Finite element implementation of incompressible, transversely isotropic hyperelasticity

This paper describes a three-dimensional constitutive model for biological soft tissues and its finite element implementation for fully incompressible material behavior. The necessary continuum mechanics background is presented, along with derivations of the stress and elasticity tensors for a transversely isotropic, hyperelastic material. A particular form of the strain energy for biological soft tissues is motivated and a finite element implementation of this model based on a three-field variational principle (deformation, pressure and dilation) is discussed. Numerical examples are presented that demonstrate the utility and effectiveness of this approach for incompressible, transversely isotropic materials.