Scaling relation for low energy states in a single‐slip model in finite crystal plasticity

We derive a scaling‐relation, for the infimum of the energy for small ϵ,δ > 0, where p, q ≥ 1, u: Ω → ℝ 2 is a deformation with suitable affine boundary conditions and γ: Ω → ℝ is a suitable slip variable. This model is motivated by a two‐dimensional single‐slip model in finite crystal plasticity. We show, that the infimum of the energy J ϵ,δ scales as . This scaling‐relation is attained by an asymptotically self‐similar branching construction.