非线性流变学的Kramers-Kronig关系：2。中等振幅振荡剪切（MAOS）测量的确认
Kramers-Kronig Relations for Nonlinear Rheology: 2. Validation of Medium Amplitude Oscillatory Shear (MAOS) Measurements
摘要：
三次谐波介质振幅振荡剪切（MAOS）模量$G_{33}^{*}(ω)$的频率依赖性提供了在渐近非线性制度的材料行为和微观结构的洞察。由于MAOS模量测量的困难，我们提出了一种基于非线性Kramers-Kronig关系的数据验证测试。我们扩展的方法来评估线性粘弹性数据的一致性表示的实部和虚部的$G_{33}^{*}(ω)$作为麦克斯韦元素的线性组合：MAOS内核的功能形式的灵感来自时间应变可分性（TSS）。我们提出了一种统计拟合技术，称为SMEL测试，它适用于广泛的材料和模型，包括那些不服从TSS。它成功地处理了有噪声或局限于有限频率范围的实验数据。当从SMEL测试获得的Maxwell模式用于预测一次谐波MAOS模量$G_{31}^{*}$时，可以确定材料表现TSS的时间尺度范围。
英文摘要：
The frequency dependence of third-harmonic medium amplitude oscillatory shear (MAOS) modulus $G_{33}^{*}(ω)$ provides insight into material behavior and microstructure in the asymptotically nonlinear regime. Motivated by the difficulty in the measurement of MAOS moduli, we propose a test for data validation based on nonlinear Kramers-Kronig relations. We extend the approach used to assess the consistency of linear viscoelastic data by expressing the real and imaginary parts of $G_{33}^{*}(ω)$ as a linear combination of Maxwell elements: the functional form for the MAOS kernels is inspired by time-strain separability (TSS). We propose a statistical fitting technique called the SMEL test, which works well on a broad range of materials and models including those that do not obey TSS. It successfully copes with experimental data that are noisy, or confined to a limited frequency range. When Maxwell modes obtained from the SMEL test are used to predict the first-harmonic MAOS modulus $G_{31}^{*}$, it is possible to identify the range of timescales over which a material exhibits TSS.
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