Evolution of Phase Transitions : A Continuum Theory

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.