Comparison of hexahedral and tetrahedral elements in finite element analysis of the foot and footwear.

Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation.

[1]  Kai-Nan An,et al.  Effects of plantar fascia stiffness on the biomechanical responses of the ankle-foot complex. , 2004, Clinical biomechanics.

[2]  J. Lee,et al.  Effects of internal stress concentrations in plantar soft-tissue--A preliminary three-dimensional finite element analysis. , 2010, Medical engineering & physics.

[3]  Ahmet Erdemir,et al.  An inverse finite-element model of heel-pad indentation. , 2006, Journal of biomechanics.

[4]  Arturo Cifuentes,et al.  A performance study of tetrahedral and hexahedral elements in 3-D finite element structural analysis , 1992 .

[5]  P. Cavanagh,et al.  New developments in the biomechanics of the diabetic foot , 2000, Diabetes/metabolism research and reviews.

[6]  Isabel C N Sacco,et al.  Plantar pressures during shod gait in diabetic neuropathic patients with and without a history of plantar ulceration. , 2009, Journal of the American Podiatric Medical Association.

[7]  Steven E. Benzley,et al.  A Comparison of All Hexagonal and All Tetrahedral Finite Element Meshes for Elastic and Elasto-plastic Analysis , 2011 .

[8]  E. Morag,et al.  Structural and functional aspects of the diabetic foot. , 1997, Clinical biomechanics.

[9]  Ming Zhang,et al.  Three-dimensional finite element analysis of the foot during standing--a material sensitivity study. , 2005, Journal of biomechanics.

[10]  Ahmet Erdemir,et al.  Local plantar pressure relief in therapeutic footwear: design guidelines from finite element models. , 2005, Journal of biomechanics.

[11]  M Arcan,et al.  Biomechanical analysis of the three-dimensional foot structure during gait: a basic tool for clinical applications. , 2000, Journal of biomechanical engineering.

[12]  H. Yack,et al.  Relationships between segmental foot mobility and plantar loading in individuals with and without diabetes and neuropathy. , 2010, Gait & posture.

[13]  Hasan Ocak,et al.  Prediction of plantar shear stress distribution by artificial intelligence methods. , 2009, Journal of biomechanical engineering.

[14]  P. Cavanagh,et al.  The Mechanism of Plantar Unloading in Total Contact Casts: Implications for Design and Clinical Use , 1997, Foot & ankle international.

[15]  Amit Gefen,et al.  Stress analysis of the standing foot following surgical plantar fascia release. , 2002, Journal of biomechanics.

[16]  Ahmet Erdemir,et al.  Reduction of plantar heel pressures: Insole design using finite element analysis. , 2006, Journal of biomechanics.

[17]  Dequan Zou,et al.  Plantar Stresses on the Neuropathic Foot During Barefoot Walking , 2008, Physical Therapy.

[18]  M. J. Muêller,et al.  Novel Award 2002. Comparison of physical activity and cumulative plantar tissue stress among subjects with and without diabetes mellitus and a history of recurrent plantar ulcers. , 2003, Clinical biomechanics.

[19]  Sicco A Bus,et al.  Plantar pressure relief in the diabetic foot using forefoot offloading shoes. , 2009, Gait & posture.

[20]  A Ramos,et al.  Tetrahedral versus hexahedral finite elements in numerical modelling of the proximal femur. , 2006, Medical engineering & physics.

[21]  T. M. Owings,et al.  Plantar pressures in diabetic patients with foot ulcers which have remained healed , 2009, Diabetic medicine : a journal of the British Diabetic Association.

[22]  Ming Zhang,et al.  Parametric design of pressure-relieving foot orthosis using statistics-based finite element method. , 2008, Medical engineering & physics.

[23]  R. V. Deursen,et al.  The effectiveness of footwear and offloading interventions to prevent and heal foot ulcers and reduce plantar pressure in diabetes: a systematic review , 2008, Diabetes/metabolism research and reviews.

[24]  Brian L Davis,et al.  Plantar shear stress distributions: comparing actual and predicted frictional forces at the foot-ground interface. , 2007, Journal of biomechanics.