Determination of elastic modulus of thin coating materials using nanoindentation and finite element analysis

A deconvolution method that combines nanoindentation and finite element analysis was developed to determine elastic modulus of thin coating layer in a coating-substrate bilayer system. In this method, the nanoindentation experiments were conducted to obtain the modulus of both the bilayer system and the substrate. The finite element analysis was then applied to deconvolve the elastic modulus of the coating. The results demonstrated that the elastic modulus obtained using the developed method was in good agreement with that reported in literature.

An experimental and finite element investigation of the biomechanics of vertebral compression fractures

Osteoporosis is a disease characterized by low bone mass and micro-architectural deterioration of bone tissue, with a consequent increase in bone fragility and susceptibility to fracture. Osteoporosis affects over 200 million people worldwide, with an estimated 1.5 million fractures annually in the United States alone, and with attendant costs exceeding $10 billion dollars per annum. Osteoporosis reduces bone density through a series of structural changes to the honeycomb-like trabecular bone structure (micro-structure). The reduced bone density, coupled with the microstructural changes, results in significant loss of bone strength and increased fracture risk. Vertebral compression fractures are the most common type of osteoporotic fracture and are associated with pain, increased thoracic curvature, reduced mobility, and difficulty with self care. Surgical interventions, such as kyphoplasty or vertebroplasty, are used to treat osteoporotic vertebral fractures by restoring vertebral stability and alleviating pain. These minimally invasive procedures involve injecting bone cement into the fractured vertebrae. The techniques are still relatively new and while initial results are promising, with the procedures relieving pain in 70-95% of cases, medium-term investigations are now indicating an increased risk of adjacent level fracture following the procedure. With the aging population, understanding and treatment of osteoporosis is an increasingly important public health issue in developed Western countries. The aim of this study was to investigate the biomechanics of spinal osteoporosis and osteoporotic vertebral compression fractures by developing multi-scale computational, Finite Element (FE) models of both healthy and osteoporotic vertebral bodies. The multi-scale approach included the overall vertebral body anatomy, as well as a detailed representation of the internal trabecular microstructure. This novel, multi-scale approach overcame limitations of previous investigations by allowing simultaneous investigation of the mechanics of the trabecular micro-structure as well as overall vertebral body mechanics. The models were used to simulate the progression of osteoporosis, the effect of different loading conditions on vertebral strength and stiffness, and the effects of vertebroplasty on vertebral and trabecular mechanics. The model development process began with the development of an individual trabecular strut model using 3D beam elements, which was used as the building block for lattice-type, structural trabecular bone models, which were in turn incorporated into the vertebral body models. At each stage of model development, model predictions were compared to analytical solutions and in-vitro data from existing literature. The incremental process provided confidence in the predictions of each model before incorporation into the overall vertebral body model. The trabecular bone model, vertebral body model and vertebroplasty models were validated against in-vitro data from a series of compression tests performed using human cadaveric vertebral bodies. Firstly, trabecular bone samples were acquired and morphological parameters for each sample were measured using high resolution micro-computed tomography (CT). Apparent mechanical properties for each sample were then determined using uni-axial compression tests. Bone tissue properties were inversely determined using voxel-based FE models based on the micro-CT data. Specimen specific trabecular bone models were developed and the predicted apparent stiffness and strength were compared to the experimentally measured apparent stiffness and strength of the corresponding specimen. Following the trabecular specimen tests, a series of 12 whole cadaveric vertebrae were then divided into treated and non-treated groups and vertebroplasty performed on the specimens of the treated group. The vertebrae in both groups underwent clinical-CT scanning and destructive uniaxial compression testing. Specimen specific FE vertebral body models were developed and the predicted mechanical response compared to the experimentally measured responses. The validation process demonstrated that the multi-scale FE models comprising a lattice network of beam elements were able to accurately capture the failure mechanics of trabecular bone; and a trabecular core represented with beam elements enclosed in a layer of shell elements to represent the cortical shell was able to adequately represent the failure mechanics of intact vertebral bodies with varying degrees of osteoporosis. Following model development and validation, the models were used to investigate the effects of progressive osteoporosis on vertebral body mechanics and trabecular bone mechanics. These simulations showed that overall failure of the osteoporotic vertebral body is initiated by failure of the trabecular core, and the failure mechanism of the trabeculae varies with the progression of osteoporosis; from tissue yield in healthy trabecular bone, to failure due to instability (buckling) in osteoporotic bone with its thinner trabecular struts. The mechanical response of the vertebral body under load is highly dependent on the ability of the endplates to deform to transmit the load to the underlying trabecular bone. The ability of the endplate to evenly transfer the load through the core diminishes with osteoporosis. Investigation into the effect of different loading conditions on the vertebral body found that, because the trabecular bone structural changes which occur in osteoporosis result in a structure that is highly aligned with the loading direction, the vertebral body is consequently less able to withstand non-uniform loading states such as occurs in forward flexion. Changes in vertebral body loading due to disc degeneration were simulated, but proved to have little effect on osteoporotic vertebra mechanics. Conversely, differences in vertebral body loading between simulated invivo (uniform endplate pressure) and in-vitro conditions (where the vertebral endplates are rigidly cemented) had a dramatic effect on the predicted vertebral mechanics. This investigation suggested that in-vitro loading using bone cement potting of both endplates has major limitations in its ability to represent vertebral body mechanics in-vivo. And lastly, FE investigation into the biomechanical effect of vertebroplasty was performed. The results of this investigation demonstrated that the effect of vertebroplasty on overall vertebra mechanics is strongly governed by the cement distribution achieved within the trabecular core. In agreement with a recent study, the models predicted that vertebroplasty cement distributions which do not form one continuous mass which contacts both endplates have little effect on vertebral body stiffness or strength. In summary, this work presents the development of a novel, multi-scale Finite Element model of the osteoporotic vertebral body, which provides a powerful new tool for investigating the mechanics of osteoporotic vertebral compression fractures at the trabecular bone micro-structural level, and at the vertebral body level.

Creation of a validated 3D finite element model of an ovine tibia

Introduction Ovine models are widely used in orthopaedic research. To better understand the impact of orthopaedic procedures computer simulations are necessary. 3D finite element (FE) models of bones allow implant designs to be investigated mechanically, thereby reducing mechanical testing. Hypothesis We present the development and validation of an ovine tibia FE model for use in the analysis of tibia fracture fixation plates. Material & Methods Mechanical testing of the tibia consisted of an offset 3-pt bend test with three repetitions of loading to 350N and return to 50N. Tri-axial stacked strain gauges were applied to the anterior and posterior surfaces of the bone and two rigid bodies – consisting of eight infrared active markers, were attached to the ends of the tibia. Positional measurements were taken with a FARO arm 3D digitiser. The FE model was constructed with both geometry and material properties derived from CT images of the bone. The elasticity-density relationship used for material property determination was validated separately using mechanical testing. This model was then transformed to the same coordinate system as the in vitro mechanical test and loads applied. Results Comparison between the mechanical testing and the FE model showed good correlation in surface strains (difference: anterior 2.3%, posterior 3.2%). Discussion & Conclusion This method of model creation provides a simple method for generating subject specific FE models from CT scans. The use of the CT data set for both the geometry and the material properties ensures a more accurate representation of the specific bone. This is reflected in the similarity of the surface strain results.

Development of a multi-scale finite element model of the osteoporotic lumbar vertebral body for the investigation of apparent level vertebra mechanics and micro-level trabecular mechanics.

Osteoporotic spinal fractures are a major concern in ageing Western societies. This study develops a multi-scale finite element (FE) model of the osteoporotic lumbar vertebral body to study the mechanics of vertebral compression fracture at both the apparent (whole vertebral body) and micro-structural (internal trabecular bone core)levels. Model predictions were verified against experimental data, and found to provide a reasonably good representation of the mechanics of the osteoporotic vertebral body. This novel modelling methodology will allow detailed investigation of how trabecular bone loss in osteoporosis affects vertebral stiffness and strength in the lumbar spine.

Tooth fracture risk analysis based on a new finite element dental structure models using micro-CT data

The finite element (FE) analysis is an effective method to study the strength and predict the fracture risk of endodontically-treated teeth. This paper presents a rapid method developed to generate a comprehensive tooth FE model using data retrieved from micro-computed tomography (μCT). With this method, the inhomogeneity of material properties of teeth was included into the model without dividing the tooth model into different regions. The material properties of the tooth were assumed to be related to the mineral density. The fracture risk at different tooth portions was assessed for root canal treatments. The micro-CT images of a tooth were processed by a Matlab software programme and the CT numbers were retrieved. The tooth contours were obtained with thresholding segmentation using Amira. The inner and outer surfaces of the tooth were imported into Solidworks and a three-dimensional (3D) tooth model was constructed. An assembly of the tooth model with the periodontal ligament (PDL) layer and surrounding bone was imported into ABAQUS. The material properties of the tooth were calculated from the retrieved CT numbers via ABAQUS user's subroutines. Three root canal geometries (original and two enlargements) were investigated. The proposed method in this study can generate detailed 3D finite element models of a tooth with different root canal enlargements and filling materials, and would be very useful for the assessment of the fracture risk at different tooth portions after root canal treatments.

A dynamic wheel-rail impact analysis of railway track under wheel flat by Finite Element Analysis

Wheel–rail interaction is one of the most important research topics in railway engineering. It involves track impact response, track vibration and track safety. Track structure failures caused by wheel–rail impact forces can lead to significant economic loss for track owners through damage to rails and to the sleepers beneath. Wheel–rail impact forces occur because of imperfections in the wheels or rails such as wheel flats, irregular wheel profiles, rail corrugations and differences in the heights of rails connected at a welded joint. A wheel flat can cause a large dynamic impact force as well as a forced vibration with a high frequency, which can cause damage to the track structure. In the present work, a three-dimensional (3-D) finite element (FE) model for the impact analysis induced by the wheel flat is developed by use of the finite element analysis (FEA) software package ANSYS and validated by another validated simulation. The effect of wheel flats on impact forces is thoroughly investigated. It is found that the presence of a wheel flat will significantly increase the dynamic impact force on both rail and sleeper. The impact force will monotonically increase with the size of wheel flats. The relationships between the impact force and the wheel flat size are explored from this finite element analysis and they are important for track engineers to improve their understanding of the design and maintenance of the track system.

Finite element shoulder models

Shoulder joint is a complex integration of soft and hard tissues. It plays an important role in performing daily activities and can be considered as a perfect compromise between mobility and stability. However, shoulder is vulnerable to complications such as dislocations and osteoarthritis. Finite element (FE) models have been developed to understand shoulder injury mechanisms, implications of disease on shoulder complex and in assessing the quality of shoulder implants. Further, although few, Finite element shoulder models have also been utilized to answer important clinical questions such as the difference between a normal and osteoarthritic shoulder joint. However, due to the absence of experimental validation, it is questionable whether the constitutive models applied in these FE models are adequate to represent mechanical behaviors of shoulder elements (Cartilages, Ligaments, Muscles etc), therefore the confidence of using current models in answering clinically relevant question. The main objective of this review is to critically evaluate the existing FE shoulder models that have been used to investigate clinical problems. Due concern is given to check the adequacy of representative constitutive models of shoulder elements in drawing clinically relevant conclusion. Suggestions have been given to improve the existing shoulder models by inclusion of adequate constitutive models for shoulder elements to confidently answer clinically relevant questions.

A finite element model of seat cushion indentation with a soft tissue human occupant model

Effective digital human model (DHM) simulation of automotive driver packaging ergonomics, safety and comfort depends on accurate modelling of occupant posture, which is strongly related to the mechanical interaction between human body soft tissue and flexible seat components. This paper presents a finite-element study simulating the deflection of seat cushion foam and supportive seat structures, as well as human buttock and thigh soft tissue when seated. The three-dimensional data used for modelling thigh and buttock geometry were taken on one 95th percentile male subject, representing the bivariate percentiles of the combined hip breadth (seated) and buttock-to-knee length distributions of a selected Australian and US population. A thigh-buttock surface shell based on this data was generated for the analytic model. A 6mm neoprene layer was offset from the shell to account for the compression of body tissue expected through sitting in a seat. The thigh-buttock model is therefore made of two layers, covering thin to moderate thigh and buttock proportions, but not more fleshy sizes. To replicate the effects of skin and fat, the neoprene rubber layer was modelled as a hyperelastic material with viscoelastic behaviour in a Neo-Hookean material model. Finite element (FE) analysis was performed in ANSYS V13 WB (Canonsburg, USA). It is hypothesized that the presented FE simulation delivers a valid result, compared to a standard SAE physical test and the real phenomenon of human-seat indentation. The analytical model is based on the CAD assembly of a Ford Territory seat. The optimized seat frame, suspension and foam pad CAD data were transformed and meshed into FE models and indented by the two layer, soft surface human FE model. Converging results with the least computational effort were achieved for a bonded connection between cushion and seat base as well as cushion and suspension, no separation between neoprene and indenter shell and a frictional connection between cushion pad and neoprene. The result is compared to a previous simulation of an indentation with a hard shell human finite-element model of equal geometry, and to the physical indentation result, which is approached with very high fidelity. We conclude that (a) SAE composite buttock form indentation of a suspended seat cushion can be validly simulated in a FE model of merely similar geometry, but using a two-layer hard/soft structure. (b) Human-seat indentation of a suspended seat cushion can be validly simulated with a simplified human buttock-thigh model for a selected anthropomorphism.

Geometric sensitivity of patient-specific finite element models of the spine to variability in user-selected anatomical landmarks

Software to create individualised finite element (FE) models of the osseoligamentous spine using pre-operative computed tomography (CT) data-sets for spinal surgery patients has recently been developed. This study presents a geometric sensitivity analysis of this software to assess the effect of intra-observer variability in user-selected anatomical landmarks. User-selected landmarks on the osseous anatomy were defined from CT data-sets for three scoliosis patients and these landmarks were used to reconstruct patient-specific anatomy of the spine and ribcage using parametric descriptions. The intra-observer errors in landmark co-ordinates for these anatomical landmarks were calculated. FE models of the spine and ribcage were created using the reconstructed anatomy for each patient and these models were analysed for a loadcase simulating clinical flexibility assessment. The intra-observer error in the anatomical measurements was low in comparison to the initial dimensions, with the exception of the angular measurements for disc wedge and zygapophyseal joint (z-joint) orientation and disc height. This variability suggested that CT resolution may influence such angular measurements, particularly for small anatomical features, such as the z-joints, and may also affect disc height. The results of the FE analysis showed low variation in the model predictions for spinal curvature with the mean intra-observer variability substantially less than the accepted error in clinical measurement. These findings demonstrate that intra-observer variability in landmark point selection has minimal effect on the subsequent FE predictions for a clinical loadcase.

Comparison of eight published static finite element models of the intact lumbar spine : predictive power of models improves when combined together

Finite element (FE) model studies have made important contributions to our understanding of functional biomechanics of the lumbar spine. However, if a model is used to answer clinical and biomechanical questions over a certain population, their inherently large inter-subject variability has to be considered. Current FE model studies, however, generally account only for a single distinct spinal geometry with one set of material properties. This raises questions concerning their predictive power, their range of results and on their agreement with in vitro and in vivo values. Eight well-established FE models of the lumbar spine (L1-5) of different research centres around the globe were subjected to pure and combined loading modes and compared to in vitro and in vivo measurements for intervertebral rotations, disc pressures and facet joint forces. Under pure moment loading, the predicted L1-5 rotations of almost all models fell within the reported in vitro ranges, and their median values differed on average by only 2° for flexion-extension, 1° for lateral bending and 5° for axial rotation. Predicted median facet joint forces and disc pressures were also in good agreement with published median in vitro values. However, the ranges of predictions were larger and exceeded those reported in vitro, especially for the facet joint forces. For all combined loading modes, except for flexion, predicted median segmental intervertebral rotations and disc pressures were in good agreement with measured in vivo values. In light of high inter-subject variability, the generalization of results of a single model to a population remains a concern. This study demonstrated that the pooled median of individual model results, similar to a probabilistic approach, can be used as an improved predictive tool in order to estimate the response of the lumbar spine.

Porohyperelastic finite element model for the kangaroo humeral head cartilage based on experimental study and the consolidation theory

Solid-extracellular fluid interaction is believed to play an important role in the strain-rate dependent mechanical behaviors of shoulder articular cartilages. It is believed that the kangaroo shoulder joint is anatomically and biomechanically similar to human shoulder joint and it is easy to get in Australia. Therefore, the kangaroo humeral head cartilage was used as the suitable tissue for the study in this paper. Indentation tests from quasi-static (10-4/sec) to moderately high strain-rate (10-2/sec) on kangaroo humeral head cartilage tissues were conduced to investigate the strain-rate dependent behaviors. A finite element (FE) model was then developed, in which cartilage was conceptualized as a porous solid matrix filled with incompressible fluids. In this model, the solid matrix was modeled as an isotropic hyperelastic material and the percolating fluid follows Darcy’s law. Using inverse FE procedure, the constitutive parameters related to stiffness, compressibility of the solid matrix and permeability were obtained from the experimental results. The effect of solid-extracellular fluid interaction and drag force (the resistance to fluid movement) on strain-rate dependent behavior was investigated by comparing the influence of constant, strain dependent and strain-rate dependent permeability on FE model prediction. The newly developed porohyperelastic cartilage model with the inclusion of strain-rate dependent permeability was found to be able to predict the strain-rate dependent behaviors of cartilages.

Finite element analysis of CFRP strengthened steel hollow sections under tension

This paper presents a nonlinear finite element (FE) model for the analysis of very high strength (VHS) steel hollow sections wrapped by high modulus carbon fibre rein forced polymer (CFRP) sheets. The bond strength of CFRP wrapped VHS circular steel hollow section under tension is investigated using the FE model. The three dimensional FE model by Nonlinear static analysis has been carried out by Strand 7 finite element software. The model is validated by the experimental data obtained from Fawzia et al [1]. A detail parametric study has been performed to examine the effect of number of CFRP layers, different diameters of VHS steel tube and different bond lengths of CFRP sheet. The analytical model developed by Fawzia et al. [1] has been used to determine the load carrying capacity of different diameters of CFRP strengthened VHS steel tube by using the capacity from each layer of CFRP sheet. The results from FE model have found in reasonable agreement with the analytical model developed by Fawzia et al [1]. This validation was necessary because the analytical model by Fawzia et al [1] was developed by using only one diameter of VHS steel tube and fixed (five) number of CFRP layers. It can be concluded that the developed analytical model is valid for CFRP strengthened VHS steel tubes with diameter range of 38mm to 100mm and CFRP layer range of 3 to 5 layers. Based on the results it can also be concluded that the effective bond length is consistent for different diameters of steel tubes and different layers of CFRP. Three layers of CFRP is considered most effective wrapping scheme due to the cost effectiveness. Finally the distribution of longitudinal and hoop stress has been determined by the finite element model for different diameters of CFRP strengthened VHS steel tube.

Comparison of eight published lumbar spine finite element models

Due to its ability to represent intricate systems with material nonlinearities as well as irregular loading, boundary, geometrical and material domains, the finite element (FE) method has been recognized as an important computational tool in spinal biomechanics. Current FE models generally account for a single distinct spinal geometry with one set of material properties despite inherently large inter-subject variability. The uncertainty and high variability in tissue material properties, geometry, loading and boundary conditions has cast doubt on the reliability of their predictions and comparability with reported in vitro and in vivo values. A multicenter study was undertaken to compare the results of eight well-established models of the lumbar spine that have been developed, validated and applied for many years. Models were subjected to pure and combined loading modes and their predictions were compared to in vitro and in vivo measurements for intervertebral rotations, disc pressures and facet joint forces. Under pure moment loading, the predicted L1-5 rotations of almost all models fell within the reported in vitro ranges; their median values differed on average by only 2° for flexion-extension, 1° for lateral bending and 5° for axial rotation. Predicted median facet joint forces and disc pressures were also in good agreement with previously published median in vitro values. However, the ranges of predictions were larger and exceeded the in vitro ranges, especially for facet joint forces. For all combined loading modes, except for flexion, predicted median segmental intervertebral rotations and disc pressures were in good agreement with in vivo values. The simulations yielded median facet joint forces of 0 N in flexion, 38 N in extension, 14 N in lateral bending and 60 N in axial rotation that could not be validated due to the paucity of in vivo facet joint forces. In light of high inter-subject variability, one must be cautious when generalizing predictions obtained from one deterministic model. This study demonstrates however that the predictive power increases when FE models are combined together. The median of individual numerical results can hence be used as an improved tool in order to estimate the response of the lumbar spine.

Finite element modeling of carbon fibre reinforced polymer (CFRP) strengthened steel tubes under axial impact

Steel hollow sections used in structures such as bridges, buildings and space structures involve different strengthening techniques according to their structural purpose and shape of the structural member. One such technique is external bonding of CFRP sheets to steel tubes. The performance of CFRP strengthening for steel structures has been proven under static loading while limited studies have been conducted on their behaviour under impact loading. In this study, a comprehensive numerical investigation is carried out to evaluate the response of CFRP strengthened steel tubes under dynamic axial impact loading. Impact force, axial deformation impact velocities are studied. The results of the numerical investigations are validated by experimental results. Based on the developed finite element (FE) model several output parameters are discussed. The results show that CFRP wrapping is an effective strengthening technique to increase the axial dynamic load bearing capacity by increasing the stiffness of the steel tube.

Two-dimensional Cartesian air-gap element (CAGE) for dynamic finite-element modeling of electrical machines with a flat air gap

This paper extends the air-gap element (AGE) to enable the modeling of flat air gaps. AGE is a macroelement originally proposed by Abdel-Razek et al.for modeling annular air gaps in electrical machines. The paper presents the theory of the new macroelement and explains its implementation within a time-stepped finite-element (FE) code. It validates the solution produced by the new macroelement by comparing it with that obtained by using an FE mesh with a discretized air gap. It then applies the model to determine the open-circuit electromotive force of an axial-flux permanent-magnet machine and compares the results with measurements.