A finite shell element for heart mitral valve leaflet mechanics, with large deformations and 3D constitutive material model

This paper presents a shell finite element formulation appropriate for simulating the heart valve leaflet mechanics, including three-dimensional (3D) stress and strain effects. A 4-node mixed-interpolation shell is formulated in convected coordinates. This shell model is made capable of handling arbitrary 3D material models by use of an algorithm that satisfies the shell stress assumption at every element integration point. A method for tracking the fiber direction is incorporated. The resulting shell element operates under the same conditions as a standard 4-node shell element with 5 degrees of freedom per node, but extends the modeling capabilities to handle large-deformation and anisotropic behavior.