This chapter provides a brief introduction to the following basic ideas pertaining to thermoelastic phase transitions: the lattice theory of martensite, phase boundaries, energy minimization, Weierstrass-Erdmann corner conditions, phase equilibrium, nonequilibrium processes, hysteresis, the notion of driving force, dynamic phase transitions, nonuniqueness, kinetic law, nucleation condition, and microstructure.

Introduction

This chapter provides an introduction to some basic ideas associated with the modeling of solid-solid phase transitions within the continuum theory of finite thermoelasticity. No attempt is made to be complete, either in terms of our selection of topics or in the depth of coverage. Our goal is simply to give the reader a flavor for some selected ideas.

This subject requires an intimate mix of continuum and lattice theories, and in order to describe it satisfactorily one has to draw on tools from crystallography, lattice dynamics, thermodynamics, continuum mechanics and functional analysis. This provides for a remarkably rich subject which in turn has prompted analyses from various distinct points of view. The free-energy function has multiple local minima, each minimum being identified with a distinct phase, and each phase being characterized by its own lattice Crystallography plays a key role in characterizing the lattice structure and material symmetry, and restricts deformations through geometric compatibility. The thermodynamics of irreversible processes provides the framework for describing evolutionary processes. Lattice dynamics describes the mechanism by which the material transforms from one phase to the other. And eventually all of this needs to be described at the continuum scale.