Reformulation of nodally integrated continuum elements to attain insensitivity to distortion

The nodally integrated continuum element (NICE) formulation is an assumed-strain finite element technique derived from a weighted residual statement that weakly enforces both the balance equation and the kinematic equation. The original NICE formulation has a number of desirable attributes (e.g., resistance to volumetric locking), but, similar to classical finite elements, it is sensitive to a geometrical distortion of the finite element mesh. The present work analyzes the NICE technique from this viewpoint, the source of the sensitivity to the shape of the element is identified, and an improvement of the NICE formulation is proposed. We illustrate the performance of the revised NICE formulation on extremely distorted meshes. The tetrahedral meshes contain zero-volume or negative-volume elements, including slivers, and the new NICE formulation is shown to have the condition number of the stiffness matrix under control even in the presence of slivers. Furthermore, insensitivity to distortions is demonstrated for quadratic and cubic hexahedral elements. The proposed improvement confers robustness to all element shapes treated by the NICE formulation. The approximation properties of the original NICE formulation are preserved, in particular the improved version is also locking free, and at the same time, the need for stabilization also carries over. Copyright (c) 2011 John Wiley & Sons, Ltd.