不同应力分量下广义开尔文模型粘性系数探讨

Generalized Kelvin Model under Different Stress State

对不同应力分量下的广义开尔文模型应力应变关系进行了研究,推导了在不同应力分量下的广义开尔文模型的粘性应变增量计算式;通过对这些粘性应变增量计算式的比较分析,得到结论:对于线性粘弹性模型,当应力张量引起粘性变形的规律与应力偏量和球应力分别引起粘性变形的规律相同时,它们的系数满足关系式Ek/ηk=Gsk/ηsk=Kmk/ηmk;否则,这个关系式不成立。现有文献采用应力张量表示的粘性变形有限元计算式隐含假定了球应力与应力偏量产生的粘性变形规律相同。对于复杂的工程材料而言,这种假定并不总是合适的。这在工程问题粘性分析时值得注意。

The generalized Kelvin model stress-strain relations under different stress states were analyzed The vis-coelastic strain increment expression was deduced Comparing with these viscoelastic strain increment expressions, it is concluded that for linear viscoelastic model, if the viscoelastic deformation law under different stress states, such as stress tensor, deviation stress and bulk stress, are the same, their parameters yield as Ek/ηk=Gsk/ηsk= Kmk/ηmk. The viscoelastic deformation law due to deviation stress gets the same as the bulk stress viscoelastic deformation law when the viscoelastic deformation FEM formula is expressed by stress tensor as in the references, which does not hold for complicated engineering materials.