Assumed-metric spherically interpolated quadrilateral shell element

An alternative approach for the analysis of non-linear shells is adopted, based on mixed forms of the spatial metric (both enriched and assumed), spherical linear interpolation for quadrilaterals (for the first time) and covariant fixed frames to ensure the satisfaction of all patch tests (also an innovation). The motivation for the spherical interpolation was the work of Crisfield and Jelenić on geometrically exact beams. Shear deformation is included and rotations are defined relative to the Kirchhoff director. A systematic mixed method for deriving high-performance shell elements is presented in the sense that specific mixed shape functions can be inserted without altering the overall framework. A long-standing restriction of assumed-strain elements in FeFpFeFp plasticity is circumvented for metal plasticity by using the elastic left Cauchy–Green tensor. Enhanced-assumed metric is also included directly in the metric components. The forces are exactly linearized to obtain an asymptotically quadratic convergence rate in Newton's method. Verification tests of the formulation are performed with very good performance being observed. Applications to hyperelasticity and plasticity are shown with excellent robustness and accuracy.

► Spherical interpolation of shell directors (SLERP).
► Exact linearization.
► Consistent mixed methods (ANS+EAS) constructed over SLERP.
► Nonlinear shell element based on multiplicative plasticity.