In this paper, we use an implicit generalization of the celebrated Kelvin–Voigt solid constitutive equation to study the problem of circumferential shearing of a cylindrical annulus of viscoelastic material. This generalization of the Kelvin–Voigt model allows one to take into consideration the possibility of the body undergoing shear thinning or shear thickening and allows the material moduli to depend on the mechanical pressure. Most importantly, the constitutive relation is a relation in the true mathematical sense in that neither the stress, nor the strain nor the symmetric part of the velocity gradient can be expressed explicitly in terms of the other quantities, thereby making the balance of linear momentum and the constitutive relation requiring solution simultaneously, unlike the case of the Kelvin–Voigt model where we can substitute the constitutive expression for the stress into the equilibrium equations to obtain an equation for the displacement field.

在本文中，我们使用著名的Kelvin-Voigt固体本构方程的隐式推广来研究粘弹性材料圆柱环面的周向剪切问题。Kelvin-Voigt模型的这种泛化使人们可以考虑物体进行剪切变薄或剪切变厚的可能性，并使材料的模量取决于机械压力。最重要的是，本构关系是真正的数学意义上的关系，因为应力，应变，速度梯度的对称部分都不能用其他量来明确表示，从而使线性动量和同时需要解的本构关系，