On the characterization of geometrically necessary dislocations in finite plasticity

We develop a general theory of geometrically necessary dislocations based on the decomposition F = (FFp)-F-e. The incompatibility of F-e and that of F-p are characterized by a single tenser G giving the Burgers vector, measured and reckoned per unit area in the microstructural (intermediate) configuration. We show that G may be expressed in terms of F-p and the referential curl of F-p. Or equivalently in terms of Fe-1 and the spatial curl of Fe-1. We derive explicit relations for G in terms of Euler angles for a rigid-plastic material and - without neglecting elastic strains - for strict plane strain and strict anti-plane shear. We discuss the relationship between G and the distortion of microstructural planes. We show that kinematics alone yields a balance law for the transport of geometrically necessary dislocations. (C) 2001 Published by Elsevier Science Ltd.