Journal of Elasticity

, Volume 120, Issue 2, pp 129–160 | Cite as

Hyperelastic Energy Densities for Soft Biological Tissues: A Review

  • G. Chagnon
  • M. Rebouah
  • D. Favier


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.


Hyperelasticity Anisotropy 

Mathematics Subject Classification




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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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Université de Grenoble Alpes/CNRS/TIMC-IMAG UMR 5525GrenobleFrance

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