Plane Strain Finite Element Model Research Articles

Finite element simulation of a polycrystalline ferroelectric based on a multidomain single crystal switching model

In this paper, we compute the constitutive behavior of a ferroelectric ceramic by a plane strain finite element model, where each element represents a single grain in the polycrystal. The properties of a grain are described by the microscopic model for switching in multidomain single crystals of ferroelectric materials presented by Huber et al. [J. Mech. Phys. Solids 47 (1999) 1663]. The poling behavior of the polycrystal is obtained by employing the finite element formulation for electromechanical boundary value problems developed by Landis [Int. J. Numer. Meth. Eng. 55 (2002) 613]. In particular, we address the influence of the single grain properties and the interaction between grains, respectively.

Finite element simulation of woven fabric composites

Abstract Two dimensional generalised plane strain finite element models have been developed to simulate some of the different local fabric geometries which influence the damage development seen in woven fabric laminates as a function of number of reinforcing layers. It is shown that the stiffness is relatively insensitive to such geometric variations, but that the strain energy release rate associated with crack formation is influenced significantly by the crack location. In particular, where the formation of a crack is associated with local bending deformation, the energy release rate increases with the degree of bending; for configurations leading to a high degree of bending, a geometrically non-linear analysis is required to determine the energy release rate accurately. For several of the crack geometries studied, the values of the energy release rates for crack formation are significantly larger than the values for central 90° ply cracking and surface 90° ply cracking in equivalent (0/90) s and (90/0) s cross-ply laminates. The implications of the various effects for simulation of crack development in woven cross-ply laminates are discussed.

A nonlinear finite element analysis of the periodontal ligament under orthodontic tooth loading

The stressed state of the periodontal ligament (PDL) is understood to play a critical role in the tooth movement initiated by orthodontic treatment. Finite element simulations have been used to describe PDL stresses for orthodontic loading; however, these models have predominantly assumed linear mechanical properties for the PDL. The present study sought to determine the importance of using nonlinear mechanical properties and nonuniform geometric data in computer predictions of periodontal ligament stresses and tooth movements. A 2-dimensional plane-strain finite element model of a mandibular premolar was constructed based on anatomic data of transverse sections of tooth, PDL, and bone from a 24-year-old cadaveric man. A second model was constructed of the same tooth but with a PDL of uniform thickness. Each of these was prescribed linear or nonlinear elastic mechanical properties, as obtained in our own experiments. Predictions of the maximum and minimum principal stresses and von Mises stresses in the PDL were determined for extrusive and tipping forces. The results indicated that biofidelic finite element models predicted substantially different stresses in the PDL for extrusive loading than did the uniform thickness model, suggesting that incorporation of the hourglass shape of the PDL is warranted. In addition, incorporation of nonlinear mechanical properties for the PDL resulted in dramatic increases in the stresses at the apex and cervical margin as compared with the linear models.

Finite element simulation of profile rolling of wire

The profile rolling or wire is investigated by means of a finite element model. Three-dimensional simulation of wire rolling process with a round cross-section of wire by two cylindrical rolls is considered. The same example is simulated by a 2D generalised plane strain finite element model. The results for lateral spread from those two models are compared with the experimental one. The results for more complicated shape of rolls for three passes rolling are shown.

In situ measurement of reinforcement stress in an aluminum–alumina metal matrix composite under compressive loading

The phenomena of stress partitioning between the matrix and the reinforcements in a loaded metal matrix composite dominate the mechanical behavior of these materials. Numerical models for estimating the stress in the matrix and the reinforcement under load are well developed. However, direct experimental measurements (e.g. measurement of reinforcement stress) are more difficult and have not been widely undertaken at present. The objective of the present work was to measure in situ the hydrostatic stress in the ceramic reinforcements in a continuously reinforced metal matrix composite loaded under transverse compression (i.e. loading perpendicular to the fiber axis). A single crystal sapphire reinforced AA6061 matrix model composite (reinforcement volume fraction ∼10%) was used for the measurements, which were undertaken at applied strains of 5, 10 and 20%. The stress measurements utilized the piezo-spectroscopic property of the Cr 3+ ions which were present as impurities in the sapphire reinforcements. The compressive deformation of the composite was simulated using an isotropic, plane strain finite element model. The reinforcement hydrostatic stress estimates from the isotropic FEM model were suitably modified to incorporate the effects of anisotropy in properties of the sapphire single crystal. The mean values of the experimental measurements of reinforcement hydrostatic stress matched well with the numerical estimates.

Abfraction lesion formation in maxillary incisors, canines and premolars: A finite element study

Abfraction lesions are angular, wedge-shaped defects found at the cervical region of teeth and are caused by mechanical overloading initiated by cuspal flexure. Clinically, these lesions are more prevalent on the labial aspect of maxillary incisors. The aim of this study was to provide a biomechanical explanation for this clinical variation. Two-dimensional plane strain finite element models of an maxillary incisor, canine and first premolar were developed and the cervical stress profiles were examined along a horizontal plane 1.1 mm above the amelo-cemental junction. The local X (horizontal) stress on the labial/buccal side was 176.4 MPa for the incisor, 57.8 MPa for the premolar, and 3.4 MPa for the canine. Similarly, the maximum labial/buccal principal stress was 181.4 MPa for the incisor, 25.2 MPa for the premolar, and 66.8 MPa for the canine. The labial/buccal stress profile in the cervical region of an maxillary incisor was always greater than that found in an maxillary canine or premolar tooth. These findings provide a biomechanical explanation for the clinical variation seen in the prevalence of cervical abfraction lesions.

Investigations into the influence of asymmetric factors and rolling parameters on strip curvature during hot rolling

Finite element (FE) techniques have been used to analyse the effect of asymmetrical factors and rolling parameters on the direction and severity of strip curvature. A plane strain FE model has been constructed to simulate the rolling of low carbon steel strip at high temperatures. The asymmetric factors considered were workpiece temperature differentials, roll speed mismatch and differential interface friction conditions. The rolling parameters include initial strip height, reduction, average roll speed, average workpiece temperature and average coefficient of friction. In addition to the FE model predictions, trials have been carried out on the reversing rougher of Corus, Port Talbot hot mill. Trials were conducted to investigate the effectiveness of roll speed mismatch as a means of controlling strip curvature.

Investigation of thickness variation and corner filling in tube hydroforming

Tube hydroforming is a near-net shape metal forming process in which a straight or a pre-bent tubular blank is placed in a closed die cavity and its cross-sectional shape is changed using internal hydraulic pressure that forces the tube to conform to the shape of the die cavity. This paper reports on the results of two-dimensional plane-strain finite element models of the tube hydroforming process, which were conducted using the commercial finite element code ABAQUS/Standard. The objective of the study is to examine the interaction of material properties and die geometry on the selection of hydroforming process parameters. The paper discusses the effects of the strain-hardening exponent, initial tube wall thickness, and die corner radii on corner filling and thickness distribution of the hydroformed tube.

Buried Corrugated Thermoplastic Pipe: Simulation and Design

The objective of this study was to demonstrate a computational method for assessing the allowable depth of fill over a buried thermoplastic profile wall (corrugated) plastic pipe and to compare the results with those of the recently adopted AASHTO design method. The computational method is demonstrated for a 1,500-mm (60-in.) diameter high-density polyethylene profile wall pipe but is applicable to all profile wall thermoplastic pipe that exhibits local buckling limit states. The computational model compares strain demands predicted from a two-dimensional plane strain finite element model of buried pipe in the embankment condition with strain capacity predicted from a three-dimensional finite element model of a pipe–soil segment undergoing thrust or positive and negative bending, or both. The strain demands indicate the dominance of thrust strains as opposed to bending strains in the overall behavior, particularly for intermediate to larger fill depths. In the examined profile the ultimate strain capacity is limited by local buckling for thrust strains and positive bending (crest in compression) and inward radial movement of the crest for negative bending (liner in compression). Predictions for depth of fill by the new AASHTO design method for thermoplastic pipe and the computational method agree within 10% of one another when uniform soil distribution is considered and within 20% of one another when a soft haunch and other soft soils are considered in the pipe–soil envelope.

Plastic deformation of corrugated rails—a numerical approach using material data of rail steel

This paper investigates the influence of plastic deformation as a possible saturation mechanism on corrugation growth. For a track segment of two sleeper bays, plastic deformation and wear are considered in the process of corrugation growth. The dynamic Hertzian contact stress distribution over the rail section is analysed in the frequency domain taking into account the structural dynamics of the system. This stress distribution along the surface is applied on a plane strain finite element model as a moving load. The plastic deformations due to this loading are calculated using the Chaboche material law. Superimposing the plastic deformed surface to the initial measured profile, a mechanism can be observed which results in a corrugation decrease. The common action of wear and plastic deformations should lead to a steady-state situation and a physical as well as geometric shake-down phenomenon is observed for the corrugated system.

Assessment of a finite element model for plate shearing

A study was conducted to assess the robustness of a plane strain finite element model that was developed to simulate plate shearing using the Cockroft-Latham fracture criterion and element deletion. Model predictions for blade gap, ductility and edge wear were compared with published experimental results. Results showed that the model was able to simulate initiation and propagation of fracture lines at the punch and die corners and the resultant break angle along the edge was found to be close to values observed in practice. Simulated edge geometry and microhardness were found to be in reasonable agreement with published experimental results for the steel plate considered although the model was unable to simulate double cutting at 0.8 per cent clearance. Results also suggest that edge hardness is independent of the starting ductility in the plate and that increasing the edge radii does not effectively simulate edge wear. Based on the results obtained, it may be concluded that the plane strain model is able to simulate plate shearing with sufficient accuracy in the range of normal process conditions.

The effect of variation in occlusal loading on the development of abfraction lesions: a finite element study.

Abfraction or non-carious cervical tooth loss is poorly understood and one factor thought to contribute to the development of these lesions is the effect of occlusal loading. The aim of this study was to examine the effect that varying the position of an occlusal load would have on the stress contour in the cervical region of a lower second premolar using a two-dimensional plane strain finite element model. A 500 N load was applied vertically to either of the cusp tips or in various positions along the cuspal inclines. It was found that loads applied to the inner aspects of the buccal or the lingual cuspal inclines produced maximum principal stress values of up to 358 MPa that exceed the known failure stresses for enamel.

A Plane Strain Model for Process-Induced Deformation of Laminated Composite Structures

We present a plane strain finite element model for simulation of the development of process-induced deformation during autoclave processing of complex-shaped composite structures. A “cure-hardening, instantaneously linear elastic” constitutive model is employed to represent the mechanical behaviour of the composite matrix resin, and micromechanics models are used to determine composite ply mechanical properties and behaviour, including thermal expansion and cure-shrinkage. Structures with multiple composite and non-composite components can be simulated through the use of such strategies as adaptive time-stepping and incorporation of multiple composite plies into each finite element. The effect of process tooling can also be directly modelled through simulation of tool/part interfaces and post-processing tool removal. Integration of the residual deformation model with models for heat transfer and resin cure and resin flow permits analysis of all major identified sources of process-induced deformation during the autoclave process. Model application is demonstrated through prediction of process-induced deformation of a number of variations of a simple L-shaped laminate. The model is shown to provide accurate predictions of both spring-back angle and warped shape of the final part.

Effect of friction on deformation during rolling as revealed by embedded pin technique

The paper investigates the effects of friction on the heterogeneity of deformation during rolling through studies using plane strain (2D) and three-dimensional (3D) finite element models designed to simulate the deformation of the embedded pin inserts during rolling. Redundant work due to friction is defined as a path function along the arc of contact. Since deformation during rolling is profoundly influenced by the amount of redundant work, which depends on friction as a path function along the arc of contact, the study has focused especially on methods of representing these frictional effects. The friction studied has been in one of two classes: the coefficient of friction being constant or varying parabolically along the arc of contact. The results show that the values of shear stress and normal pressure along the arc of contact depend upon the friction profile. The magnitude of these frictional effects is revealed by the through thickness variation of the relative pin insert displacement. This displacement changes in the 3D model because transverse spread reduces the amount of displacement along the axial direction. Comparison of the simulations with experimental pin insert shapes shows close agreement between the predicted and experimental results, while revealing the direction of further work needed to provide suitable mechanics models to interpret experimental pin insert data.

An investigation into the importance of the periodontal ligament and alveolar bone as supporting structures in finite element studies.

Many finite element analyses studies have been published in the dental literature. Some of these have analysed just the crown of the tooth, others have included part or all of the root, while others have included the supporting periodontal ligament and alveolar bone. The aim of this study was to examine which of the supporting structures was important to the model when analysing the stress distribution within a tooth. A two-dimensional plane strain finite element model of a lower second pre-molar was developed, which included the supporting periodontal ligament and alveolar bone. Two 50 N loads were applied to simulate the effect of a load in centric occlusion. The nodal x, y and shear stresses were recorded along two horizontal planes, one in the crown and one in the cervical region. Each of the supporting structures was systematically removed and the remaining structures reanalysed. It was found that it was particularly important to include both the periodontal ligament and alveolar bone when undertaking the finite element analyses of teeth.

Contribution to Piled Raft Foundation Design

Raft foundations enhanced with deep foundation elements (typically piles), simply known as piled rafts, were examined to develop a more integrated, displacement-based, design methodology. Illustrative piled rafts were analyzed using simplified linear elastic and nonlinear plane strain finite element models. The effects of raft and pile group system geometries and pile group compression capacity were evaluated on the average and differential displacements, raft bending moments, and pile butt load ratio of the piled rafts. The results were synthesized into an updated, displacement-based, design methodology for piled rafts.

Simulation of the development of frontal head impact injury

This paper describes the results of computational simulations of a frontal impact to the head and the predicted development of coup and contrecoup contusion (i.e., at and opposite the site of impact, respectively) within brain tissue. Three separate two-dimensional plane strain finite element models of the head, each of which incorporated the skull, the cerebrospinal fluid and the brain, were constructed. Two of these models represented the coronal plane of the head as being elliptic whilst the third model was geometrically representative of an actual human head. This third model was taken in an off-centre mid-sagittal plane in an anterior–posterior direction and all three models were used to investigate the dynamic response of the human head when subject to direct translational impact events. The physiological consequences of modelling the human brain as being elastic were established. Compressive and tensile strains were predicted at the coup and contrecoup sites for a simulated frontal impact event by means of a simple elastic analysis. These distributions of most severe strain correspond directly to the occurrence of coup and contrecoup contusion such as are witnessed in clinical studies which arise under the action of translational acceleration.

Testing and Analysis of Composite Skin/Stringer Debonding under Multi-Axial Loading

A consistent step-wise approach is presented to investigate the damage mechanism in composite bonded skin/stringer constructions under uniaxial and biaxial (in-plane/out-of-plane) loading conditions. The approach uses experiments to detect the failure mechanism, computational stress analysis to determine the location of first matrix cracking and computational fracture mechanics to investigate the potential for delamination growth. In a first step, tests were performed on specimens, which consisted of a tapered composite flange, representing a stringer or frame, bonded onto a composite skin. Tests were performed under monotonic loading conditions in tension, three-point bending, and combined tension/bending to evaluate the debonding mechanisms between the skin and the bonded stringer. For combined tension/bending testing, a unique servohydraulic load frame was used that was capable of applying both in-plane tension and out-of-plane bending loads simultaneously. Specimen edges were examined on the microscope to document the damage occurrence and to identify typical damage patterns. For all three load cases, observed failure initiated in the flange, near the flange tip, causing the flange to almost fully debond from skin. In a second step, a two dimensional plane-strain finite element model was developed to analyze the different test cases using a geometrically nonlinear solution. For all three loading conditions, computed principal stresses exceeded the transverse strength of the material in those areas of the flange where the matrix cracks had developed during the tests. In a third step, delaminations of various lengths were simulated in two locations where delaminations were observed during the tests. The analyses showed that at the loads corresponding to matrix ply crack initiation computed strain energy release rates exceeded the values obtained from a mixed mode failure criterion in one location. Hence, unstable delamination propagation is likely to occur as observed in the experiments.

The influence of the acetabular labrum on hip joint cartilage consolidation: a poroelastic finite element model

The goal of this study was to investigate the influence of the acetabular labrum on the consolidation, and hence the solid matrix strains and stresses, of the cartilage layers of the hip joint. A plane-strain finite element model was developed, which represented a coronal slice through the acetabular and femoral cartilage layers and the acetabular labrum. Elements with poroelastic properties were used to account for the biphasic solid/fluid nature of the cartilage and labrum. The response of the joint over an extended period of loading (10,000 s) was examined to simulate the nominal compressive load that the joint is subjected to throughout the day. The model demonstrated that the labrum adds an important resistance in the flow path of the fluid being expressed from the cartilage layers of the joint. Cartilage layer consolidation was up to 40% quicker in the absence of the labrum. Following removal of the labrum from the model, the solid-on-solid contact stresses between the femoral and acetabular cartilage layers were greatly increased (up to 92% higher), which would increase the friction between the joint surfaces. In the absence of the labrum, the centre of contact shifted towards the acetabular rim. Subsurface strains and stresses were much higher without the labrum, which could contribute to fatigue damage of the cartilage layers. Finally, the labrum provided some structural resistance to lateral motion of the femoral head within the acetabulum, enhancing joint stability and preserving joint congruity.

A study of fatigue crack closure in polycarbonate CT specimens

Plane strain and plane stress finite element (FE) models were built to simulate fatigue crack closure behaviour in polycarbonate. Effective driving forces for crack growth were determined in terms of crack closure, where the opening load was taken either as corresponding to full opening of the two crack faces (Definition 1), or identified by the instant when the principal stress perpendicular to the crack-tip stress becomes tensile (Definition 2). Experimental work was conducted to determine crack growth rates and to characterise crack closure levels, using the compliance technique, in compact tension specimens either 2 mm (plane stress) or 10 mm (plane strain) thick. The FE predictions of crack closure using Definition 1 were found to agree reasonably with the experimental results. It was also found that higher crack closure levels were predicted from Definition 2. A two-parameter function of Δ K eff and K max was utilised to model the fatigue crack growth rate data. The equation derived from Definition 1 theoretical results described the growth rate data better than that obtained from Definition 2.