Efficient isogeometric thin shell formulations for soft biological materials

Abstract

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.

arXiv commentTypos 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 results

References in corpus (1)

• A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries

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