Abstract
Consideration is given to a non-convex variational model for a shear experiment in the framework of single-crystal linearised plasticity with infinite cross-hardening. 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 energy-scaling bounds, expressed in terms of the amount of prescribed shear.
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Anguige, K., Dondl, P. Optimal energy scaling for a shear experiment in single-crystal plasticity with cross-hardening. Z. Angew. Math. Phys. 65, 1011–1030 (2014). https://doi.org/10.1007/s00033-013-0379-0
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DOI: https://doi.org/10.1007/s00033-013-0379-0