| Автор | Hill, James, M. |
| Автор | Katoanga, Tui, L. |
| Дата выпуска | 1997 |
| dc.description | For axially symmetric flows of dilatant granular materials, the velocity equations uncouple from the stress equations in certain plastic regimes, and assuming either a plastic potential or dilatant double shearing, a set of three first-order partial differential equations is obtained. These equations turn out to be deceptive, because although they are simple in appearance, the determination of simple exact solutions is nontrivial. For one of the known families of solutions, the authors present a simple and straightforward asymptotic expansion for the stress angle and show that in a restricted range, this expansion provides an accurate solution of the nonlinear ordinary differential equation. In addition, for the same family of solutions, the authors examine a special case that permits one integration and enables the velocity components to be given explicitly in terms of the stress angle. This partial analytical solution may then be coupled either with the asymptotic expansion or with a full numerical solution of the governing first-order differential equation for the stress angle. In addition, the authors show that a special case of the nonlinear ordinary differential equation admits a simple first integral that has not been given previously. Finally, a detailed numerical comparison is made for various parameter values of the asymptotic expansion, the full numerical solution, and with known exact analytical solutions. |
| Издатель | Sage Publications |
| Название | On a Family of Axially Symmetric Kinematically Determined Plastic Flows |
| Тип | Journal Article |
| DOI | 10.1177/108128659700200302 |
| Print ISSN | 1081-2865 |
| Журнал | Mathematics and Mechanics of Solids |
| Том | 2 |
| Первая страница | 275 |
| Последняя страница | 290 |
| Аффилиация | Katoanga, Tui, L., Department of Mathematics, University of Wollongong, Wollongong, NSW, Australia |
| Выпуск | 3 |
| Библиографическая ссылка | [1] Spencer, A.J.M.: A theory of the kinematics of ideal soils under plane strain conditions. Journal of the Mechanics and Physics of Solids, 12, 337-351 (1964). |
| Библиографическая ссылка | [2] Mehrabadi, M. M. and Cowin, S. C.: Initial planar deformation of dilatant granular materials. Journal of the Mechanics and Physics of Solids, 26, 269-284 (1978). |
| Библиографическая ссылка | [3] Hill, J. M. and Wu, Y -H.: Some axially symmetric flows of Mohr-Coulomb compressible granular materials. Proceedings of the Royal Society of London A, 438, 67-93 (1992). |
| Библиографическая ссылка | [4] Hill, J. M.: Double-shearing theory for dilatant granular materials, in Proceedings of IUTAM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics (University of Nottingham, 1994), pp. 169-182, ed., D. F. Parker & A. H. England, Kluwer, London, 1995. |
| Библиографическая ссылка | [5] Hill, J. M. and Katoanga, T. L.: The velocity equations for dilatant granular flow and a new exact solution. Journal of Applied Mathematics and Physics (ZAMP)48, 1-8 (1997). |
| Библиографическая ссылка | [6] Spencer, A.J.M.: Plastic flow past a smooth cone. Acta Mechanica, 54, 63-74 (1984). |
| Библиографическая ссылка | [7] Hill, J. M. and Wu, Y -H.: Kinematically determined axially symmetric plastic flows of metals and granular materials. Quarterly Journal of Mechanics and Applied Mathematics, 44, 451-469 (1991). |
