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@MISC{,
            author = {Anguige, K. and Dondl, P. and Kruž{\'{\i}}k, Martin},
             title = {ON THE EXISTENCE OF MINIMISERS FOR STRAIN-GRADIENT SINGLE-CRYSTAL PLASTICITY},
              year = {2017},
          abstract = {We prove the existence of minimisers for a family of models related to the singleslip-
to-single-plane relaxation of single-crystal, strain-gradient elastoplasticity with Lp-hardening
penalty. In these relaxed models, where only one slip-plane normal can be activated at each material
point, the main challenge is to show that the energy of geometrically necessary dislocations
is lower-semicontinuous along bounded-energy sequences which satisfy the single-plane condition,
meaning precisely that this side condition should be preserved in the weak Lp-limit. This is done
with the aid of an `exclusion' lemma of Conti & Ortiz, which essentially allows one to put a lower
bound on the dislocation energy at interfaces of (single-plane) slip patches, thus precluding ne
phase-mixing in the limit. Furthermore, using div-curl techniques in the spirit of Mielke & Muller,
we are able to show that the usual multiplicative decomposition of the deformation gradient into
plastic and elastic parts interacts with weak convergence and the single-plane constraint in such a
way as to guarantee lower-semicontinuity of the (polyconvex) elastic energy, and hence the total
elasto-plastic energy, given sucient (p > 2) hardening, thus delivering the desired result.},
  Preprint project = {NCMM},
     Preprint year = {2017},
   Preprint number = {01},
       Preprint ID = {NCMM/2017/01}
}