Abstract

The initial-boundary value problems of acceleration from a state of rest of a two-constant viscoplastic medium (Bingham body) in a half-plane is investigated when the tangential stress is given at the boundary as a piecewise continuous monotonically nondecreasing function of time. As an additional condition at an unknown interface between a flow zone that increases with time in thickness and a stationary semi-infinite rigid zone, the requirement is chosen that the solution of this problem with a tendency to zero of the yield strength of the material at each point and at each moment of time tends to the solution of the corresponding viscous flow problem known as the generalized vortex layer diffusion problem. The exact analytical solutions are found for tangential stress and velocity profiles in nonstationary one-dimensional flow. The cases of self-similarity and so-called quasi-self-similarity are distinguished. The nature of the tendency at \(t\to\infty\) of the thickness of the layer, in which the shear is realized, to infinity is of particular interest.

中文翻译：

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粘塑性流动理论中一些抛物线问题的拟自相似解

摘要

当边界处的切向应力作为时间的分段连续单调非递减函数时，研究了半平面中两个常数粘塑性介质（宾汉体）的静止状态加速度的初始边值问题。作为厚度随时间增加的流动区域与静止半无限刚性区域之间的未知界面处的附加条件，选择的要求是该问题的解决方案在以下条件下材料的屈服强度趋于零每个点和每个时刻都趋于解决相应的粘性流问题，称为广义涡层扩散问题。找到了非平稳一维流中切向应力和速度分布的精确解析解。自相似性和所谓的准自相似性的情况是有区别的。实现剪切的层厚度在\(t\to\infty\)处趋向无穷大的性质特别令人感兴趣。