Hyperelastic Energy Densities for Soft Biological Tissues: A Review

Abstract

Many soft tissues are naturally made of a matrix and fibres that present some privileged directions. They are known to support large reversible deformations. The mechanical behaviour of these tissues highlights different phenomena as hysteresis, stress softening or relaxation. A hyperelastic constitutive equation is typically the basis of the model that describes the behaviour of the material. The hyperelastic constitutive equation can be isotropic or anisotropic, it is generally expressed by means of strain components or strain invariants. This paper proposes a review of these constitutive equations.

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Fig. 1

Notes

  1. 1.

    Details about the link between structural tensors and a method to link a fictitious isotropic configuration to render an anisotropic, undeformed reference configuration via an appropriate linear tangent map is given in [163].

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Acknowledgements

The authors thank Prof. Roger Fosdick for his valuable comments. This work is supported by the French National Research Agency Program ANR-12-BS09-0008-01 SAMBA (Silicone Architectured Membranes for Biomedical Applications).

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Chagnon, G., Rebouah, M. & Favier, D. Hyperelastic Energy Densities for Soft Biological Tissues: A Review. J Elast 120, 129–160 (2015). https://doi.org/10.1007/s10659-014-9508-z

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Keywords

  • Hyperelasticity
  • Anisotropy

Mathematics Subject Classification

  • 74B20