Modeling of biological tissues with anisotropic hyperelastic laws - Theoretical study and finite element analysis.

Modeling of biological tissues with anisotropic hyperelastic laws - Theoretical study and finite element analysis. To determine the strain and stress in the biological soft tissues such as ligaments, tendons or arterial walls, anisotropic hyperelastic constitutive laws are often used in the context of finite element analysis [J.A. Weiss, B.N. Maker, S. Govindjee, Finite element implementation of incompressible, transversely isotropic hyperelasticity, Comp. Meth. Appl. Mech. Engng. 135 (1996) 107-128]. In the present paper, we propose to realize such a study together with a analytical study. This study allows for the understanding of the reason why it does not exist a one-to-one correspondence between the principal stretch lambda(2) and the fourth invariant of the dilatation tensor for the material model proposed by Holzapfel, Gasser and Ogden [G.A. Holzapfel, T.C. Gasser, R.W. Ogden, A new constitutive framework for arterial wall mechanics and a comparative study of material models, J. Elasticity 61 (2000) 1-48; T.C. Gasser, R.W. Ogden, G.A. Holzapfel, Hyperelastic modelling of arterial layers with distributed collagen fibre orientations, J. R. Soc. Interface 3 (2006) 15-35]. In fact, the relationship becomes non-bijective when the angle between the collagen fibers and the circumferential direction is greater that a critical angle of 54.73 degrees. Importance of this critical angle was also discussed by Guo et al. (2006). To cite this article: E Peyraut et al., C R. Mecanique 337 (2009). (c) 2009 Publie par Elsevier Masson SAS pour I'Academie des sciences.