ON THE EXISTENCE OF MINIMISERS FOR STRAIN-GRADIENT SINGLE-CRYSTAL PLASTICITY
| Type of publication: | Misc |
| Citation: | |
| 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 |
| Keywords: | |
| Authors | |
| Added by: | [JP] |
| Total mark: | 0 |
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