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Some unexpected predictions from strongly anisotropic hyperelastic constitutive models of soft tissue

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Abstract

It is shown that a widely used class of constitutive models for the mechanical response of elastic arteries, which includes the so-called HGO model, responds as if it were inextensible in simple tension in the zero limit of a non-dimensional ratio of material parameters. A significant auxetic response is predicted for an incompressible hyperelastic elastic sheet reinforced with inextensible cords. Thus, a significant lateral deformation of arterial specimens modelled by this class of materials should be observed in simple tension for small values of the non-dimensional parameter. However, such a response has not been observed experimentally. The analysis therefore suggests that predictions for this class of strongly anisotropic constitutive models for arteries should be treated with caution.

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Acknowledgements

We are grateful to the reviewers for their constructive comments on an earlier version of the manuscript.

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Authors and Affiliations

  1. School of Engineering and Applied Science, University of Virginia, Charlottesville, VA, 22904, USA

    C. O. Horgan

  2. Department of Mechanical Engineering, Dublin City University, Glasnevin, Dublin, D09 W6Y4, Ireland

    J. G. Murphy

  3. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, University Road, Galway, Ireland

    J. G. Murphy

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  1. C. O. Horgan
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  2. J. G. Murphy
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Correspondence to J. G. Murphy.

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Horgan, C.O., Murphy, J.G. Some unexpected predictions from strongly anisotropic hyperelastic constitutive models of soft tissue. Mech Soft Mater 2, 9 (2020). https://doi.org/10.1007/s42558-020-00024-5

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