Finite element simulation of articular contact mechanics with quadratic tetrahedral elements

Abstract

Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics.

FEBio: History and Advances

“…In addition, they can represent curved boundaries more accurately than linear elements since their edges and faces are curved, reducing the need for fine meshes for representing curved structures. In addition, as reported in a recent publication (76), it turns out that quadratic tetrahedral elements perform similarly and sometimes even better, both in terms of computational cost and in terms of accuracy, than the “gold standard” linear hexahedral element (Figure 7). …”

Finite Element Modelling Simulated Meniscus Translocation and Deformation during Locomotion of the Equine Stifle

“…Femur and tibia were defined as rigid bodies following common practice in FEA [27,36]. For the articular cartilage surfaces of tibia and femur, a Mooney–Rivlin model was defined with the following material properties: density = 1.5 × 10 −9 tons/mm 3 ; Mooney–Rivlin material coefficient C 1 = 0.856 MPa (Mega Pascal) Mooney–Rivlin material coefficient C 2 X = 0 MPa; Bulk modulus (K+) = 8 MPa; X = C 2 set to zero to get a Neo Hookean material [34,37].…”

A Plugin Framework for Extending the Simulation Capabilities of FEBio

“…FEBio uses the FE method to discretize the equations for conservation of mass, linear momentum, and charge. The resulting equations allow fully coupled simulation of solid mechanics, solid-fluid mixtures (9), fluid mechanics (10), fluid-solid interactions, transport (11,12), reaction and diffusion of neutral and charged species (12,13), contact (11,(14)(15)(16)(17), prestrain (18), and growth and remodeling (13). The governing equations are formulated based on mixture theory.…”