The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we use part of our exact solution for shear stress to arrive at unique exact analytical solutions for the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses at a frequency higher than twice the test frequency higher harmonics. We find the new exact analytical solutions to be compact and intrinsically beautiful. These solutions reduce to those of our previous work on the special case of the corotational Maxwell fluid. Our solutions also agree with our new truncated Goddard integral expansion for the special case of the corotational Jeffreys fluid. The limiting behaviors of these exact solutions also yield new explicit expressions. Finally, we use our exact solutions to see how η...

中文翻译：

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Oldroyd 8 常数框架的法向应力差异：大振幅振荡剪切流的精确解析解

连续统本构理论的 Oldroyd 8 常数框架包含丰富多样的聚合物液体流行特例。在本文中，我们使用剪切应力精确解的一部分来获得对大振幅振荡剪切 (LAOS) 流的法向应力差响应的独特精确解析解。由 LAOS 触发的聚合物液体的非线性导致这些响应甚至是测试频率的倍数。我们称频率高于两倍测试频率的响应为高次谐波。我们发现新的精确分析解决方案紧凑且内在美观。这些解决方案简化为我们之前在共旋麦克斯韦流体的特殊情况下的工作。我们的解决方案也与我们新的截断戈达德积分展开式一致，用于共旋杰弗里流体的特殊情况。这些精确解的限制行为也产生了新的显式表达式。最后，我们使用我们的精确解来看看 η...