The Hellan-Herrmann-Johnson Method for Nonlinear Shells
This work provides a new discretization approach for nonlinear shell problems, addressing the need for robust finite elements in structural mechanics.
The paper generalizes the Hellan-Herrmann-Johnson mixed finite element method to nonlinear shells, enabling finite strains and large rotations. The method is validated on benchmark examples, showing accurate performance for structures with kinks.
In this paper we derive a new finite element method for nonlinear shells. The Hellan-Herrmann-Johnson (HHJ) method is a mixed finite element method for fourth order Kirchhoff plates. It uses convenient Lagrangian finite elements for the vertical deflection, and introduces sophisticated finite elements for the moment tensor. In this work we present a generalization of this method to nonlinear shells, where we allow finite strains and large rotations. The geometric interpretation of degrees of freedom allows a straight forward discretization of structures with kinks. The performance of the proposed elements is demonstrated by means of several established benchmark examples.