Optimized FE mesh generation procedure based on a user-defined spatial refinement gradient. Application to a motion segment

Abstract

Finite Element (FE) meshes are usually highly refined and dense and, consequently, computationally very expensive. Therefore, after the preliminary FE mesh generation, it is necessary to decrease its size by diminishing the total number of nodes and elements while maintaining both geometrical accuracy and a physically-meaningful FE mesh refinement. The aim of this work is to describe an optimized FE mesh simplification procedure based on edge contraction and on a user-defined spatial refinement gradient criterion. The main idea is that, for normal mechanical loadings applied to a motion segment, the vertebrae shall behave almost as an incompressible medium, and only the intervertebral disc (IVD) should undergo relevant strains. In this case, it is acceptable (and desirable) to attain a problem-functional FE mesh, in which the FE mesh should be more refined at the IVD and coarser at vertebrae. On the other hand, an optimized FE mesh should be more refined at the annulus fibrosus than at the nucleus pulposus. In summary, the proposed FE mesh generation and simplification procedure, being based on a user-definable spatial FE mesh refinement gradient, allows the user to define precisely the required refinement and thus to reduce drastically the number of elements in the final FE mesh and consequently to diminish the computation time required for the FE analysis, while keeping the necessary physical meaning on the FE mesh. The aforesaid procedure will be applied to the FE mesh generation (based on [1]) of a motion segment initially characterized by medical imaging.