We derive new analytical solutions for the non-affine Johnson-Segalman/Gordon-Schowalter (JS/GS) constitutive equation with a general relaxation kernel in medium-amplitude oscillatory shear (MAOS) deformation. The results show time-strain separable (TSS) nonlinearity, therefore providing new physically-meaningful interpretation to the heuristic TSS nonlinear parameter in MAOS (Martinetti & Ewoldt Phys. Fl. (2019)). The upper-convected, lower-convected, and corotational Maxwell models are all subsets of the results presented here. The model assumes that the microscale elements causing stress in the material slip compared to the continuum deformation. We introduce a visualization of the non-affine deformation field that acts on stress-generating elements to reinforce the physical interpretation of the JS/GS class of models. Finally, a case study is presented where previously published results, from fitting TSS models to MAOS data, can be re-interpreted based on the concept of non-affine motion of the JS/GS framework.

中文翻译：

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Johnson-Segalman/Gordon-Schowalter 模型的弱非线性响应和非仿射解释

我们推导出了非仿射 Johnson-Segalman/Gordon-Schowalter (JS/GS) 本构方程的新解析解，在中等幅度振荡剪切 (MAOS) 变形中具有一般松弛核。结果显示时间应变可分离 (TSS) 非线性，因此为 MAOS 中启发式 TSS 非线性参数提供了新的物理意义解释（Martinetti & Ewoldt Phys. Fl. (2019)）。上部对流、下部对流和共旋 Maxwell 模型都是此处显示的结果的子集。该模型假设与连续变形相比，微尺度元素在材料滑移中引起应力。我们引入了作用于应力生成元素的非仿射变形场的可视化，以加强对 JS/GS 类模型的物理解释。最后，