Dynamic mechanical oscillatory shear measurements with torsional rectangular geometry are widely carried out in order to determine the mechanical properties of soft solid materials in a quick and practical way. This technique has the advantage of avoiding slip effects, thus being particularly attractive for testing stiff elastomers such as vulcanized rubber compounds. However, one of its drawbacks is the clamping system required to keep the specimen edges in place. Since it imposes a constraint to warping deformations (i.e., out-of-plane cross-section distortions about the torsional axis), a certain increase of dynamic moduli with respect to their values in simple shear is observed and considered as an experimental artifact (i.e., de Saint-Venant's assumption of primary torsion of the specimen is no longer valid). The increase of dynamic moduli in torsion depends on the specimen's cross-section geometry and relative dimensions. We test here the capability of different torsion models to describe the constrained warping effect for an industrial rubber with rectangular specimen cross section using a wide range of different geometric parameters (length-to-width p ratio and width-to-thickness u ratio). We compare two theoretical models (Vlasov's model and Timoshenko's approach) and a phenomenological model (based on finite element simulations by Diani and Gilormini) with our experimental data set. We propose a slight modification of Vlasov's model to obtain realistic predictions of torsion over a wider parameter range. It is shown to be particularly useful in soft rubber testing, and the limitations in the choice of specimen geometry to obtain sufficient torque signal are overcome.

中文翻译：

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具有扭转矩形几何形状的动态力学分析：约束翘曲模型的关键评估

为了快速而实用地确定软固体材料的机械性能，广泛地进行了具有扭转矩形几何形状的动态机械振荡剪切测量。该技术具有避免打滑效果的优点，因此对于测试硬质弹性体（例如硫化橡胶混合物）特别有吸引力。但是，其缺点之一是需要将样品边缘保持在适当位置的夹持系统。由于它对翘曲变形（即绕扭转轴的平面外横截面变形）施加了约束，因此，相对于简单剪切中的值，动态模量会有所增加，并被视为实验假象（即，de Saint-Venant对样品一次扭转的假设不再成立。扭转动态模量的增加取决于样品的横截面几何形状和相对尺寸。我们在这里测试不同扭转模型的能力，以使用各种不同的几何参数（长到宽）描述具有矩形试样横截面的工业橡胶的受约束翘曲效应。p比和宽度与厚度u比）。我们将两个理论模型（Vlasov模型和Timoshenko的方法）和一个现象学模型（基于Diani和Gilormini的有限元模拟）与我们的实验数据集进行了比较。我们提议对Vlasov模型进行些微修改，以获得在更宽的参数范围内的实际扭力预测。它在软橡胶测试中特别有用，并且克服了选择试样几何形状以获得足够扭矩信号的局限性。