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Swelling–twist interaction in fiber-reinforced hyperelastic materials: the example of azimuthal shear

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Abstract

We study how fiber-reinforced materials will naturally undergo swelling deformations in which a relatively greater stretch occurs transverse to the fibers than in the fiber direction. This means that a pattern of initially curved fibers prior to swelling will tend to straighten out as swelling proceeds. This can lead to swelling-induced deformations with a high degree of localized shearing and significant overall twisting. Such a process is examined for a plane strain swelling deformation that combines twist with radial expansion. Analytical results are obtained for both types: small and large swelling. Of particular interest is the relation of the extensible fiber theory to a theory for inextensible fibers. We examine the extent to which the former approaches the latter in the limit as the fibers are taken to be progressively stiffer.

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Notes

  1. The asymptote is \(39.7^{\circ }\) and the slope of the inextensible theory curve at \(v=1\) is also \(39.7^{\circ }\) (per unit swelling). This is an artifact of the parameter choice \(\alpha =\pi /4\). For example, if \(\alpha =\pi /3\) with \(R_o/R_i=2\), then the asymptote is \(68.8^{\circ }\) and the initial slope is \(33.5^{\circ }\) (per unit swelling).

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Acknowledgements

This publication was made possible by NPRP Grant # 8-2424-1-477 from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the authors.

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Authors and Affiliations

  1. Carnegie Mellon University in Qatar, Doha, Qatar

    Hasan Demirkoparan

  2. Michigan State University, East Lansing, MI, USA

    Thomas J. Pence

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  1. Hasan Demirkoparan
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  2. Thomas J. Pence
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Correspondence to Hasan Demirkoparan.

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Demirkoparan, H., Pence, T.J. Swelling–twist interaction in fiber-reinforced hyperelastic materials: the example of azimuthal shear. J Eng Math 109, 63–84 (2018). https://doi.org/10.1007/s10665-017-9906-x

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  • DOI: https://doi.org/10.1007/s10665-017-9906-x

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