A bridging transition technique for the combination of meshfree method with finite element method in 2D solids and structures

For certain continuum problems, it is desirable and beneficial to combine two different methods together in order to exploit their advantages while evading their disadvantages. In this paper, a bridging transition algorithm is developed for the combination of the meshfree method (MM) with the finite element method (FEM). In this coupled method, the meshfree method is used in the sub-domain where the MM is required to obtain high accuracy, and the finite element method is employed in other sub-domains where FEM is required to improve the computational efficiency. The MM domain and the FEM domain are connected by a transition (bridging) region. A modified variational formulation and the Lagrange multiplier method are used to ensure the compatibility of displacements and their gradients. To improve the computational efficiency and reduce the meshing cost in the transition region, regularly distributed transition particles, which are independent of either the meshfree nodes or the FE nodes, can be inserted into the transition region. The newly developed coupled method is applied to the stress analysis of 2D solids and structures in order to investigate its’ performance and study parameters. Numerical results show that the present coupled method is convergent, accurate and stable. The coupled method has a promising potential for practical applications, because it can take advantages of both the meshfree method and FEM when overcome their shortcomings.

Simulation of the nutrient supply in fracture healing

The healing process for bone fractures is sensitive to mechanical stability and blood supply at the fracture site. Most currently available mechanobiological algorithms of bone healing are based solely on mechanical stimuli, while the explicit analysis of revascularization and its influences on the healing process have not been thoroughly investigated in the literature. In this paper, revascularization was described by two separate processes: angiogenesis and nutrition supply. The mathematical models for angiogenesis and nutrition supply have been proposed and integrated into an existing fuzzy algorithm of fracture healing. The computational algorithm of fracture healing, consisting of stress analysis, analyses of angiogenesis and nutrient supply, and tissue differentiation, has been tested on and compared with animal experimental results published previously. The simulation results showed that, for a small and medium-sized fracture gap, the nutrient supply is sufficient for bone healing, for a large fracture gap, non-union may be induced either by deficient nutrient supply or inadequate mechanical conditions. The comparisons with experimental results demonstrated that the improved computational algorithm is able to simulate a broad spectrum of fracture healing cases and to predict and explain delayed unions and non-union induced by large gap sizes and different mechanical conditions. The new algorithm will allow the simulation of more realistic clinical fracture healing cases with various fracture gaps and geometries and may be helpful to optimise implants and methods for fracture fixation.

Behaviour of an in-service cast iron water reticulation pipe buried in expansive soil

This paper presents the measurements of strain and the subsequent stress analysis on an in-service cast iron water main buried in reactive soil. The results indicate that the pipe crown experienced predominantly tensile stresses during drying in summer and, subsequently, these stresses reduce, eventually leading to compressive stresses as the soil swells with increase in moisture content with the approach of winter. It is also evident that flexural movement caused by thermal stresses and soil pressure has led to downward bending of the pipe in summer and subsequent upward movement in winter. The limited data collected from pipe strains and strengths indicate that it is possible for pipe capacity to be exceeded by thermal and soil stresses leading to pipe failure, provided the pipe has undergone significant corrosion.

Local buckling behaviour of steel plate elements supported by a plastic foam material

Sandwich panels comprising steel facings and a polystyrene foam core are increasingly used as roof and wall claddings in buildings in Australia. When they are subjected to loads causing bending and/or axial compression, the steel plate elements of their profiled facing are susceptible to local buckling. However, when compared to panels with no foam core, they demonstrate significantly improved local buckling behaviour because they are supported by foam. In order to quantify such improvements and to validate the use of available design buckling stress formulae, an investigation using finite element analyses and laboratory experiments was carried out on steel plates that are commonly used in Australia of varying yield stress and thickness supported by a polystyrene foam core. This paper presents the details of this investigation, the buckling results and their comparison with available design buckling formulae.

Universal crack closure integral for SIF estimation

Numerical analysis of cracked structures often involves numerical estimation of stress intensity factors (SIFs) at a crack tip/front. A newly developed formulation called universal crack closure integral (UCCI) for the evaluation of potential energy release rates (PERRs) and the corresponding SIFs is presented in this paper. Unlike the existing element dedicated forms of crack closure integrals (MCCI, VCCI) with application limited to finite element analysis, this new numerical SIF/PERR estimation technique is independent of the basic stress analysis procedure, making it universally applicable. The second merit of this procedure is that it avoids the generally error-producing zones close to the crack tip/front singularity. The UCCI procedure, based on Irwin's original CCI, is formulated and explored using a simple 2D problem of a straight crack in an infinite sheet. It is then applied to some three-dimensional crack geometries with the stresses and displacements obtained from a boundary element program.

Association between biomechanical structural stresses of atherosclerotic carotid plaques and subsequent ischaemic cerebrovascular events - A longitudinal in vivo magnetic resonance imaging-based finite element study

Background: High-resolution magnetic resonance (MR) imaging has been used for MR imaging-based structural stress analysis of atherosclerotic plaques. The biomechanical stress profile of stable plaques has been observed to differ from that of unstable plaques; however, the role that structural stresses play in determining plaque vulnerability remains speculative. Methods: A total of 61 patients with previous history of symptomatic carotid artery disease underwent carotid plaque MR imaging. Plaque components of the index artery such as fibrous tissue, lipid content and plaque haemorrhage (PH) were delineated and used for finite element analysis-based maximum structural stress (M-C Stress) quantification. These patients were followed up for 2 years. The clinical end point was occurrence of an ischaemic cerebrovascular event. The association of the time to the clinical end point with plaque morphology and M-C Stress was analysed. Results: During a median follow-up duration of 514 days, 20% of patients (n=12) experienced an ischaemic event in the territory of the index carotid artery. Cox regression analysis indicated that M-C Stress (hazard ratio (HR): 12.98 (95% confidence interval (CI): 1.32-26.67, pZ0.02), fibrous cap (FC) disruption (HR: 7.39 (95% CI: 1.61e33.82), p Z 0.009) and PH (HR: 5.85 (95% CI: 1.27e26.77), p Z 0.02) are associated with the development of subsequent cerebrovascular events. Plaques associated with future events had higher M-C Stress than those which had remained asymptomatic (median (interquartile range, IQR): 330 kPa (229e494) vs. 254 kPa (166-290), p Z0.04). Conclusions: High biomechanical structural stresses, in addition to FC rupture and PH, are associated with subsequent cerebrovascular events.

Fluid-structure interaction study on human arterial plaque with patient specific geometry and boundary conditions

Atherosclerotic plaque rupture has been extensively considered as the leading cause of death in western countries. It is believed that high stresses within plaque can be an important factor on triggering the rupture of the plaque. Stress analysis in the coronary and carotid arteries with plaque have been developed by many researchers from 2D to 3-D models, from structure analysis only to the Fluid-Structure Interaction (FSI) models[1].

Flow of metal in a wedge-shaped cavity

The wedge shape is a fairly common cross-section found in many non-axisymmetric components used in machines, aircraft, ships and automobiles. If such components are forged between two mutually inclined dies the metal displaced by the dies flows into the converging as well as into the diverging channels created by the inclined dies. The extent of each type of flow (convergent/divergent) depends on the die—material interface friction and the included die angle. Given the initial cross-section, the length as well as the exact geometry of the forged cross-section are therefore uniquely determined by these parameters. In this paper a simple stress analysis is used to predict changes in the geometry of a wedge undergoing compression between inclined platens. The flow in directions normal to the cross-section is assumed to be negligible. Experiments carried out using wedge-shaped lead billets show that, knowing the interface friction and as long as the deformation is not too large, the dimensional changes in the wedge can be predicted with reasonable accuracy. The predicted flow behaviour of metal for a wide range of die angles and interface friction is presented: these characteristics can be used by the die designer to choose the die lubricant (only) if the die angle is specified and to choose both of these parameters if there is no restriction on the exact die angle. The present work shows that the length of a wedge undergoing compression is highly sensitive to die—material interface friction. Thus in a situation where the top and bottom dies are inclined to each other, a wedge made of the material to be forged could be put between the dies and then compressed, whereupon the length of the compressed wedge — given the degree of compression — affords an estimate of the die—material interface friction.

Fracture Behavior of Multidirectional DCB Specimen: Higher-Order Beam Theories

Mathematical models, for the stress analysis of symmetric multidirectional double cantilever beam (DCB) specimen using classical beam theory, first and higher-order shear deformation beam theories, have been developed to determine the Mode I strain energy release rate (SERR) for symmetric multidirectional composites. The SERR has been calculated using the compliance approach. In the present study, both variationally and nonvariationally derived matching conditions have been applied at the crack tip of DCB specimen. For the unidirectional and cross-ply composite DCB specimens, beam models under both plane stress and plane strain conditions in the width direction are applicable with good performance where as for the multidirectional composite DCB specimen, only the beam model under plane strain condition in the width direction appears to be applicable with moderate performance. Among the shear deformation beam theories considered, the performance of higher-order shear deformation beam theory, having quadratic variation for transverse displacement over the thickness, is superior in determining the SERR for multidirectional DCB specimen.

On higher order shear deformation theory of laminated composite panels

In this paper we examine the suitability of higher order shear deformation theory based on cubic inplane displacements and parabolic normal displacements, for stress analysis of laminated composite plates including the interlaminar stresses. An exact solution of a symmetrical four layered infinite strip under static loading has been worked out and the results obtained by the present theory are compared with the exact solution. The present theory provides very good estimates of the deflections, and the inplane stresses and strains. Nevertheless, direct estimates of strains and stresses do not display the required interlaminar stress continuity and strain discontinuity across the interlaminar surface. On the other hand, ‘statically equivalent stresses and strains’ do display the required interlaminar stress continuity and strain discontinuity and agree very closely with the exact solution.

Microtensile testing of a free-standing Pt-aluminide bond coat

A finite element method (FEM)-based study has been carried out for the design of flat microtensile samples to evaluate tensile properties of Pt-aluminide (PtAl) bond coats. The critical dimensions of the sample have been determined using a two-dimensional elastic stress analysis. In the present testing scheme, the ratio of the dimensions of the holding length to the fillet radius of the sample was found important to achieve failure within the gage length. The effect of gage length and grip head length also has been examined. The simulation predictions have been experimentally verified by conducting microtensile test of an actual PtAl bond coat at room temperature. The sample design and testing scheme suggested in this study have also been found suitable for evaluation of tensile properties at high temperature. (C) 2010 Elsevier Ltd. All rights reserved.

Thickness-dependent fcc-hcp phase transformation in polycrystalline titanium thin films

Polycrystalline Ti thin films are shown to gradually transform from face-centered cubic (fcc) to hexagonal close-packed structure (hcp) with increasing film thickness. Diffraction stress analysis revealed that the fcc phase is formed in a highly compressive hcp matrix (>= 2 GPa), the magnitude of which decreases with increasing film thickness. A correlation between stress and crystallographic texture vis-a-vis the fcc-hcp phase transformation has been established. The total free energy change of the system upon phase transformation calculated using the experimental results shows that the fcc-hcp transformation is theoretically possible in the investigated film thickness regime (144-720 nm) and the hcp structure is stable for films thicker than 720 nm, whereas the fcc structure can be stabilized in Ti films much thinner than 144 nm. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.