Improved Linear Tetrahedral Element for Surgical Simulation

Automatic hexahedral mesh generation for complex geometries is still a challenging problem, and therefore tetrahedral or mixed meshes are preferred. Unfortunately the standard formulation of the linear tetrahedral element exhibits volumetric locking in case of almost incompressible materials. In this paper we propose a new linear tetrahedral element based on the average nodal Jacobian. This element improves the volumetric locking behavior of the standard formulation and requires only a small additional computation effort, providing an element that has an increased accuracy while maintaining the computational efficiency. We show how easy an existing TLED (Total Lagrangian Explicit Dynamics) algorithm can be modified in order to support the new element formulation. The performance evaluation of the new element shows a clear improvement in reaction force and displacement predictions compared to the standard formulation.