This 2006 work began with the author''s exploration of the
applicability of the finite deformation theory of elasticity when
various standard assumptions such as convexity of various energies
or ellipticity of the field equations of equilibrium are
relinquished. The finite deformation theory of elasticity turns out
to be a natural vehicle for the study of phase transitions in
solids where thermal effects can be neglected. This text will be of
interest to those interested in the development and application of
continuum-mechanical models that describe the macroscopic response
of materials capable of undergoing stress- or temperature-induced
transitions between two solid phases. The focus is on the evolution
of phase transitions which may be either dynamic or quasi-static,
controlled by a kinetic relation which in the framework of
classical thermomechanics represents information that is
supplementary to the usual balance principles and constitutive laws
of conventional theory.
目錄:
Part I. Introduction: 1. What this monograph is about
2. Some experiments
3. Continuum mechanics
4. Quasilinear systems
5. Outline of monograph
Part II. Two-Well Potentials, Governing Equations and Energetics:
1. Introduction
2. Two-phase nonlinearly elastic materials
3. Field equations and jump conditions
4. Energetics of motion, driving force and dissipation
inequality
Part III. Equilibrium Phase Mixtures and Quasistatic Processes: 1.
Introduction
2. Equilibrium states
3. Variational theory of equilibrium mixtures of phases
4. Quasistatic processes
5. Nucleation and kinetics
6. Constant elongation rate processes
7. Hysteresis
Part IV. Impact-Induced Transitions in Two-Phase Elastic Materials:
1. Introduction
2. The impact problem for trilinear two-phase materials
3. Scale-invariant solutions of the impact problem
4. Nucleation and kinetics
5. Comparison with experiment
6. Other types of kinetic relations
7. Related work
Part V. Multiple-Well Free Energy Potentials: 1. Introduction
2. Helmholtz free energy potential
3. Potential energy function and the effect of stress
4. Example 1: the van der Waals fluid
5. Example 2: two-phase martensitic material with cubic and
tetragonal phases
Part VI. The Continuum Theory of Driving Force: 1.
Introduction
2. Balance laws, field equations and jump conditions
3. The second law of thermodynamics and the driving force
Part VII. Thermoelastic Materials: 1. Introduction
2. The thermoelastic constitutive law
3. Stability of a thermoelastic material
4. A one-dimensional special case: uniaxial strain
Part VIII. Kinetics and Nucleation: 1. Introduction
2. Nonequilibrium processes, thermodynamic fluxes and forces,
kinetic relation
3. Phenomenological examples of kinetic relations
4. Micromechanically-based examples of kinetic relations
5. Nucleation
Part IX. Models for Two-Phase Thermoelastic Materials in One
Dimension: 1. Preliminaries
2. Materials of Mie-Gruneisen type
3. Two-phase Mie-Gruneisen materials
Part X. Quasistatic Hysteresis in Two-Phase Thermoelastic Tensile
Bars: 1. Preliminaries
2. Thermomechanical equilibrium states for a two-phase
material
3. Quasistatic processes
4. Trilinear thermoelastic material
5. Stress cycles at constant temperature
6. Temperature cycles at constant stress
7. The shape-memory cycle
8. The experiments of Shaw and Kyriakides
9. Slow thermomechanical processes
Part XI. Dynamics of Phase Transitions in Uniaxially Strained
Thermoelastic Solids: 1. Introduction
2. Uniaxial strain in adiabatic thermoelasticity
3. The impact problem
Part XII. Statics: Geometric Compatibility: 1. Preliminaries
2. Examples
Part XIII. Dynamics: Impact-Induced Transition in a CuA1Nl Single
Crystal: 1. Introduction
2. Preliminaries
3. Impact without phase transformation
4. Impact with phase transformation
5. Application to austenite-B1 martensite transformation in
CuA1Nl
Part XIV. Quasistatics: Kinetics of Martensitic Twinning: 1.
Introduction
2. The material and loading device
3. Observations
4. The model
5. The energy of the system
6. The effect of the transition layers: further observations
7. The effect of the transition layers: further modeling
8. Kinetics.