A model for twinning

Abstract

The modelling of twins in crystals with strain gradient theories provides interesting problems both in thermodynamics and in the calculus of variations. Here, Dunn and Serrin's thermomechanical theory of interstitial working is used to obtain a variational principle that governs the equilibria of materials with non-convex Helmholtz free energy. In some geometries, this principle reduces to a novel calculus of variations problem; an example is described in which symmetry-related uniform equilibrium states can be connected by nonconstant extremals which realise local minima of the free energy. Certain implications of different definitions of local minima are also discussed.

Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions

“…To set our analysis in the proper context, we briefly review the modelling of phase transition in solids based on minimisation of the energy /, /(«) = f W(Vu) dx (1.2) (see for instance [27,5]). If the material occurs in several phases, then W has several local minimia.…”