The mechanical heterogeneity of the hard callus influences local tissue strains during bone healing : a finite element study based on sheep experiments

During secondary fracture healing, various tissue types including new bone are formed. The local mechanical strains play an important role in tissue proliferation and differentiation. To further our mechanobiological understanding of fracture healing, a precise assessment of local strains is mandatory. Until now, static analyses using Finite Elements (FE) have assumed homogenous material properties. With the recent quantification of both the spatial tissue patterns (Vetter et al., 2010) and the development of elastic modulus of newly formed bone during healing (Manjubala et al., 2009), it is now possible to incorporate this heterogeneity. Therefore, the aim of this study is to investigate the effect of this heterogeneity on the strain patterns at six successive healing stages. The input data of the present work stemmed from a comprehensive cross-sectional study of sheep with a tibial osteotomy (Epari et al., 2006). In our FE model, each element containing bone was described by a bulk elastic modulus, which depended on both the local area fraction and the local elastic modulus of the bone material. The obtained strains were compared with the results of hypothetical FE models assuming homogeneous material properties. The differences in the spatial distributions of the strains between the heterogeneous and homogeneous FE models were interpreted using a current mechanobiological theory (Isakson et al., 2006). This interpretation showed that considering the heterogeneity of the hard callus is most important at the intermediate stages of healing, when cartilage transforms to bone via endochondral ossification.

Experimental and finite element analysis of a double strap joint between steel plates and normal modulus CFRP

Strengthening of steel structures using externally-bonded carbon fibre reinforced polymers ‘CFRP’ is a rapidly developing technique. This paper describes the behaviour of axially loaded flat steel plates strengthened using carbon fibre reinforced polymer sheets. Two steel plates were joined together with adhesive and followed by the application of carbon fibre sheet double strap joint with different bond lengths. The behaviour of the specimens was further investigated by using nonlinear finite element analysis to predict the failure modes and load capacity. In this study, bond failure is the dominant failure mode for normal modulus (240 GPa) CFRP bonding which closely matched the results of finite elements. The predicted ultimate loads from the FE analysis are found to be in good agreement with experimental values.

A new method for the in vivo identification of mechanical properties in arteries from cine MRI images: Theoretical framework and validation

Quantifying the stiffness properties of soft tissues is essential for the diagnosis of many cardiovascular diseases such as atherosclerosis. In these pathologies it is widely agreed that the arterial wall stiffness is an indicator of vulnerability. The present paper focuses on the carotid artery and proposes a new inversion methodology for deriving the stiffness properties of the wall from cine-MRI (magnetic resonance imaging) data. We address this problem by setting-up a cost function defined as the distance between the modeled pixel signals and the measured ones. Minimizing this cost function yields the unknown stiffness properties of both the arterial wall and the surrounding tissues. The sensitivity of the identified properties to various sources of uncertainty is studied. Validation of the method is performed on a rubber phantom. The elastic modulus identified using the developed methodology lies within a mean error of 9.6%. It is then applied to two young healthy subjects as a proof of practical feasibility, with identified values of 625 kPa and 587 kPa for one of the carotid of each subject.

Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.

Concurrent multi-scale modeling of civil infrastructures for analyses on structural deterioration—Part I : Modeling methodology and strategy

This paper aims to develop the methodology and strategy for concurrent finite element modeling of civil infrastructures at the different scale levels for the purposes of analyses of structural deteriorating. The modeling strategy and method were investigated to develop the concurrent multi-scale model of structural behavior (CMSM-of-SB) in which the global structural behavior and nonlinear damage features of local details in a large complicated structure could be concurrently analyzed in order to meet the needs of structural-state evaluation as well as structural deteriorating. In the proposed method, the “large-scale” modeling is adopted for the global structure with linear responses between stress and strain and the “small-scale” modeling is available for nonlinear damage analyses of the local welded details. A longitudinal truss in steel bridge decks was selected as a case to study how a CMSM-of-SB was developed. The reduced-scale specimen of the longitudinal truss was studied in the laboratory to measure its dynamic and static behavior in global truss and local welded details, while the multi-scale models using constraint equations and substructuring were developed for numerical simulation. The comparison of dynamic and static response between the calculated results by different models indicated that the proposed multi-scale model was found to be the most efficient and accurate. The verification of the model with results from the tested truss under the specific loading showed that, responses at the material scale in the vicinity of local details as well as structural global behaviors could be obtained and fit well with the measured results. The proposed concurrent multi-scale modeling strategy and implementation procedures were applied to Runyang cable-stayed bridge (RYCB) and the CMSM-of-SB of the bridge deck system was accordingly constructed as a practical application.

Concurrent multi-scale modeling of civil infrastructures for analyses on structural deteriorating—Part II : Model updating and verification

This paper is a continuation of the paper titled “Concurrent multi-scale modeling of civil infrastructure for analyses on structural deteriorating—Part I: Modeling methodology and strategy” with the emphasis on model updating and verification for the developed concurrent multi-scale model. The sensitivity-based parameter updating method was applied and some important issues such as selection of reference data and model parameters, and model updating procedures on the multi-scale model were investigated based on the sensitivity analysis of the selected model parameters. The experimental modal data as well as static response in terms of component nominal stresses and hot-spot stresses at the concerned locations were used for dynamic response- and static response-oriented model updating, respectively. The updated multi-scale model was further verified to act as the baseline model which is assumed to be finite-element model closest to the real situation of the structure available for the subsequent arbitrary numerical simulation. The comparison of dynamic and static responses between the calculated results by the final model and measured data indicated the updating and verification methods applied in this paper are reliable and accurate for the multi-scale model of frame-like structure. The general procedures of multi-scale model updating and verification were finally proposed for nonlinear physical-based modeling of large civil infrastructure, and it was applied to the model verification of a long-span bridge as an actual engineering practice of the proposed procedures.

End-winding effect on shalft voltage in AC generators

This paper presents effects of end-winding on shaft voltage in AC generators. A variety of design parameters have been considered to calculate the parasitic capacitive couplings in the machine structure with Finite Elements simulations and mathematical calculations. End-winding capacitances have also been calculated to have a precise estimation of shaft voltage and its relationship with design parameters in AC generators.

Modelling water droplet movement on a leaf surface

The central aim for the research undertaken in this PhD thesis is the development of a model for simulating water droplet movement on a leaf surface and to compare the model behavior with experimental observations. A series of five papers has been presented to explain systematically the way in which this droplet modelling work has been realised. Knowing the path of the droplet on the leaf surface is important for understanding how a droplet of water, pesticide, or nutrient will be absorbed through the leaf surface. An important aspect of the research is the generation of a leaf surface representation that acts as the foundation of the droplet model. Initially a laser scanner is used to capture the surface characteristics for two types of leaves in the form of a large scattered data set. After the identification of the leaf surface boundary, a set of internal points is chosen over which a triangulation of the surface is constructed. We present a novel hybrid approach for leaf surface fitting on this triangulation that combines Clough-Tocher (CT) and radial basis function (RBF) methods to achieve a surface with a continuously turning normal. The accuracy of the hybrid technique is assessed using numerical experimentation. The hybrid CT-RBF method is shown to give good representations of Frangipani and Anthurium leaves. Such leaf models facilitate an understanding of plant development and permit the modelling of the interaction of plants with their environment. The motion of a droplet traversing this virtual leaf surface is affected by various forces including gravity, friction and resistance between the surface and the droplet. The innovation of our model is the use of thin-film theory in the context of droplet movement to determine the thickness of the droplet as it moves on the surface. Experimental verification shows that the droplet model captures reality quite well and produces realistic droplet motion on the leaf surface. Most importantly, we observed that the simulated droplet motion follows the contours of the surface and spreads as a thin film. In the future, the model may be applied to determine the path of a droplet of pesticide along a leaf surface before it falls from or comes to a standstill on the surface. It will also be used to study the paths of many droplets of water or pesticide moving and colliding on the surface.

Calculations of capacitive couplings in induction generators to analyse shaft voltage

This paper deals with the analysis of the parameters which are effective in shaft voltage generation of induction generators. It focuses on different parasitic capacitive couplings by mathematical equations, finite element simulations and experiments. The effects of different design parameters have been studied on proposed capacitances and resultant shaft voltage. Some parameters can change proposed capacitive coupling such as: stator slot tooth, the gap between slot tooth and winding, and the height of the slot tooth, as well as the air gap between the rotor and the stator. This analysis can be used in a primary stage of a generator design to reduce motor shaft voltage and avoid additional costs of resultant bearing current mitigation.

A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM- LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very ‘‘tight’’ lower and upper bound solutions can be obtained using PIM-LS2.