Some three–dimensional problems related to dielectric breakdown and polycrystal plasticity
The well-known Sachs and Taylor bounds provide easy inner and outer estimates for the effective yield set of a polycrystal. It is natural to ask whether they can be improved. We examine this question for two model problems, involving three-dimensional gradients and divergence-free vector fields. For...
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| Veröffentlicht in: | Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2003-10, Vol.459 (2038), p.2613-2625 |
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| container_issue | 2038 |
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| container_title | Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences |
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| creator | Garroni, Adriana Kohn, Robert V. |
| description | The well-known Sachs and Taylor bounds provide easy inner and outer estimates for the effective yield set of a polycrystal. It is natural to ask whether they can be improved. We examine this question for two model problems, involving three-dimensional gradients and divergence-free vector fields. For three-dimensional gradients, the Taylor bound is far from optimal: we derive an improved estimate that scales differently when the yield set of the basic crystal is highly eccentric. For three-dimensional divergence-free vector fields, the Taylor bound may not be optimal, but it has the optimal scaling law. In both settings, the Sachs bound is optimal. |
| doi_str_mv | 10.1098/rspa.2003.1152 |
| format | Article |
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| ispartof | Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, 2003-10, Vol.459 (2038), p.2613-2625 |
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| language | eng |
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| source | Jstor Complete Legacy; Alma/SFX Local Collection; JSTOR Mathematics & Statistics |
| subjects | Crystals Cubes Cylinders Determinants Dielectric Breakdown Dielectric materials Gradient fields Homogenization Nonlinear Homogenization Polycrystal Plasticity Polycrystals Power laws Sachs Bound Taylor Bound Vector fields |
| title | Some three–dimensional problems related to dielectric breakdown and polycrystal plasticity |
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