A closed form solution for the uniaxial tension test of biological soft tissues

François Peyraut (1) , Zhi-Qiang Feng (2) , Nadia Labed (1) , Christine Renaud (2)

1 M3M - Laboratoire Mécatronique 3M - Méthodes, Modèles , Métiers
2 LMEE - Laboratoire de Mécanique et d'Energétique d'Evry

This paper concerns the modeling of biological soft tissues in the framework of anisotropic hyperelasticity. A closed form solution is proposed in the special case where uniaxial unconstrained tension loading is applied to a strip modeled by Holzapfel-Gasser-Ogden's (HGO) strain energy. The classical Cardano's formula is used to calculate the solution. This solution is investigated for different values of β which represents the angle between the collagen fibers and the circumferential direction. This study allows for the understanding of the reason why a one-to-one correspondence does not exist between the principal stretch and the fourth invariant of the right Cauchy-Green deformation tensor. It is demonstrated that the relationship becomes non-bijective when β is greater than a critical angle of 54 . 73{ring operator}. The HGO model is implemented into an in-house finite element program and numerical results are in good agreement with theoretical ones.

Mots clés: Anisotropic hyperelasticity; Biological soft tissues; HGO model; Theory and modeling

Domaines: Biomécanique [physics.med-ph]

François Peyraut, Zhi-Qiang Feng, Nadia Labed, Christine Renaud. A closed form solution for the uniaxial tension test of biological soft tissues. International Journal of Non-Linear Mechanics, 2010, 45 (5), pp.535--541. ⟨10.1016/j.ijnonlinmec.2010.02.003⟩. ⟨hal-01176160⟩