Gareth P. Parry

Kinematics and mechanics of defective crystals

The project is to investigate the kinematics and mechanics of some specific crystals with smooth distributions of defects. The particular defect distributions that we will consider are selected so that the following properties hold;

• the (continuum) dislocation density tensor is constant throughout the body.
• the iteration that derives from the (continuum) lattice vectors produces sets of points such that there is a finite minimum distance between those points.
• the sets of points produced in this way are generated by lattice vectors which are small (in a precise sense).

These assumptions restrict the dislocation density quite severely, to the extent that crystal states with the same defect densities are related to each other in a manner which may be correlated with basic kinematical ideas in classical plasticity theory. In fact, for such states, one has available rigorous notions of intermediate configuration, and the slip mechanism emerges in abstract fashion as the class of changes of state that preserves defectiveness.

The intention is to develop the mechanics of such crystals using recent ideas about configurational forces, etc..