A constitutive model of the posterior cruciate ligament

Abstract

Further to our previous work on the development of a general constitutive framework for transversely isotropic viscohyperelasticity (Limbert, G, Middleton, J. A transversely isotropic viscohyperelastic material. Application to the modelling of biological soft connective tissues. Int J Solids Struct 2004;41(15):4237–60.), we propose a phenomenological constitutive law to describe the anisotropic viscohyperelastic behaviour of the human posterior cruciate ligament (PCL) at high strain rates. The mechanical formulation is based on the definition of a Helmholtz free energy function containing a hyperelastic and a viscous potential. The equations are valid for arbitrary kinematics and satisfy elemental thermodynamic principles. Identification of the constitutive model with experimental data obtained from human PCL specimens was performed and showed the ability of the model to capture accurately the mechanical characteristics of the PCL at various strain rates. Influence of the isotropic and directional viscous stress responses on the global mechanical response are discussed in connection with the modelling hypotheses. This work was motivated by the need to provide an accurate constitutive model of the PCL to be used in finite element analyses of human occupants in car crash simulations. Besides uniaxial tests along the natural fibre orientation of the PCL, additional tests such as equibiaxial, strip biaxial compression–tension and shear tests were also performed in order to assess the physical response of the model in different loading situations. It was found that the model performed as well in these conditions.