A Comparison of the Performance of Hexahedral and Tetrahedral Elements in Finite Element Models of the Foot

Abstract

Characterization of the contact pressure patterns under the foot provides significant insight into pathological conditions such as diabetic peripheral neuropathy [1]. The finite element method (FEM) is widely used in foot biomechanics for predictive simulations of plantar pressures in barefoot and shod conditions [2–6]. In the analysis of the foot, mesh generation accounts for most of the labor in model development, due to the complex structure of the foot including highly partitioned, embedded, and branching geometries. In FEM, hexahedral elements are preferred over tetrahedral elements because of their superior performance in terms of convergence and accuracy of the solution [7]. This becomes more apparent as the convergence behavior of the simulations are hindered by large deformation, material incompressibility, and contact with friction, mechanical features which are commonly seen in foot biomechanics. Unfortunately, unlike tetrahedral meshing which is highly automated [8], hexahedral mesh generation is a time consuming process requiring considerable operator intervention. Despite their reputed advantages, the relative performance of tetrahedral meshes in foot models has not been well established; to our knowledge, there has not been a comprehensive study comparing the performance of hexahedral and tetrahedral elements when material and geometric nonlinearity are included combined with material incompressibility and shear force loading conditions. Hence, the objective of the present study was to evaluate various types of meshes that can be used to model the interaction of a bone-soft tissue construct and rigid floor complex under compressive and shear loading in a heel-pad analog model.