Dubbeldam J L A, Olmsted P D
Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands.
Eur Phys J E Soft Matter. 2009 Aug;29(4):363-78. doi: 10.1140/epje/i2009-10501-0. Epub 2009 Jul 31.
We present an analytical study of a toy model for shear banding, without normal stresses, which uses a piecewise linear approximation to the flow curve (shear stress as a function of shear rate). This model exhibits multiple stationary states, one of which is linearly stable against general two-dimensional perturbations. This is in contrast to analogous results for the Johnson-Segalman model, which includes normal stresses, and which has been reported to be linearly unstable for general two-dimensional perturbations. This strongly suggests that the linear instabilities found in the Johnson-Segalman can be attributed to normal stress effects.
我们对一个用于剪切带化的玩具模型进行了分析研究，该模型不考虑法向应力，采用了流动曲线（剪切应力作为剪切速率的函数）的分段线性近似。此模型展现出多个稳态，其中之一对于一般二维扰动是线性稳定的。这与约翰逊 - 西格尔曼模型的类似结果形成对比，后者考虑法向应力，且据报道对于一般二维扰动是线性不稳定的。这强烈表明，在约翰逊 - 西格尔曼模型中发现的线性不稳定性可归因于法向应力效应。
