A few remarks about the computer implementation and the verification of some hyperelastic constitutive laws and an illustration with the mechanical response of an artery

In this short technical note, we are interested in the constitutive equations used to model macroscopically the mechanical function of soft tissues under mechanical loading. Soft tissues have the ability to undergo large elastic reversible deformations under quasi-static loading and are usually modelled using hyperelastic constitutive laws. Several constitutive equations have been defined in the literature by means of strain components or strain invariants isotropic hyperelastic models. This short technical note recalls how to derive the weak form for hyperelasticity equations, and how this weak form can be linearized. It also presents a semi-analytical solution for a simplified geometry representing the mechanical response of an artery modelled under pressure loading.