Development and experimental validation of a finite element model of total ankle replacement.

Total ankle replacement remains a less satisfactory solution compared to other joint replacements. The goal of this study was to develop and validate a finite element model of total ankle replacement, for future testing of hypotheses related to clinical issues. To validate the finite element model, an experimental setup was specifically developed and applied on 8 cadaveric tibias. A non-cemented press fit tibial component of a mobile bearing prosthesis was inserted into the tibias. Two extreme anterior and posterior positions of the mobile bearing insert were considered, as well as a centered one. An axial force of 2kN was applied for each insert position. Strains were measured on the bone surface using digital image correlation. Tibias were CT scanned before implantation, after implantation, and after mechanical tests and removal of the prosthesis. The finite element model replicated the experimental setup. The first CT was used to build the geometry and evaluate the mechanical properties of the tibias. The second CT was used to set the implant position. The third CT was used to assess the bone-implant interface conditions. The coefficient of determination (R-squared) between the measured and predicted strains was 0.91. Predicted bone strains were maximal around the implant keel, especially at the anterior and posterior ends. The finite element model presented here is validated for future tests using more physiological loading conditions.

Nonlinear Finite Element Study of Piles in Integral Abutment Bridges, HR-227, Part 2, 1982

The highway departments of the states which use integral abutments in bridge design were contacted in order to study the extent of integral abutment use in skewed bridges and to survey the different guidelines used for analysis and design of integral abutments in skewed bridges. The variation in design assumptions and pile orientations among the various states in their approach to the use of integral abutments on skewed bridges is discussed. The problems associated with the treatment of the approach slab, backfill, and pile cap, and the reason for using different pile orientations are summarized in the report. An algorithm based on a state-of-the-art nonlinear finite element procedure previously developed by the authors was modified and used to study the influence of different factors on behavior of piles in integral abutment bridges. An idealized integral abutment was introduced by assuming that the pile is rigidly cast into the pile cap and that the approach slab offers no resistance to lateral thermal expansion. Passive soil and shear resistance of the cap are neglected in design. A 40-foot H pile (HP 10 X 42) in six typical Iowa soils was analyzed for fully restrained pile head and pinned pile head. According to numerical results, the maximum safe length for fully restrained pile head is one-half the maximum safe length for pinned pile head. If the pile head is partially restrained, the maximum safe length will lie between the two limits. The numerical results from an investigation of the effect of predrilled oversized holes indicate that if the length of the predrilled oversized hole is at least 4 feet below the ground, the vertical load-carrying capacity of the H pile is only reduced by 10 percent for 4 inches of lateral displacement in very stiff clay. With no predrilled oversized hole, the pile failed before the 4-inch lateral displacement was reached. Thus, the maximum safe lengths for integral abutment bridges may be increased by predrilling. Four different typical Iowa layered soils were selected and used in this investigation. In certain situations, compacted soil (> 50 blow count in standard penetration tests) is used as fill on top of natural soil. The numerical results showed that the critical conditions will depend on the length of the compacted soil. If the length of the compacted soil exceeds 4 feet, the failure mechanism for the pile is similar to one in a layer of very stiff clay. That is, the vertical load-carrying capacity of the H pile will be greatly reduced as the specified lateral displacement increases.

Finite Element Analysis of Electrically Excited Quartz Tuning Fork Devices

Quartz Tuning Fork (QTF)-based Scanning Probe Microscopy (SPM) is an important field of research. A suitable model for the QTF is important to obtain quantitative measurements with these devices. Analytical models have the limitation of being based on the double cantilever configuration. In this paper, we present an electromechanical finite element model of the QTF electrically excited with two free prongs. The model goes beyond the state-of-the-art of numerical simulations currently found in the literature for this QTF configuration. We present the first numerical analysis of both the electrical and mechanical behavior of QTF devices. Experimental measurements obtained with 10 units of the same model of QTF validate the finite element model with a good agreement.

Modeling the transport phenomena within arterial wall: porous media approach

The transport of macromolecules, such as low-density lipoprotein (LDL), and their accumulation in the layers of the arterial wall play a critical role in the creation and development of atherosclerosis. Atherosclerosis is a disease of large arteries e.g., the aorta, coronary, carotid, and other proximal arteries that involves a distinctive accumulation of LDL and other lipid-bearing materials in the arterial wall. Over time, plaque hardens and narrows the arteries. The flow of oxygen-rich blood to organs and other parts of the body is reduced. This can lead to serious problems, including heart attack, stroke, or even death. It has been proven that the accumulation of macromolecules in the arterial wall depends not only on the ease with which materials enter the wall, but also on the hindrance to the passage of materials out of the wall posed by underlying layers. Therefore, attention was drawn to the fact that the wall structure of large arteries is different than other vessels which are disease-resistant. Atherosclerosis tends to be localized in regions of curvature and branching in arteries where fluid shear stress (shear rate) and other fluid mechanical characteristics deviate from their normal spatial and temporal distribution patterns in straight vessels. On the other hand, the smooth muscle cells (SMCs) residing in the media layer of the arterial wall respond to mechanical stimuli, such as shear stress. Shear stress may affect SMC proliferation and migration from the media layer to intima. This occurs in atherosclerosis and intimal hyperplasia. The study of blood flow and other body fluids and of heat transport through the arterial wall is one of the advanced applications of porous media in recent years. The arterial wall may be modeled in both macroscopic (as a continuous porous medium) and microscopic scales (as a heterogeneous porous medium). In the present study, the governing equations of mass, heat and momentum transport have been solved for different species and interstitial fluid within the arterial wall by means of computational fluid dynamics (CFD). Simulation models are based on the finite element (FE) and finite volume (FV) methods. The wall structure has been modeled by assuming the wall layers as porous media with different properties. In order to study the heat transport through human tissues, the simulations have been carried out for a non-homogeneous model of porous media. The tissue is composed of blood vessels, cells, and an interstitium. The interstitium consists of interstitial fluid and extracellular fibers. Numerical simulations are performed in a two-dimensional (2D) model to realize the effect of the shape and configuration of the discrete phase on the convective and conductive features of heat transfer, e.g. the interstitium of biological tissues. On the other hand, the governing equations of momentum and mass transport have been solved in the heterogeneous porous media model of the media layer, which has a major role in the transport and accumulation of solutes across the arterial wall. The transport of Adenosine 5´-triphosphate (ATP) is simulated across the media layer as a benchmark to observe how SMCs affect on the species mass transport. In addition, the transport of interstitial fluid has been simulated while the deformation of the media layer (due to high blood pressure) and its constituents such as SMCs are also involved in the model. In this context, the effect of pressure variation on shear stress is investigated over SMCs induced by the interstitial flow both in 2D and three-dimensional (3D) geometries for the media layer. The influence of hypertension (high pressure) on the transport of lowdensity lipoprotein (LDL) through deformable arterial wall layers is also studied. This is due to the pressure-driven convective flow across the arterial wall. The intima and media layers are assumed as homogeneous porous media. The results of the present study reveal that ATP concentration over the surface of SMCs and within the bulk of the media layer is significantly dependent on the distribution of cells. Moreover, the shear stress magnitude and distribution over the SMC surface are affected by transmural pressure and the deformation of the media layer of the aorta wall. This work reflects the fact that the second or even subsequent layers of SMCs may bear shear stresses of the same order of magnitude as the first layer does if cells are arranged in an arbitrary manner. This study has brought new insights into the simulation of the arterial wall, as the previous simplifications have been ignored. The configurations of SMCs used here with elliptic cross sections of SMCs closely resemble the physiological conditions of cells. Moreover, the deformation of SMCs with high transmural pressure which follows the media layer compaction has been studied for the first time. On the other hand, results demonstrate that LDL concentration through the intima and media layers changes significantly as wall layers compress with transmural pressure. It was also noticed that the fraction of leaky junctions across the endothelial cells and the area fraction of fenestral pores over the internal elastic lamina affect the LDL distribution dramatically through the thoracic aorta wall. The simulation techniques introduced in this work can also trigger new ideas for simulating porous media involved in any biomedical, biomechanical, chemical, and environmental engineering applications.

An alternative finite element formulation for determination of streamlines in two-dimensional problems

It is well known that the numerical solutions of incompressible viscous flows are of great importance in Fluid Dynamics. The graphics output capabilities of their computational codes have revolutionized the communication of ideas to the non-specialist public. In general those codes include, in their hydrodynamic features, the visualization of flow streamlines - essentially a form of contour plot showing the line patterns of the flow - and the magnitudes and orientations of their velocity vectors. However, the standard finite element formulation to compute streamlines suffers from the disadvantage of requiring the determination of boundary integrals, leading to cumbersome implementations at the construction of the finite element code. In this article, we introduce an efficient way - via an alternative variational formulation - to determine the streamlines for fluid flows, which does not need the computation of contour integrals. In order to illustrate the good performance of the alternative formulation proposed, we capture the streamlines of three viscous models: Stokes, Navier-Stokes and Viscoelastic flows.

Numerical simulation of two-chamber plasma sources using finite element method

Numerical simulation of plasma sources is very important. Such models allows to vary different plasma parameters with high degree of accuracy. Moreover, they allow to conduct measurements not disturbing system balance.Recently, the scientific and practical interest increased in so-called two-chamber plasma sources. In one of them (small or discharge chamber) an external power source is embedded. In that chamber plasma forms. In another (large or diffusion chamber) plasma exists due to the transport of particles and energy through the boundary between chambers.In this particular work two-chamber plasma sources with argon and oxygen as active mediums were onstructed. This models give interesting results in electric field profiles and, as a consequence, in density profiles of charged particles.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.

Simulation and material calibration of ultra high strength steel (UHSS) S960 welded joint under static tensile test utilizing finite element method (FEM)

The aim of this work was to calibrate the material properties including strength and strain values for different material zones of ultra-high strength steel (UHSS) welded joints under monotonic static loading. The UHSS is heat sensitive and softens by heat due to welding, the affected zone is heat affected zone (HAZ). In this regard, cylindrical specimens were cut out from welded joints of Strenx® 960 MC and Strenx® Tube 960 MH, were examined by tensile test. The hardness values of specimens’ cross section were measured. Using correlations between hardness and strength, initial material properties were obtained. The same size specimen with different zones of material same as real specimen were created and defined in finite element method (FEM) software with commercial brand Abaqus 6.14-1. The loading and boundary conditions were defined considering tensile test values. Using initial material properties made of hardness-strength correlations (true stress-strain values) as Abaqus main input, FEM is utilized to simulate the tensile test process. By comparing FEM Abaqus results with measured results of tensile test, initial material properties will be revised and reused as software input to be fully calibrated in such a way that FEM results and tensile test results deviate minimum. Two type of different S960 were used including 960 MC plates, and structural hollow section 960 MH X-joint. The joint is welded by BöhlerTM X96 filler material. In welded joints, typically the following zones appear: Weld (WEL), Heat affected zone (HAZ) coarse grained (HCG) and fine grained (HFG), annealed zone, and base material (BaM). Results showed that: The HAZ zone is softened due to heat input while welding. For all the specimens, the softened zone’s strength is decreased and makes it a weakest zone where fracture happens while loading. Stress concentration of a notched specimen can represent the properties of notched zone. The load-displacement diagram from FEM modeling matches with the experiments by the calibrated material properties by compromising two correlations of hardness and strength.

Finite-Sample Inference Methods for Simultaneous Equations and Models with Unobserved and Generated Regressors

We propose finite sample tests and confidence sets for models with unobserved and generated regressors as well as various models estimated by instrumental variables methods. The validity of the procedures is unaffected by the presence of identification problems or \"weak instruments\", so no detection of such problems is required. We study two distinct approaches for various models considered by Pagan (1984). The first one is an instrument substitution method which generalizes an approach proposed by Anderson and Rubin (1949) and Fuller (1987) for different (although related) problems, while the second one is based on splitting the sample. The instrument substitution method uses the instruments directly, instead of generated regressors, in order to test hypotheses about the \"structural parameters\" of interest and build confidence sets. The second approach relies on \"generated regressors\", which allows a gain in degrees of freedom, and a sample split technique. For inference about general possibly nonlinear transformations of model parameters, projection techniques are proposed. A distributional theory is obtained under the assumptions of Gaussian errors and strictly exogenous regressors. We show that the various tests and confidence sets proposed are (locally) \"asymptotically valid\" under much weaker assumptions. The properties of the tests proposed are examined in simulation experiments. In general, they outperform the usual asymptotic inference methods in terms of both reliability and power. Finally, the techniques suggested are applied to a model of Tobin’s q and to a model of academic performance.

Calculations of the polycentric linear molecule H^2+_3 with the finite element method

A fully numerical two-dimensional solution of the Schrödinger equation is presented for the linear polyatomic molecule H^2+_3 using the finite element method (FEM). The Coulomb singularities at the nuclei are rectified by using both a condensed element distribution around the singularities and special elements. The accuracy of the results for the 1\sigma and 2\sigma orbitals is of the order of 10^-7 au.

Accurate Hartree-Fock-Slater calculations on small diatomic molecules with the finite-element method

We report on the self-consistent field solution of the Hartree-Fock-Slater equations using the finite-element method for the three small diatomic molecules N_2, BH and CO as examples. The quality of the results is not only better by two orders of magnitude than the fully numerical finite difference method of Laaksonen et al. but the method also requires a smaller number of grid points.

Spin-polarized Hartree-Fock-Slater calculations in atoms and diatomic molecules with the finite element method

We present spin-polarized Hartree-Fock-Slater calculations performed with the highly accurate numerical finite element method for the atoms N and 0 and the diatomic radical OH as examples.

H_2 solved by the finite element method

We report on the solution of the Hartree-Fock equations for the ground state of the H_2 molecule using the finite element method. Both the Hartree-Fock and the Poisson equations are solved with this method to an accuracy of 10^-8 using only 26 x 11 grid points in two dimensions. A 41 x 16 grid gives a new Hartree-Fock benchmark to ten-figure accuracy.