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On Modelling Simple Shear for Isotropic Incompressible Rubber-Like Materials

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Abstract

In this paper we demonstrate the application of a recently proposed molecular based generalised neo-Hookean strain energy function within the family of limiting chain extensibility models to the simple shear of incompressible isotropic rubber-like hyperelastic materials. The two-parameter model of concern is capable of capturing both linear and highly nonlinear shear stress responses. It provides favourable simultaneous fits to experimental data for various components of the simple shear stress field, such as the shear stress and normal tractions/stresses, with a single set of parameter values. In addition, when used in a phenomenological context, the model also captures shear-softening behaviour and predicts an interesting instability. These modelling results are demonstrated in conjunction with a wide range of extant experimental data involving the simple shearing of biological tissue specimens and polymer and rubber samples. It will also be shown that in all these applications, the proposed model remains stable (convex) over the defined domain of deformation. These results underline the merits of the considered model for addressing some of the outstanding challenges in the constitutive modelling of the complex nonlinear behaviour of rubber-like materials.

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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. Cardiovascular Engineering Research Lab (CERL), School of Mechanical and Design Engineering, University of Portsmouth, Anglesea Road, Portsmouth, PO1 3DJ, UK

    Afshin Anssari-Benam

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

    Cornelius O. Horgan

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  1. Afshin Anssari-Benam
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Correspondence to Cornelius O. Horgan.

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Appendix: Tabulated Experimental Data

Appendix: Tabulated Experimental Data

Table 10 Budday et al. data [19]
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Table 11 Yeoh and Fleming data [15]
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Table 12 Destrade et al. data [24]
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Table 13 Nunes data [17]
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Table 14 Lahellec et al. data [16]
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Table 15 Araújo and Nunes data [40]
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Table 16 Nunes and Moreira data [41]
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Table 17 Moreira and Nunes data [42]
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Anssari-Benam, A., Horgan, C.O. On Modelling Simple Shear for Isotropic Incompressible Rubber-Like Materials. J Elast 147, 83–111 (2021). https://doi.org/10.1007/s10659-021-09869-x

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