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

Asymptotic analysis of single-slip crystal plasticity in the limit of vanishing thickness and rigid elasticity