Locking-free mixed finite element methods for nonlinear shells
Date:
The slides can be found here.
Abstract:
Deriving locking-free discretization methods for nonlinear shells is a challenging task. Recently, the Hellan-Herrmann-Johnson (HHJ) method has been extended from linear Kirchhoff-Love plates to nonlinear shells. This novel approach, which involves the use of the bending moment tensor as an additional field, rewrites the fourth-order problem as a second-order mixed saddle-point problem. Importantly, it eliminates the need for finite elements with high regularity assumptions. The usage of appropriate interpolation operators further mitigates membrane locking for shells with small thicknesses.
In this talk, we motivate the HHJ method for shells using discrete differential geometry and apply the model to simulate cell membranes and paper folding, and couple it with continuum mechanics. We discuss its extension to Reissner-Mindlin shells and present several numerical examples implemented in the finite element software NGSolve (www.ngsolve.org).