Because of its overwhelming pervasiveness and high-stakes impact on the mechanical performance of structures made of inorganic and live matter alike (bridges, airplanes, bones, ligaments,...), fracture has attracted the attention of humans, researchers and laymen the same, for centuries.
In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deformation gradient into elastic and plastic parts, we use Cartan's moving frames to describe the distorted lattice structure via differential 1-forms. In this theory the primary fields are the dislocation fields, defined as a collection of differential 2-forms. The defect content of the lattice structure is then determined by the super
Al Fin