This paper presents three different constitutive approaches to model thin
rotation-free shells based on the Kirchhoff-Love hypothesis. One approach is
based on numerical integration through the shell thickness while the other two
approaches do not need any numerical integration and so they are
computationally more efficient. The formulation is designed for large
deformations and allows for geometrical and material nonlinearities, which
makes it very suitable for the modeling of soft tissues. Furthermore, six
different isotropic and anisotropic material models, which are commonly used to
model soft biological materials, are examined for the three proposed
constitutive approaches. Following an isogeometric approach, NURBS-based finite
elements are used for the discretization of the shell surface. Several
numerical examples are investigated to demonstrate the capabilities of the
formulation. Those include the contact simulation during balloon angioplasty.Comment: Typos are removed. Remark 3.4 is added. Eq. (18) in the previous
version is removed. Thus, the equations get renumbered. Example 5.5 is
updated. Minor typos in Eqs. (17), (80), (145) and (146), are corrected. They
do not affect the result
