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On the tangent modulus tensor in hyperelasticity

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Summary

The tangent modulus tensor, denoted asD, plays a central role in nonlinear finite element simulation of elastomeric components such as seals. It is derived from the strain energy functionw for isotropic elastomers. Using Kronecker product notation, a compact expression forD has been derived in Nicholson [1] and Nicholson and Lin [2] for invariant-based strain energy functions such as the Mooney-Rivlin model. In the current investigation, a corresponding expression is derived for stretch ratio-based strain energy functions such as the Ogden model. Compressible, incompressible and near-incompressible elastomers are addressed. The derived expressions are considerably more elaborate than their counterparts for invariant based models. As illustration,D is evaluated and presented for the torsion of a natural rubber shaft described by a three term Ogden model, using coefficients reported by Treloar.

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References

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Author notes

  1. D. W. Nicholson Ph.D. & B. Lin Ph. D.

    Present address: Institute of Computational Engineering, Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, 32 816, Orlando, FL, USA

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    1. D. W. Nicholson Ph.D.
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    2. B. Lin Ph. D.
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    Nicholson, D.W., Lin, B. On the tangent modulus tensor in hyperelasticity. Acta Mechanica 131, 121–132 (1998). https://doi.org/10.1007/BF01178249

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    • DOI: https://doi.org/10.1007/BF01178249

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