Experimental impact and finite element analysis of a composite, portable road safety barrier

This thesis provides an experimental and computational platform for investigating the performance and behaviour of water filled, plastic portable road safety barriers in an isolated impact scenario. A schedule of experimental impact tests were conducted assessing the impact response of an existing design of road safety barrier utilising a novel horizontal impact testing system. A coupled finite element and smooth particle hydrodynamic model of the barrier system was developed and validated against the results of the experimental tests. The validated model was subsequently used to assess the effect of certain composite materials on the impact performance of the water filled, portable road safety barrier system.

Local stress-strain distribution and load transfer across cartilage matrix at micro-scale using combined microscopy-based finite element method

Articular cartilage is the load-bearing tissue that consists of proteoglycan macromolecules entrapped between collagen fibrils in a three-dimensional architecture. To date, the drudgery of searching for mathematical models to represent the biomechanics of such a system continues without providing a fitting description of its functional response to load at micro-scale level. We believe that the major complication arose when cartilage was first envisaged as a multiphasic model with distinguishable components and that quantifying those and searching for the laws that govern their interaction is inadequate. To the thesis of this paper, cartilage as a bulk is as much continuum as is the response of its components to the external stimuli. For this reason, we framed the fundamental question as to what would be the mechano-structural functionality of such a system in the total absence of one of its key constituents-proteoglycans. To answer this, hydrated normal and proteoglycan depleted samples were tested under confined compression while finite element models were reproduced, for the first time, based on the structural microarchitecture of the cross-sectional profile of the matrices. These micro-porous in silico models served as virtual transducers to produce an internal noninvasive probing mechanism beyond experimental capabilities to render the matrices micromechanics and several others properties like permeability, orientation etc. The results demonstrated that load transfer was closely related to the microarchitecture of the hyperelastic models that represent solid skeleton stress and fluid response based on the state of the collagen network with and without the swollen proteoglycans. In other words, the stress gradient during deformation was a function of the structural pattern of the network and acted in concert with the position-dependent compositional state of the matrix. This reveals that the interaction between indistinguishable components in real cartilage is superimposed by its microarchitectural state which directly influences macromechanical behavior.

Second-order elastic finite element analysis of steel structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included. The accuracy and efficiency of the technique is verified by comparisons with a number of plane and spatial structures, whose structural response has been reported in independent studies.

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.

Analysis of strain-rate dependent mechanical behavior of single chondrocyte : a finite element study

Various studies have been conducted to investigate the effects of impact loading on cartilage damage and chondrocyte death. These have shown that the rate and magnitude of the applied strain significantly influence chondrocyte death, and that cell death occurred mostly in the superficial zone of cartilage suggesting the need to further understand the fundamental mechanisms underlying the chondrocytes death induced at certain levels of strain-rate. To date there is no comprehensive study providing insight on this phenomenon. The aim of this study is to examine the strain-rate dependent behavior of a single chondrocyte using a computational approach based on Finite Element Method (FEM). An FEM model was developed using various mechanical models, which were Standard Neo-Hookean Solid (SnHS), porohyperelastic (PHE) and poroviscohyperelastic (PVHE) to simulate Atomic Force Microscopy (AFM) experiments of chondrocyte. The PVHE showed, it can capture both relaxation and loading rate dependent behaviors of chondrocytes, accurately compared to other models.

Second-order elastic finite element analysis of structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included.

Finite element analysis of the in-plane shear behaviour of masonry panels confined with reinforced grouted cores

A combined experimental and numerical program was conducted to study the in-plane shear behaviour of hollow concrete masonry panels containing reinforced grout cores. This paper is focused on the numerical program. A two dimensional macromodelling strategy was used to simulate the behaviour of the confined masonry (CM) shear panels. Both the unreinforced masonry and the confining element were modelled using macromasonry properties and the steel reinforcement was modelled as an embedded truss element located within the grout using perfectly bonded constraint. The FE model reproduced key behaviours observed in the experiments, including the shear strength, the deformation and the crack patterns of the unconfined and confined masonry panels. The predictions of the validated model were used to evaluate the existing in-plane shear expressions available in the national masonry standards and research publications.

Determination of strain-rate-dependent mechanical behavior of living and fixed osteocytes and chondrocytes using atomic force microscopy and inverse finite element analysis

The aim of this paper is to determine the strain-rate-dependent mechanical behavior of living and fixed osteocytes and chondrocytes, in vitro. Firstly, Atomic Force Microscopy (AFM) was used to obtain the force-indentation curves of these single cells at four different strain-rates. These results were then employed in inverse finite element analysis (FEA) using Modified Standard neo-Hookean Solid (MSnHS) idealization of these cells to determine their mechanical properties. In addition, a FEA model with a newly developed spring element was employed to accurately simulate AFM evaluation in this study. We report that both cytoskeleton (CSK) and intracellular fluid govern the strain-rate-dependent mechanical property of living cells whereas intracellular fluid plays a predominant role on fixed cells’ behavior. In addition, through the comparisons, it can be concluded that osteocytes are stiffer than chondrocytes at all strain-rates tested indicating that the cells could be the biomarker of their tissue origin. Finally, we report that MSnHS is able to capture the strain-rate-dependent mechanical behavior of osteocyte and chondrocyte for both living and fixed cells. Therefore, we concluded that the MSnHS is a good model for exploration of mechanical deformation responses of single osteocytes and chondrocytes. This study could open a new avenue for analysis of mechanical behavior of osteocytes and chondrocytes as well as other similar types of cells.

A non-linear interface element model for thin layer high adhesive mortared masonry

A nonlinear interface element modelling method is formulated for the prediction of deformation and failure of high adhesive thin layer polymer mortared masonry exhibiting failure of units and mortar. Plastic flow vectors are explicitly integrated within the implicit finite element framework instead of relying on predictor–corrector like approaches. The method is calibrated using experimental data from uniaxial compression, shear triplet and flexural beam tests. The model is validated using a thin layer mortared masonry shear wall, whose experimental datasets are reported in the literature and is used to examine the behaviour of thin layer mortared masonry under biaxial loading.

Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation

A new mesh adaptivity algorithm that combines a posteriori error estimation with bubble-type local mesh generation (BLMG) strategy for elliptic differential equations is proposed. The size function used in the BLMG is defined on each vertex during the adaptive process based on the obtained error estimator. In order to avoid the excessive coarsening and refining in each iterative step, two factor thresholds are introduced in the size function. The advantages of the BLMG-based adaptive finite element method, compared with other known methods, are given as follows: the refining and coarsening are obtained fluently in the same framework; the local a posteriori error estimation is easy to implement through the adjacency list of the BLMG method; at all levels of refinement, the updated triangles remain very well shaped, even if the mesh size at any particular refinement level varies by several orders of magnitude. Several numerical examples with singularities for the elliptic problems, where the explicit error estimators are used, verify the efficiency of the algorithm. The analysis for the parameters introduced in the size function shows that the algorithm has good flexibility.

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.

Semi-analytical finite element analysis of a strip footing on an elastic reinforced soil

A plane strain elastic interaction analysis of a strip footing resting on a reinforced soil bed has been made by using a combined analytical and finite element method (FEM). In this approach the stiffness matrix for the footing has been obtained using the FEM, For the reinforced soil bed (halfplane) the stiffness matrix has been obtained using an analytical solution. For the latter, the reinforced zone has been idealised as (i) an equivalent orthotropic infinite strip (composite approach) and (ii) a multilayered system (discrete approach). In the analysis, the interface between the strip footing and reinforced halfplane has been assumed as (i) frictionless and (ii) fully bonded. The contact pressure distribution and the settlement reduction have been given for different depths of footing and scheme of reinforcement in soil. The load-deformation behaviour of the reinforced soil obtained using the above modelling has been compared with some available analytical and model test results. The equivalent orthotropic approach proposed in this paper is easy to program and is shown to predict the reinforcing effects reasonably well.

Finite Element Solution Of Surface-Tension Driven Flows In Laser Surface-Melting

Lasers are very efficient in heating localized regions and hence they find a wide application in surface treatment processes. The surface of a material can be selectively modified to give superior wear and corrosion resistance. In laser surface-melting and welding problems, the high temperature gradient prevailing in the free surface induces a surface-tension gradient which is the dominant driving force for convection (known as thermo-capillary or Marangoni convection). It has been reported that the surface-tension driven convection plays a dominant role in determining the melt pool shape. In most of the earlier works on laser-melting and related problems, the finite difference method (FDM) has been used to solve the Navier Stokes equations [1]. Since the Reynolds number is quite high in these cases, upwinding has been used. Though upwinding gives physically realistic solutions even on a coarse grid, the results are inaccurate. McLay and Carey have solved the thermo-capillary flow in welding problems by an implicit finite element method [2]. They used the conventional Galerkin finite element method (FEM) which requires that the pressure be interpolated by one order lower than velocity (mixed interpolation). This restricts the choice of elements to certain higher order elements which need numerical integration for evaluation of element matrices. The implicit algorithm yields a system of nonlinear, unsymmetric equations which are not positive definite. Computations would be possible only with large mainframe computers.Sluzalec [3] has modeled the pulsed laser-melting problem by an explicit method (FEM). He has used the six-node triangular element with mixed interpolation. Since he has considered the buoyancy induced flow only, the velocity values are small. In the present work, an equal order explicit FEM is used to compute the thermo-capillary flow in the laser surface-melting problem. As this method permits equal order interpolation, there is no restriction in the choice of elements. Even linear elements such as the three-node triangular elements can be used. As the governing equations are solved in a sequential manner, the computer memory requirement is less. The finite element formulation is discussed in this paper along with typical numerical results.

A three-dimensional hybrid smoothed finite element method (H-SFEM) for nonlinear solid mechanics problems

This paper presents a novel three-dimensional hybrid smoothed finite element method (H-SFEM) for solid mechanics problems. In 3D H-SFEM, the strain field is assumed to be the weighted average between compatible strains from the finite element method (FEM) and smoothed strains from the node-based smoothed FEM with a parameter α equipped into H-SFEM. By adjusting α, the upper and lower bound solutions in the strain energy norm and eigenfrequencies can always be obtained. The optimized α value in 3D H-SFEM using a tetrahedron mesh possesses a close-to-exact stiffness of the continuous system, and produces ultra-accurate solutions in terms of displacement, strain energy and eigenfrequencies in the linear and nonlinear problems. The novel domain-based selective scheme is proposed leading to a combined selective H-SFEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The proposed 3D H-SFEM is an innovative and unique numerical method with its distinct features, which has great potential in the successful application for solid mechanics problems.

Correlation of carotid atheromatous plaque inflammation with biomechanical stress: Utility of USPIO enhanced MR imaging and finite element analysis

Objective: The aim of this study was to explore whether there is a relationship between the degree of MR-defined inflammation using ultra small super-paramagnetic iron oxide (USPIO) particles, and biomechanical stress using finite element analysis (FEA) techniques, in carotid atheromatous plaques. Methods and Results: 18 patients with angiographically proven carotid stenoses underwent multi-sequence MR imaging before and 36 h after USPIO infusion. T2 * weighted images were manually segmented into quadrants and the signal change in each quadrant normalised to adjacent muscle was calculated after USPIO administration. Plaque geometry was obtained from the rest of the multi-sequence dataset and used within a FEA model to predict maximal stress concentration within each slice. Subsequently, a new statistical model was developed to explicitly investigate the form of the relationship between biomechanical stress and signal change. The Spearman's rank correlation coefficient for USPIO enhanced signal change and maximal biomechanical stress was -0.60 (p = 0.009). Conclusions: There is an association between biomechanical stress and USPIO enhanced MR-defined inflammation within carotid atheroma, both known risk factors for plaque vulnerability. This underlines the complex interaction between physiological processes and biomechanical mechanisms in the development of carotid atheroma. However, this is preliminary data that will need validation in a larger cohort of patients.