Isogeometric Kirchhoff-Love shell formulations for general hyperelastic materials

We present formulations for compressible and incompressible hyperelastic thin shells which can use general 3D constitutive models. The necessary plane stress condition is enforced analytically for incompressible materials and iteratively for compressible materials. The thickness stretch is statically condensed and the shell kinematics are completely described by the first and second fundamental forms of the midsurface. We use C¹-continuous isogeometric discretizations to build the numerical models. Numerical tests, including structural dynamics simulations of a bioprosthetic heart valve, show the good performance and applicability of the presented methods.