Presented was a general theoretical framework capable of describing the finite deformation kinematics of several classes of defects prevalent in metallic crystals. The treatment relied upon powerful tools from differential geometry, including linear connections and covariant differentiation, torsion, curvature and anholonomic spaces. A length scale-dependent 3-term multiplicative decomposition of the deformation gradient was suggested, with terms representing recoverable elasticity, residual lattice deformation due to defect fields, and plastic deformation resulting from defect fluxes. Also proposed was an additional micromorphic variable representing additional degrees-of-freedom associated with rotational lattice defects (i.e. disclinations), point defects, and most generally, Somigliana dislocations. It was demonstrated how particular implementations of the general framework subsumed notable published theories and particular versions of the framework were classified using geometric terminology.

A Geometric Framework for the Kinematics of Crystals with Defects. J.D.Clayton, D.J.Bammann, D.L.McDowell: Philosophical Magazine, 2005, 85[33-35], 3983-4010