Mark Bruzzi

Calibration of a constitutive model for the post-yield behaviour of cortical bone

In this work, the post-yield behaviour of cortical bone is investigated using finite element modelling, nanoindentation and atomic force microscopy. Based on recent investigations, it is proposed that, since pressure dependent deformation mechanisms may contribute to yielding in bone, constitutive models attempting to capture its post-yield behaviour should also incorporate pressure dependence. Nanoindentation testing is performed using a spheroconical indenter tip, and subsequent atomic force microscopy at the indented site shows that bone does not exhibit surface pile-up. By simulating the nanoindentation test, it is found that a Mises based constitutive law cannot simultaneously capture the deformations and load-displacement curve produced during nanoindentation. However, an extended Drucker-Prager model can capture the post-yield behaviour of bone accurately, since it accounts for pressure dependent yield. This suggests that frictional mechanisms are central to the post-yield behaviour of bone. In this work, the extended Drucker-Prager model is calibrated and validated using further simulations.

Micromechanical modelling of the static and cyclic loading of an Al 2124-SiC MMC

Abstract The objective of this study was to use micromechanical finite element models to simulate both the static and cyclic mechanical behaviour of a metal matrix composite: a forged Al 2124 alloy reinforced with 17% SiC particles, at two different temperatures: room temperature and 150°C. In the simulations, periodic unit cell models incorporating the explicit representation of the matrix and the reinforcing particles in both 2D and 3D, were used. Micromechanical models with both idealised and realistic reinforcing particle shapes and distributions were generated. The realistic particle shapes and distributions were inferred from experimental SEM micrographs. The pattern and intensity of the plastic deformation within the matrix was studied and the macroscale behaviour of the composite was inferred from average stress and strain values. In order to include the effects of residual stresses due to the processing of the material, a quenching simulation was performed, prior to the mechanical loading, and its effects on the macroscopic tensile behaviour of the MMC was assessed. The effects of removing the periodicity constraint on the models by using a cell embedding technique was investigated. In order to try and model the deformation behaviour of the matrix more accurately, crystal plasticity models, which included the explicit representation of individual grains were examined for different matrix grain morphologies. The results of the simulations were compared with experimental results for the MMC in terms of macroscopic tensile stress–strain curves. Finally, the effects of different matrix strain hardening models were examined in order to investigate the cyclic behaviour of the MMC.

Micromechanical modelling of cortical bone

Cortical bone is a heterogeneous material with a complex hierarchical microstructure. In this work, unit cell finite element models were developed to investigate the effect of microstructural morphology on the macroscopic properties of cortical bone. The effect of lacunar and vascular porosities, percentage of osteonal bone and orientation of the Haversian system on the macroscopic elastic moduli and Poissons ratios was investigated. The results presented provide relationships for applying more locally accurate material properties to larger scale and whole bone models of varying porosity. Analysis of the effect of the orientation of the Haversian system showed that its effects should not be neglected in larger scale models. This study also provides insight into how microstructural features effect local distributions and cause a strain magnification effect. Limitations in applying the unit cell methodology approach to bone are also discussed.

Finite element comparison of performance related characteristics of balloon expandable stents

Cardiovascular stents are commonly made from 316L stainless steel and are deployed within stenosed arterial lesions using balloon expansion. Deployment involves inflating the balloon and plastically deforming the stent until the required diameter is obtained. This plastic deformation induces static stresses in the stent, which will remain for the lifetime of the device. In order to determine these stresses, finite element models of the unit cells of geometrically different, commercially available balloon expandable stents have been created, and deployment and elastic recoil have been simulated. In this work the residual stresses associated with deployment and recoil are compared for the various stent geometries, with a view to establishing appropriate initial stress states for fatigue loading for the stents. The maximum, minimum, and mean stresses induced in the stent due to systolic/diastolic pressure are evaluated, as are performance measures such as radial and longitudinal recoil.

Methodology for modelling the small crack fatigue behaviour of aluminium alloys

Abstract The objective of this study is to develop a computational modelling methodology of the small fatigue crack growth behaviour of: (1) a forged 2124 Al alloy in the T4 condition and (2) a cast 359 Al alloy in the T6 condition. In particular, the focus of this work is on correlating local crack-tip driving force conditions of an initial small crack with an experimental long crack growth rate curve, using crack closure. A defect tolerant approach is assumed. The crack tip is modelled using the finite element method, and the correlating parameter, Δ J eff (the effective range of the J -integral), is calculated. An effective crack growth rate curve is calculated, and the Δ J eff is used to obtain the crack growth increment per cycle. Small crack growth rate curves for different stress levels and initial defect sizes are presented for each alloy for a stress ratio, R , of 0.1. Predicted S – N curves are then compared with experimental results for both the Al 2124 and Al 359 alloys. A good agreement with experimental results is achieved for an appropriate choice of defect size. Finally, as a means of validating the choice of defect size, the fatigue limit vs. defect size results are compared on a Kitagawa diagram with those obtained by linear elastic fracture mechanics, for the Al 2124 alloy.

Nitinol stent design – understanding axial buckling

Nitinol׳s superelastic properties permit self-expanding stents to be crimped without plastic deformation, but its nonlinear properties can contribute towards stent buckling. This study investigates the axial buckling of a prototype tracheobronchial nitinol stent design during crimping, with the objective of eliminating buckling from the design. To capture the stent buckling mechanism a computational model of a radial force test is simulated, where small geometric defects are introduced to remove symmetry and allow buckling to occur. With the buckling mechanism ascertained, a sensitivity study is carried out to examine the effect that the transitional plateau region of the nitinol loading curve has on stent stability. Results of this analysis are then used to redesign the stent and remove buckling. It is found that the transitional plateau region can have a significant effect on the stability of a stent during crimping, and by reducing the amount of transitional material within the stent hinges during loading the stability of a nitinol stent can be increased.

Self-expanding stent modelling and radial force accuracy.

Computational simulations using finite element analysis are a tool commonly used to analyse stent designs, deployment geometries and interactions between stent struts and arterial tissue. Such studies require large computational models and efforts are often made to simplify models in order to reduce computational time while maintaining reasonable accuracy. The objective of the study is focused on computational modelling and specifically aims to investigate how different methods of modelling stent–artery interactions can affect the results, computational time taken and computational size of the model. Various different models, each with increasing levels of complexity, are used to simulate this analysis, representing the many assumptions and simplifications used in other similar studies in order to determine what level of simplification will still allow for an accurate representation of stent radial force and resulting stress concentrations on the inner lining of the vessel during self-expanding stent deployment. The main conclusions of the study are that methods used in stent crimping impact on the resulting predicted radial force of the stent; that accurate representation of stent–artery interactions can only be made when modelling the full length of the stent due to the incorporation of end effects; and that modelling self-contact of the stent struts greatly impacts on the resulting stress concentrations within the stent, but that the effect of this on the unloading behaviour and resulting radial force of the stent is negligible.

Effects of knee flexion on the femoropopliteal artery: A computational study

During knee flexion, the muscles of the upper leg impose various loads on the underlying femoropopliteal artery resulting in radial compression, bending, torsion, axial extension and axial compression. Measuring the dynamic force environment of the femoropopliteal artery and quantifying its resulting deformation characteristics is an essential input to peripheral device design. The goal of this study was to create an anatomically accurate, three dimensional finite element model capable of capturing the loading conditions and deformation characteristics of the femoropopliteal artery during knee flexion. Three dimensional geometries of the muscle, bone, arterial and soft tissues of the leg were constructed from CT scan data and meshed for finite element analysis. Knee flexion was simulated and deformation characteristics of length change (axial compression), curvature, radial compression and axial twist were quantified and compared to previous experimental studies. The model predicts 8.23% shortening and an average curvature of 0.294±0.26 cm(-1) in the vessel after knee flexion, with maximum stresses of 61.17 kPa and maximum strains of 0.16%. The model created replicates known in vivo deformation characteristics seen previously in angiographic images and for the first time associates femoropopliteal artery deformation characteristics with stress and strain levels within the arterial tissue.

A Computational Analysis of the Deformation of the Femoropopliteal Artery With Stenting

Physiological loads that act on the femoropopliteal artery, in combination with stenting, can lead to uncharacteristic deformations of the stented vessel. The overall goal of this study was to investigate the effect of stent length and stent location on the deformation characteristics of the superficial femoral artery (SFA) using an anatomically accurate, three-dimensional finite element model of the leg. For a range of different stent lengths and locations, the deformation characteristics (length change, curvature change, and axial twist) that result from physiological loading of the SFA along with the mechanical behavior of the vessel tissue are investigated. Results showed that stenting portions of the SFA leads to a change in global deformation characteristics of the vessel. Increased stress and strain values and altered deformation characteristics were observed in the various stented cases of this study, which are compared to previous results of an unstented vessel. The study concludes that shortening, twist and curvature characteristics of the stented vessel are dependent on stent length and stent location within the vessel.

The effect of crystallographic texture on stress-induced martensitic transformation in NiTi: A computational analysis.

NiTi׳s superelasticity is exploited in a number of biomedical devices, in particular self-expanding endovascular stents. These stents are often laser-cut from textured micro-tubing; texture is the distribution of crystallographic grain orientations in a polycrystalline material which has been experimentally shown to have a marked influence on mechanical properties. This study offers a computational examination into the effect of texture on the stress-induced martensite transformation (SIMT) in a micro-dogbone NiTi specimen subject to tensile loading. Finite Element Analysis (FEA) is employed to simulate the transformational behaviour of the specimen on a micro-scale level. To represent a realistic grain structure in the FEA model, grains present in a 200µm×290µm test site located at the centre edge of the specimen were identified using Scanning Electron Microscopy (SEM). Grains are assumed to have homogenous behaviour with properties varying according to their crystallographic orientation to the loading direction. Required material properties were extracted from uniaxial stress-strain curves of single crystals for each crystallographic orientation for input into the in-built UMAT/Nitinol. The orientation of each grain in the test site was identified using Electron Back-Scatter Diffraction (EBSD) techniques. In this way, a quantitative explanation is offered to the effect of crystallographic texture on SIMT. Finally, the evolution of grains in the specimen, during the transformation process, was experimentally investigated by means of an in-situ SEM tensile test.