Abstract
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 I1 and I2. 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.
Highlights
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
Our experimental procedure is briefly described; the equations summarized in Table 1 are applied to experimental data
The combination of both strain energy derivatives allows us to bypass abovementioned problems at small strain. This simple calculation extends the work of Penn and Kearsley [26] to the determination of the Cauchy stress tensor. It is well-recognized that the best method to determine hyperelastic constitutive equation of a given rubber-like material consists in calculating the derivatives of the strain energy
Summary
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. 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 wellconditioned set of kinematical quantities must be adopted to determine the strain energy density. Simultaneous tension–torsion experiments are a relevant alternative to consider combined loading conditions: the cylindrical geometry of the specimen is simple and commercial testing machines are nowadays available. Considering such experiments, the problem reduces to the determination of the constitutive equation, i.e. the stress–strain relationship, from the measurement of load and torque for prescribed extension and angle of twist. (ii) determining the stress state from experimental data, choosing a relevant strain energy function and identifying the corresponding parameters with the stress–strain experimental data,
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