Isogeometric Kirchhoff-Love shell formulations for biological membranes

Area of Science:

• Biomechanics and Mechanobiology
• Computational Modeling
• Biomaterials Science

Background:

• Thin biological membranes (skin, alveoli, blood vessels, heart valves) are crucial for medical devices.
• Existing computational models often lack the ability to represent nonlinear, anisotropic tissue properties.
• Isogeometric analysis (IGA) is suitable for membrane modeling due to its inherent smoothness requirements.

Purpose of the Study:

• To develop a thin shell formulation for computational modeling of thin biological membranes.
• To integrate nonlinear anisotropic constitutive models into an isogeometric thin shell framework.
• To enable the application of 3D constitutive models to thin shell analyses of biological tissues.

Main Methods:

• Derivation of equilibrium equations using curvilinear convective coordinates on NURBS surfaces.
• Linearization of the weak form of linear momentum balance.
• Incorporation of specific constitutive equations for collagenous tissues (Mooney-Rivlin, May Newmann-Yin, Gasser-Ogden-Holzapfel).

Main Results:

• A novel thin shell formulation for biological membranes is presented.
• The formulation accommodates nonlinear anisotropic material behavior.
• Demonstrated integration of established 3D constitutive models into a 2D thin shell analysis framework.

Conclusions:

• The developed formulation bridges the gap between 3D constitutive models and thin shell analysis for biological tissues.
• This work facilitates more accurate computational modeling of biological membranes.
• Enables improved design and analysis of medical devices interacting with biological tissues.