A corotational shell finite element for aortic valve modeling

The aim of this work is to present a finite element approach specifically suited for aortic valve simulation. During the cardiac cycle, valve leaflets undergo large displacements and rotations. A geometrically nonlinear analysis is therefore needed, and it is implemented here via a corotational formulation. The basic idea of the corotational approach is to extract the pure deformational part from the global displacement, by filtering out the rigid motion. The finite membranal deformations arising in the diastolic phase demand a special choice of the corotational filter, based on the polar decomposition. It is implement here in a computationally efficient manner, based on original closed-form formulas. A finite-elasticity formulation accounting for an hyperelastic constitutive law is adopted. A suitable core element is developed, which benefits from the lack of large rotations, filtered out by the corotational approach. In particular, exploiting the theory of small deformations superimposed on large, a facet-shell triangular element is obtained superposing a linear Discrete Kirchhoff Triangle plate and a finite-strain membrane element with drilling freedoms. The performance of the element are evaluated by comparison with available solutions of benchmark problems. Simulations of aortic valve dynamics under prescribed loads are also presented and discussed.