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Numerical studies on the identification of the material parameters of Rivlin's hyperelasticity using tension-torsion tests

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This paper deals with the identification of material parameters of elasticity relations based on Rivlin's hyperelasticity for incompressible material response, where the free energy evolves as a polynomial in the first and second invariant of the right Cauchy-Green tensor. This elasticity relation has the advantage of incorporating the material parameters linearily. The numerical studies are applied to tension, torsion and combined tension-torsion tests with cylindrical carbon black-filled rubber specimens represented in Haupt and Sedlan [1] and [2]. In the identification process the analytical solution of the resulting boundary value problem leads to a linear least square solution. In this article attention is focused on the numerical solution of several models proposed in the literature and their behavior for both a large and a small number of test data.

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Hartmann, S. Numerical studies on the identification of the material parameters of Rivlin's hyperelasticity using tension-torsion tests. Acta Mechanica 148, 129–155 (2001). https://doi.org/10.1007/BF01183674

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