A general framework for Maxwell–Oldroyd type differential constitutive models is examined, in which an unspecified nonlinear function of the stress tensor and rate-of-deformation tensor is incorporated into the well-known corotational version of the Jeffreys model discussed by Oldroyd. For medium amplitude simple shear deformations, the recently developed mathematical framework of medium amplitude parallel superposition (MAPS) rheology reveals that this generalized nonlinear Maxwell model can produce only a limited number of distinct signatures, which combine linearly in a well-posed basis expansion for the third order complex viscosity. This basis expansion represents a library of MAPS signatures for distinct constitutive models that are contained within the generalized nonlinear Maxwell model. We describe a framework for quantitative model identification using this basis expansion for the third order complex viscosity, and discuss its limitations in distinguishing distinct nonlinear features of the underlying constitutive models from medium amplitude shear stress data. The leading order contributions to the normal stress differences are also considered, revealing that only the second normal stress difference provides distinct information about the weakly nonlinear response space of the model. After briefly considering the conditions for time-strain separability within the generalized nonlinear Maxwell model, we apply the basis expansion of the third order complex viscosity to derive the medium amplitude signatures of the model in specific shear deformation protocols. Finally, we use these signatures for estimation of model parameters from rheological data obtained by these different deformation protocols, revealing that three-tone oscillatory shear deformations produce data that is readily able to distinguish all features of the medium amplitude, simple shear response space of this generalized class of constitutive models.

检查了 Maxwell-Oldroyd 型微分本构模型的一般框架，其中应力张量和变形率张量的未指定非线性函数被合并到 Oldroyd 讨论的 Jeffreys 模型的众所周知的共旋版本中。对于中等幅度的简单剪切变形，最近开发的中等幅度平行叠加 (MAPS) 流变学数学框架表明，这种广义非线性麦克斯韦模型只能产生有限数量的不同特征，这些特征线性组合为适定基扩展，用于三阶复数粘度。这种基础扩展代表了包含在广义非线性麦克斯韦模型中的不同本构模型的 MAPS 特征库。我们描述了一个使用三阶复数粘度的基础扩展进行定量模型识别的框架，并讨论了它在区分基础本构模型的不同非线性特征与中等振幅剪切应力数据方面的局限性。还考虑了对法向应力差的主阶贡献，表明只有第二法向应力差提供了有关模型弱非线性响应空间的独特信息。在简要考虑广义非线性麦克斯韦模型中时间-应变可分离性的条件后，我们应用三阶复数粘度的基础展开来推导出特定剪切变形协议中模型的中等振幅特征。最后，