses the dynamics of two-phase systems within the framework of modern continuum thermodynamics. Two general theories are considered and the resulting equations exhibit unstable growth patterns. The free boundary problems that form the basis of the subject should be of great interest to mathematicians and physical scientists.

Autoren/Hrsg.

Gurtin, Morton E.

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Werkstoffkunde, Materialwissenschaft: Forschungsmethoden
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Materialwissenschaft: Verbundwerkstoffe
• Naturwissenschaften Physik Thermodynamik

Inhaltsverzeichnis

- Introduction

- Part I: Kinematics

- 1: Curves

- 1.1: Preliminary definitions

- 1.2: Convex curves

- 1.3: Integrals

- 1.4: Piecewise-smooth curves

- 1.5: Infinitesimally wrinkled curves

- 2: Evolving curves

- 2.1: Definitions

- 2.2: Transport identities

- 2.3: Integral identities

- 2.4: Steadily evolving interfaces

- 2.5: Piecewise-smooth evolving curves

- 2.6: Variational lemmas

- 3: Phase regions, control volumes, and inflows

- 3.1: Phase regions and control volumes

- 3.2: Inflows, the pillbox lemma, and infinitesimally thin evolving control volumes

- Part II: Mechanical theory of interfacial evolution

- 4: Balance of forces

- 4.1: Balances of forces

- 4.2: The power identity

- 5: Energetics and the dissipation inequality

- 6: Constitutive theory

- 6.1: Constitutive equations and the compatibility theorem

- 6.2: Balance of capillary forces revisited; corners

- 7: Digression: Statistical theory of interfacial stability; convexity, the Frank diagram, and corners; Wulff regions

- 7.1: Preliminaries; Polar diagrams

- 7.2: Convexity; the extended and convexified energies, and the Frank diagram

- 7.3: Stability

- 7.4: Instability of the total energy

- 7.5: Equilibria of the total energy; Wulff regions

- 7.6: Wulff's theorem

- 8: Evolution equations for the interface: basic assumptions

- 8.1: Isotropic interface

- 8.2: Anisotropic interface

- 8.2.1: Basic equations

- 8.2.2.: Equations when the interface is the graph of a function

- 8.2.3: Equations when the interface is a level set

- 8.3: Plan of the next few chapters

- 9: Stationary interfaces and steadily evolving interfaces

- 9.1: Stationary interfaces

- 9.2: Steadily evolving facets

- 9.3: Steadily evolving interfaces that are not flat

- 10: Global behaviour for an interface with stable energy

- 10.1: Existence of evolving interfaces from a prescribed initial curve

- 10.2: Growth and decay of the interface

- 10.3: Evolution of curvature; fingers

- 11: Unstable interfacial energies and interfaces with corners

- 11.1: Admissibility; corner conditions

- 11.2: The initial-value problem

- 11.3: Facets and wrinklings that connect evolving curves

- 11.4: Equations near a corner when the curve is a graph

- 11.5: Interfaces with arbitrary angle-set; infinitesimal wrinklings

- 11.6: Stationary interfaces and steadily evolving interfaces with corners

- 12: Non smooth interfacial energies: crystalline energies

- 12.1: Crystalline energies

- 12.2: The Wulff region

- 12.3: The capillary force at preferred orientations

- 12.4: Corners between preferred facets

- 12.5: Crystalline motions

- 12.6: Interfaces of arbitrary orientation, infinitesimal wrinklings, and generalized motions

- 12.7: Evolution of a rectangular crystal

- 13: Regularized theory for smooth unstable energies; dependence of interfacial energy on curvature

- 13.1: Balance of forces and moments; power

- 13.2: Energetics and the dissipation inequality

- 13.3: Constitutive equations

- 13.4: Evolution equations for the interface

- 13.5: Linearized equations; spinodal decomposition on the interface

- Part III: Thermodynamical theory of interfacial evolution in the presence of bulk heat conduction

- 14: Review of single-phase thermodynamics

- 14.1: Basic equations and the first two laws

- 14.2: Constitutive equations and thermodynamic restrictions

- 14.3: The heat equation

- 15: Thermodynamics of two-phase systems

- 15.1: Basic quantities and the first two laws

- 15.2: Local forms of the interfacial laws

- 16: Constitutive theory

- 16.1: Constituive equations for the bulk material

- 16.2: The transition temperature

- 16.3: Constitutive equations for the interface

- 17: Free-boundary problems

- 17.1: Bulk equations and interface conditions

- 17.2: Initial conditions and boundary conditions

- 17.3: Free-boundary problems near the transition temperature for weak surfaces

- 17.3.1: Approximate interface conditions

- 17.3.2: Approximate free-boundary problems

- 17.3.3: The first two laws for the approximate theories

- 17.3.4: Growth theorems

- 17.3.5: Perfect conductors

- 18: Instabilities induced by supercooling the liquid phase

- 18.1: The one-dimensional problem: growth of the solid phase

- 18.2: Instability of a flat interface

- References

- Index