ON THE DETERMINATION OF THE CRYSTAL REFERENCE IN NONLINEAR CONTINUUM THEORY OF DISLOCATIONS

The paper is concerned with the determination of the anholonomic cryst al reference from the given elastic strain (metric) and dislocation de nsity (Cartan torsion). The incompatible inverse elastic deformation i s shown to satisfy a system of linear first order differential equatio ns. The integrability condition requires that the curvature of the cry stal connection should vanish. The equivalent system of equations and integrability condition for the inverse elastic rotation are also obta ined. Formulae for the inverse elastic deformation and the inverse ela stic rotation in form of tensor series are derived. The dual problem o f determining the plastic deformation and the plastic rotation from th e plastic strain and the dislocation density is solved in a similar ma nner. A linearization procedure is carried out and a comparison with K roner's theory is provided.