Normal-normal continuous symmetric stress approximation in three-dimensional linear elasticity

TL;DR

This paper introduces a new mixed finite element method for 3D linear elasticity that ensures normal-normal continuity of stress across tetrahedral mesh faces, achieving optimal convergence and being locking free.

Contribution

It presents a novel conforming mixed formulation with a specific stress element that maintains normal-normal continuity and demonstrates quasi-optimal convergence in 3D elasticity.

Findings

Scheme converges quasi-optimally

Method is locking free

Numerical experiments confirm performance

Abstract

We present a conforming setting for a mixed formulation of linear elasticity with symmetric stress that has normal-normal continuous components across faces of tetrahedral meshes. We provide a stress element for this formulation with 30 degrees of freedom that correspond to standard boundary conditions. The resulting scheme converges quasi-optimally and is locking free. Numerical experiments illustrate the performance.