| Abstract: | The equations of motion of a continuum in a thin layer are derived for a given functional dependence of the stress tensor on the strain rate tensor. The general problem of viscoplastic flow is considered in the thin-layer approximation for boundary surface material points travelling in the lateral direction in a predetermined fashion.The projections of the continuum point velocity, pressure, flow rate through a cross-section of the channel, and the power of external forces are expressed as functions of the boundary deformation law. The problem of determining the channel boundary deformation law is formulated for a given boundary pressure distribution. The expressions for the continuum flow rate and pressure and the power of external forces written as functionals of the channel width allow formulation of the problems of controlling viscoplastic flows in thin layers and optimizing the processes.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 23–31, March–April, 1996. |
