Optimal energy scaling for a shear experiment in singlecrystal plasticity with crosshardening
Abstract
Consideration is given to a nonconvex variational model for a shear experiment in the framework of singlecrystal linearised plasticity with infinite crosshardening. The rectangular shear sample is clamped at each end and is subjected to a prescribed horizontal or diagonal shear, modelled by an appropriate hard Dirichlet condition. We ask `How much energy is required to impose such a shear?' and `How does it depend on the aspect ratio?' Assuming that just two slip systems are active, we show that there is a critical aspect ratio, above which the energy is strictly positive, and below which it is zero. Furthermore, in the respective regimes determined by the aspect ratio, we prove energyscaling bounds, expressed in terms of the amount of prescribed shear.
 Publication:

Zeitschrift Angewandte Mathematik und Physik
 Pub Date:
 October 2014
 DOI:
 10.1007/s0003301303790
 arXiv:
 arXiv:1304.7377
 Bibcode:
 2014ZaMP...65.1011A
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 24 pages, 17 figures, to appear in Zeitschrift fuer angewandte Mathematik und Physik (ZAMP). Comments on mollification in intro adjusted. Comment on lamination above Thm 3.1 corrected