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首页> 外文期刊>International journal of non-linear mechanics >How to identify a hyperelastic constitutive equation for rubber-like materials with multiaxial tension-torsion experiments
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How to identify a hyperelastic constitutive equation for rubber-like materials with multiaxial tension-torsion experiments

机译：如何通过多轴拉伸-扭转实验识别类橡胶材料的超弹性本构方程

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摘要

This paper discusses the different approaches that can be used to determine the strain energy density of a given rubber-like material based on tension-torsion experimental results. More precisely, the aim is to answer the question: how to handle the measured macroscopic quantities, i.e. load and torque, to determine the constitutive equation with the less possible assumptions? The method initially proposed by Penn and Kearsley [Trans. Soc. Rheol. 20 (1976) 227-238] is adopted: the strain energy derivatives with respect to kinematical quantities have to be calculated in terms of the measured load and torque. Here, we propose to consider different sets of kinematical quantities to overcome the incoherence encountered with the classical Cauchy-Green strain invariants I_1 and I_2. Two new sets are considered: the principal stretch ratios and two specific invariants of the logarithmic (true) Hencky strain tensor. The corresponding derivations coupled with new experimental results permit (ⅰ) to calculate the Cauchy stress tensor on the outer surface of the cylindrical samples, and (ⅱ) to demonstrate that a well-conditioned set of kinematical quantities must be adopted to determine the strain energy density. It is proved here that the principal stretch ratios are good candidates to express and determine the strain energy density with tension-torsion experiments.
机译：本文讨论了基于张力-扭转实验结果可用于确定给定橡胶状材料的应变能密度的不同方法。更准确地说，目的是要回答这个问题：如何处理测量的宏观量，即负载和扭矩，以尽可能少的假设来确定本构方程？该方法最初由Penn和Kearsley提出[Trans。 Soc。 he 20（1976）227-238]：相对于运动量的应变能导数必须根据测得的载荷和扭矩来计算。在这里，我们建议考虑不同的运动量集，以克服经典柯西-格林应变不变量I_1和I_2遇到的不连贯性。考虑了两个新集合：对数（真实）Hencky应变张量的主拉伸比和两个特定不变式。相应的推导加上新的实验结果允许（ⅰ）计算圆柱样品外表面上的柯西应力张量，并且（ⅱ）证明必须采用一组条件良好的运动量来确定应变能密度。在此证明，通过拉伸-扭转实验，主要拉伸比是表达和确定应变能密度的良好候选者。

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