  We perform via $\Gamma$-convergence a 2d-1d dimension reduction analysis of a
single-slip elastoplastic body in large deformations. Rigid plastic and
elastoplastic regimes are considered. In particular, we show that limit
deformations can essentially freely bend even if subjected to the most
restrictive constraints corresponding to the elastically rigid single-slip
regime. The primary challenge arises in the upper bound where the differential
constraints render any bending without incurring an additional energy cost
particularly difficult. We overcome this obstacle with suitable non-smooth
constructions and prove that a Lavrentiev phenomenon occurs if we artificially
restrict our model to smooth deformations. This issue is absent if the
differential constraints are appropriately softened.
