Invertible structured deformations and the geometry of multiple slip in single crystals

Invertible structured deformations are employed to derive the basic kinematical relations of crystalline plasticity without the use of an intermediate configuration. All of the quantities appearing in these relations have definite geometrical interpretations in terms of either smooth or non-smooth geometrical changes (disarrangements) occuring at macroscopic or sub-macroscopic length scales. For f.c.c. crystals, the kinematical relations are valid for each family of invertible structured deformations. For other single crystals, an appropriate collection of invertible structured deformations is identified and the validity of the kinematical relations is established within this (possibly smaller) collection.