**3. Plasticity framework**

We begin this section with the kinematic definitions of crystal-plasticity theory, citing the basic equations. The kinematic development of a single-crystal plasticity model has been well documented by several authors and is the subject of recent works (Kocks et al., 1998; Roters et al., 2010). Here we assume that, during plastic forming operations, it is possible to neglect the elastic contribution to deformation. Consequently, we will restrict ourselves to a rate-dependent plastic response at the single-crystal level.
