Plane Strain Finite Element Model Research Articles

Extended formulation of macro-element based modelling – Application to single-lap bonded joints

An extended formulation of the macro-element (ME) based models, representing for both adherends and adhesive along the entire overlap in only one four-node element, is presented. Compared to earlier modelling, continuum ME (CME) and discrete ME (DME) based models, the adherend parts are also modelled as plane continuum media, for which high order displacement fields are freely supposed. Both extended CME (ECME) and extended DME (EDME) based modelling can have their displacement field orders of each continuum layer be set individually, and can be enriched using springs for interfaces or boundary conditions modelling, allowing the stresses to vanish at the free edges. The methodology and formulation of the stiffness matrix for both the adherend without adhesive and the bonded overlap is presented. The assessment is performed for a single-lap joint geometry by comparison results from a plane strain finite element (FE) model with extended ME-based models. Good agreements are shown for both thin and thick adhesive case studies.

Scalar- and vector-valued seismic fragility assessment of segmental shield tunnel lining in liquefiable soil deposits

Seismic fragility analysis can quantitatively evaluate the seismic performance of structures from a probabilistic viewpoint and accurately characterize the relationship between the degree of structural damage and ground motion intensity. This study investigates the seismic fragility of shield tunnels in three different liquefiable and non-liquefiable soils. A plane-strain finite element model of the saturated soil and shield tunnel is established via the OpenSees computational platform employing the multi-yield surface elastoplastic PressureDependMultiYield and PressureIndependMultiYield models to simulate the constitutive behaviour of liquefiable and non-liquefiable soils. The developed model is utilized to conduct nonlinear dynamic effective stress time history analyses to generate the seismic fragility curves and surfaces based on the incremental dynamic analysis method. Meanwhile, appropriate scalar- and vector-valued intensity measures are identified based on their correlation, efficiency, practicality and proficiency. Compared with the fragility curves based on scalar-valued intensity measures, the fragility surfaces based on the vector-valued intensity measures can better describe the effect of ground motion characteristics on the structural seismic demand, and thus can more accurately assess the structural seismic performance. The seismic damage probabilities derived from the fragility curves and surfaces reveal that the seismic damage risk of the shield tunnel in sandwiched liquefiable soil deposit is higher than that of the tunnel structure located in entirely liquefiable or non-liquefiable soil profiles. This finding underscores the importance of carefully evaluating the seismic safety of shield tunnels situated in sandwiched liquefiable soil deposits.

Recent advanced thermal interfacial materials: A review of conducting mechanisms and parameters of carbon materials

Understanding the effect of process-induced residual stresses on the final shape of fiber-reinforced polymer composites is critical due to their widespread use in structural applications. It is crucial for more dependable composite production, as residual stresses change the internal stress level of the composite component during service life, and residual shape distortions may prevent the part from achieving the required geometrical tolerances. Residual strains are the result of many interplays among physical processes, such as heat transfer, material flow, polymerization, crystallization, or heat transfer. Numerical process models must be constructed instead of time-consuming and inefficient trial-and-error procedures to design and optimize the composite manufacturing process digitally. This study aims to review the model creation and applications for predicting residual stresses and form distortions in composite manufacturing. Uses for both thermoset and thermoplastic composites are investigated in detail. Predictions of the process-induced deformations of laminated composite structures have been made using elastic constitutive models, such as a plane strain finite element model with a cure-hardening, instantaneous linear elastic constitutive model. to learn more about the factors that lead to shape distortion and how they can be reduced, such as by adjusting cure cycles, tool surfaces, geometry, or lay-up.

Finite Element Simulation of the Effect of Phase Transformation on Residual Stress in a Thick Section T-Joint

It has long been known that residual stresses can profoundly affect the integrity of engineering components. Evidence has recently emerged to confirm that solid-state phase transformations in steels can significantly influence the as-welded residual stresses. A two-dimensional thermo-mechanical, generalized plane strain finite element model was created to simulate the effect of phase transformation on residual stress during the multi-pass weld process in a thick section T-joint. The effect of phase transformation and martensite start temperatures was investigated. The results showed that phase transformation generated compressive residual stress underneath the last bead to be deposited for this multi-pass weld model. However, some constraints around the bead were essential to provide that stress. Tensile residual stress was generated in the bulk of the weld area when phase transformation was considered. Therefore, phase transformation may be helpful for single pass and other groove welds but may be unhelpful in the case of the T-joint examined here. The effect of the martensite start temperature is small compared with the main difference between having a phase transformation and not having one.

Plasticity-induced damage and material loss in oscillatory contacts

Knowledge of plasticity-induced damage leading to the loss of material in oscillatory contacts is of paramount importance to various electromechanical systems comprising contact-mode elements exposed to high-frequency vibrations. However, experimental investigation of the wear behavior of devices experiencing microscopic oscillatory contact (fretting) is complex, time consuming, and expensive. More importantly, the progression of critical damage processes, such as the decrease of the material’s strength with the accumulation of plastic deformation in the vicinity of the contact interface and the removal of material in the form of microscopic wear debris, cannot be tracked in real time, necessitating cumbersome and costly post-testing microanalysis. Alternatively, computational wear modeling is more effective than experiments and can provide valuable insight into the effect of important parameters, such as load, coefficient of friction, oscillation amplitude, and material behavior, on the loss of material during oscillatory sliding contact. Accordingly, the principal objective of this study was to introduce a computational approach, which can be used to analyze the loss of material due to plasticity-induced damage in oscillatory mechanical components. To achieve this aim, a plane-strain finite element model of a rigid cylinder in reciprocating sliding contact with an elastic-plastic half-space exhibiting isotropic strain hardening was used to study how the evolution of damage due to the progression of plasticity leads to the loss of material. A quasi-static, isothermal damage model based on a ductile failure criterion was implemented in the finite element analysis to simulate the removal of the fully damaged elements. Numerical results illuminate the effects of the load and coefficient of friction on the development of plasticity, cumulative damage, and loss of material with accruing oscillation cycles. The deviation of the wear behavior from classical wear theory in the high-load simulations is explained by the plastic shear strain distribution and less slip at the contact interface encountered at high loads. The novelty of this study is the development of a computational methodology, which sheds light into the evolution of plasticity, damage, and loss of material in reciprocating sliding contacts and provides an effective computational capability for assessing the effects of load, friction, and material behavior on the mechanical performance of components operating in oscillatory contact mode.

Failure behavior of copper Laser-Welded joints in lap shear specimens

In this study, the failure behavior of laser-welded (LWed) lap shear (LS) specimens in copper (Cu) sheets with unequal thickness has been studied through experimental and numerical approaches. LWed LS specimens with unequal thickness represented the tab-to-electrode joints of batteries in a module. Quasi-static tensile testing has been performed for studying the load–displacement curves, failure loads, and failure modes of LS specimens and the stress–strain curve of Cu. Microstructures and failure modes of LWs have been examined by exploring the micrographs before and after the failure. Necking failure was observed at the heat affected zone (HAZ) in the upper right sheet of LWed LS specimens. Microhardness distributions of LWs were obtained to estimate the stress–strain curves of the fusion zone (FZ), HAZ, and base metal (BM). Based on the stress–strain curves, a two-dimensional plane strain finite element model has been developed for LWed LS specimens. In order to develop a damage criterion for finite element models to simulate the failure mode of LWed LS specimens, a series of quasi-static tensile tests for one shear, one smooth, and four notched specimens made of Cu were conducted to derive the equivalent plastic strains at the onset of damage ε¯Dpl and the corresponding triaxialities η. A damage criterion of BM (Cu) comprised of ε¯Dpl and η was developed. Then a damage criterion of HAZ where the necking failure occurred was estimated based on the damage criterion of BM and the maximum values of ε¯Dpl and η in HAZ derived by the finite element model subjected to the failure load. Finally, it has been concluded that based on stress–strain curves of FZ, HAZ, BM, damage criterion of HAZ, computational simulations of failure behavior of LWed LS specimens are in good agreement with the experimental results..

Displacement based seismic assessment of base restrained retaining walls

The present work deals with assessment of earthquake-induced displacement of the base restrained retaining walls (RW’s). A detailed and rigorous finite element (FE) investigation has been carried out following the shaking table experiments on a scaled-down RW model. The FE simulations were performed by conducting several nonlinear time history analyses on a two-dimensional (2D) plane strain FE model of a prototype RW. The hardening and softening of backfill have been simulated by calibrating the Mohr Coulomb material model against the triaxial test results. Role of different backfill into the seismic performance of base restrained RW has also been investigated. It was observed that the cohesionless backfill has a slight influence on the earthquake induced displacement of base restrained RW’s. Amplification of horizontal acceleration in backfill has been observed with no direct correlation with the applied earthquake excitation. The understanding and findings based on shaking table experiment and FE simulations have been used for development of an analytical model for estimation of earthquake induced displacement of base restrained RW. The validity of proposed analytical model has also been examined against the shaking table experiment and FE simulation results.

Biomechanical Response of the Human Foot Model Exposed to Vibrations: A Finite Element Analysis

Prolonged exposure to mechanical vibration has been associated with many musculoskeletal, vascular and sensorineural disorders of the foot from simple Plantar fasciitis and Achilles Tendonitis to complex ones as Tarsal tunnel syndrome (TTS) and Vibration white feet/toes. Foot-transmitted vibrations (FTV) are exposed to the occupants using vibrating equipment’s or standing on vibrating platforms. Prolonged exposure to foot-transmitted vibrations (FTV) can lead to syndromes like vibration white feet/toes may result in tingling sensation, blanching of the toes and even numbness in the feet and toes. A multi-layered two dimensional, plane strain finite element model is developed from the actual cross-section of the human foot to study the stresses and strains developed in the skin and soft tissues. The foot is assumed to be in contact with a steel plate, mimicking the interaction between the foot and the work platform. The skin and the subcutaneous tissue are considered as hyperelastic and viscoelastic. The effects of loading in the form of displacements and the frequency of sinusoidal vibration on a time-dependent stress/strain distribution at various depths in the subcutaneous tissue of the foot are investigated. The simulations indicate that lower frequency vibrations penetrate deep into the subcutaneous tissue while higher frequencies are concentrated in the outer skin layer. The present biomechanical model may serve as a valuable tool to study the response of foot of those who work on a vibrating platform.

An XFEM-VCCT coupled approach for modeling mode I fatigue delamination in composite laminates under high cycle loading

In this study, virtual crack closure technique (VCCT) and extended finite element method (XFEM) are coupled to each other as XFEM-VCCT approach to simulate mode I fatigue delamination growth in composites, employing the direct cyclic method in Abaqus. Both two-dimensional plane strain and three-dimensional finite element models under force and displacement control are considered. Numerical simulation results are compared with the existed experimental test data for double cantilever beam (DCB) specimens and validated. Finally, challenges ahead of VCCT and XFEM-VCCT are discussed in detail and the appropriate method for modeling fatigue delamination growth in laminated composites under high cycle loading is suggested. It is found that simulation of the DCB fatigue delamination via the displacement control loading leads to more accurate results in comparison to the force control. VCCT was found as a suitable method for simulation of fatigue delamination growth in 2D and 3D-shell models. While XFEM-VCCT shows high accuracy and low computational time in 3D-solid finite element models. The key conclusion is that the XFEM-VCCT coupled approach is independent of time increment, whereas the time increment is more effective on the results of VCCT analysis, and it affects the run-time significantly.

Basin effects and limitations of 1D site response analysis from 2D numerical models of the Thorndon basin

Plane strain (2D) finite element models are used to examine factors contributing to basin effects observed for multiple seismic events at sites in the Thorndon basin of Wellington, New Zealand. The models consider linear elastic soil and rock response when subjected to vertically-propagating shear waves. Depth-dependent shear wave velocities are considered in the soil layers, and the effects of random variations of soil velocity within layers are modelled. Various rock shear wave velocity configurations are considered to evaluate their effect on the modelled surficial response. It is shown that these simple 2D models are able to capture basin reverberations and compare more favourably to observations from strong motion recordings than conventional 1D site response models. It is also shown that consideration of a horizontal impedance contrast across the Wellington Fault affects spectral response and amplification at longer periods, suggesting the importance of this feature in future ground motion modelling studies in the Wellington region.

Assessment of damage zone thickness and wall convergence for tunnels excavated in strain-softening rock masses

There are two fundamental issues in all underground excavations, which are safety and economy. To ensure safety and expedite excavations, level of tunnel wall convergences and damage zone thickness should be predicted before the excavation starts, should be determined accurately, and monitored during the excavation by the tunnel designer. However, accurate prediction of these two parameters is difficult unless in-situ stress and deformation measurement tools are used. In this study, damage zone thickness and tunnel wall convergence relation was investigated for horseshoe-shaped highway tunnels by using empirical methods. For this aim two-dimensional plane strain finite element models were used. Totally 9 tunnel sections were selected for the empirical analysis from 5 different ongoing tunnel excavations, which are excavated in weak and fair quality rock masses and show strain softening post-failure behavior. With the help of data gathered through in-situ convergence measurements and predicted convergences and rock mass geotechnical properties an empirical analysis was conducted. Engineering characteristics of the tunnel routes were determined by means of geological mapping, drillings and laboratory studies. Tunnel wall convergences were measured by optical measurement devices in three-dimensional space. Then, numerical models have been created for each of the tunnel sections studied. For evaluation of damaged zone thickness; yielded elements, volumetric strain, and principal stress concentrations have been used. Damage zone thickness and convergences were estimated from the numerical models and the whole data were compared with the real convergence results. Findings have been compared with previous researchers’ convergence predictions and plastic zone calculation approaches. The results are in agreement both with the field measurements and previous empirical approaches. In this way, an empirical relation has been obtained for tunnel wall convergences and damage zone thicknesses. Besides, through an analysis of the relations of convergences at each query points in plane strain finite element model, a new empirical relation has also been put forth that gives “Convergence Constant” for modelled cross-section. This constant can be used as an auxiliary tool for prediction of next section convergences, on the condition that excavation has similar geological, geotechnical properties and topography.

Finite element modeling of fretting wear in anisotropic composite coatings: Application to HVOF Cr3C2–NiCr coating

This paper presents a two-dimensional (2D) plane strain finite element model to simulate fretting wear in composite cermet coating. The coating considered in this investigation is High Velocity Oxy-Fuel (HVOF) sprayed Cr3C2–NiCr with 55% volume fraction of Cr3C2. The material microstructure is modelled using Voronoi tessellations with a log-normal variation of grain size. Moreover, the individual phases of the material in the coating were assigned randomly to resemble the microstructure from an actual SEM micrograph. The ceramic carbide phase is orthorhombic and the cubic matrix possesses a high anisotropy index. As a result, each grain was modelled with random orientation to account for material anisotropy. The RVE dimensions were chosen such that its elastic response represented the overall response of a poly-aggregate. In order to simulate debonding of the ceramic carbide phase from the matrix, cohesive elements were used at the grain boundaries. Damage mechanics was used to model degradation of cohesive elements resulting from repeated fretting cycles. A grain deletion algorithm was developed to simulate removal of material from fretting wear. The crack patterns predicted from the model match closely with the patterns observed in experimental studies on wear of HVOF Cr3C2–NiCr coating. The model also predicts carbide pullout, a major damage mechanism in HVOF Cr3C2–NiCr coating subjected to wear. Experiments were also conducted to evaluate and corroborate the wear rate of HVOF Cr3C2–NiCr coating. The wear rate from the model matches closely with experiments at a constant load and displacement amplitude. The results from the model were then extended to obtain a fretting wear map under a combination of various loads and displacement amplitudes.

Nuclear plasticity increases susceptibility to damage during confined migration.

Large nuclear deformations during migration through confined spaces have been associated with nuclear membrane rupture and DNA damage. However, the stresses associated with nuclear damage remain unclear. Here, using a quasi-static plane strain finite element model, we map evolution of nuclear shape and stresses during confined migration of a cell through a deformable matrix. Plastic deformation of the nucleus observed for a cell with stiff nucleus transiting through a stiffer matrix lowered nuclear stresses, but also led to kinking of the nuclear membrane. In line with model predictions, transwell migration experiments with fibrosarcoma cells showed that while nuclear softening increased invasiveness, nuclear stiffening led to plastic deformation and higher levels of DNA damage. In addition to highlighting the advantage of nuclear softening during confined migration, our results suggest that plastic deformations of the nucleus during transit through stiff tissues may lead to bending-induced nuclear membrane disruption and subsequent DNA damage.

Measurement and Simulation on Consolidation Behaviour of Soft Foundation Improved with Prefabricated Vertical Drains

Prefabricated vertical drains (PVDs) were used in accelerating the consolidation process of a soft soil foundation in the lower reach of the Yangtze river. Field monitoring was carried out during the embankment construction. The settlement, lateral deformation and pore pressure of the soft foundation were collected. The consolidation was also predicted with a coupled mechanical and hydraulic plane strain finite element model. The results indicate that the consolidation process of soft ground followed the loading steps. The PVDs can efficiently reduce the excess pore pressure in the soft ground and shorten the consolidation period. The pore pressure in the PVD reinforced zone is less than 20.0 kPa at the end of the construction in contrast to 52.0 kPa for unimproved foundation. The excellent drainage capacity of PVDs is useful in improving the shear strength of soft ground. Deformation form of the improved foundation is mainly the settlement and the lateral displacement at embankment toe is less than 9.0 cm. Stability analysis shows that the foundation is more stable during the construction with a factor of safety more than 1.20. Research results prove the feasibility of PVD technique in improving the soft ground in the lower reaches of the Yangtze river.

Finite Element Analysis of Interface Undulation and Interface Delamination in the MCrAlY Coating System Under Thermal Cycling: Considering Oxide Thickness and Top-Coat Effects

Thermal cycling is able to cause interface undulation and interface delamination in the MCrAlY coating system. A generalized plane strain finite element model was built in this work to analyze interface undulation and interface delamination. Increasing thermally grown oxide (TGO) thickness facilitates interface undulation. The possible reason for this is that increase in TGO thickness causes the TGO film to be subjected to larger bending moments. Nonetheless, interface undulation can be suppressed in the case of the existence of the top-coat. Simultaneously, the incorporation of the top-coat leads to an obvious reduction in the maximum tensile stresses within the bond-coat/TGO interface. Furthermore, whether the top-coat is incorporated into the coating system model or not, the bond-coat/TGO interface is subjected to compressive stresses, at its concave region and tensile stresses, at its convex region. Therefore, the convex region is thought to be the most likely place where cracks nucleate at the bond-coat/TGO interface. Additionally, the TGO thickness has a significant influence on the in-plane strain energy stored within the TGO film, and the in-plane strain energy is also thought to be one of the mechanisms for the interface delamination.

Friction between a plane strain circular indenter and a thick poroelastic substrate

This paper presents a computational study on the role of poroelasticity in gel friction. Motivated by recent experimental studies in the literature, we develop a plane strain finite element model to elucidate the contact mechanics between a circular indenter and a thick poroelastic substrate under both normal and shear loadings. Two cases are considered: i) steady state sliding under fixed normal displacements, and ii) relaxation under fixed normal and shear displacements. In steady state sliding, we find that a net friction force can arise even if no intrinsic adhesive or frictional interaction is implemented at the indenter/substrate interface. Such friction force exhibits a non-monotonic dependence on the sliding velocity and peaks at an intermediate velocity. Our model reveals that this friction force is induced by poroelastic diffusion in the gel substrate which can lead to considerable asymmetry in both the contact profile and contact pressure. In terms of relaxation, if the indenter/substrate interface is set to be frictionless, we find that the friction force induced by poroelasticity relaxes to zero with a characteristic time much faster than that of the normal force. When a finite friction coefficient is introduced at the interface, the normalized relaxation curve for the friction force approaches that for the normal force as the friction coefficient increases. These modeling results suggest that poroelasticity can be an important contributing mechanism for gel friction.

Vibration annoyance assessment of train induced excitations from tunnels embedded in rock

Train movements generate oscillations that are transmitted as waves through the track support system into its surroundings. The vibration waves propagate through the soil layers and reach to nearby buildings creating distractions for human activities and causing equipment malfunctioning. Not only the train components and the rails, but also the surrounding tunnel, soil and rock strata have dynamic characteristics that play significant roles in the vibration levels felt in a nearby structure. This paper presents a finite element study conducted to investigate the vibrations resulting from train movements in nearby subway tunnels. The subway line is located at an average horizontal distance of 50 ft (15.2 m) from the structure in assessment, which is a six-story office building. The main goal of the work is to assess the train-induced vibrations at the ground level of the building through a case study and sensitivity analysis. A plane strain finite element model is built to represent the railroad tunnel embedded in the rock and the soil stratum above it. The one train loading function is applied to the model as a point source at the track level and compared to the two-train scenario. Other simulations are undertaken for sensitivity analysis involving increased loading, decreased damping and decreased distance to tunnels. Even though there are several numerical studies on the propagation of train induced vibrations in the literature; a finite element model accompanied with a sensitivity analysis has not been discussed in detail in a technical publication before. The paper not only presents the finite element modeling but also compares the results with the criteria of Transit Noise and Vibration Impact Assessment Manual, which was published by the Federal Transit Administration (FTA) of the U.S. Department of Transportation.

Stress perturbations around the deep salt structure of Kuqa depression in the Tarim Basin

Drilling into and around salt bodies can present different kinds of geohazards, such as shrinkage or stuck and crushed casings, resulting in well abandonment and huge economic losses. These engineering disasters are more likely to happen when ignoring the stress perturbations caused by the geomechanical interactions between the salt and surrounding sediments. For a better understanding of the stress perturbations, we use a commercial finite-element software, Abaqus, to build a 2D plane-strain finite-element model of the salt structure of Kuqa depression in the Tarim Basin and simulate the stress perturbations around the salt body in the environment of tectonic compression. By analyzing the patterns of stress perturbations due to different salt geometries such as concave and convex salt, we have come to the conclusion that the convex salt causes compressional stresses on the horizontal and out-of-plane directions but the extensional stress on the vertical direction. On the contrary, the concave salt induces extensional stresses on the horizontal and out-of-plane directions but compressional stress on the vertical direction. The results of stress perturbations near a salt structure in the environment of compressional tectonic stress are opposite to those in the environment of extensional tectonic stress, such as the Mad Dog, in the deepwater northern Gulf of Mexico. The shear stress ([Formula: see text]) near the salt structure is bigger than those far away from the salt structure, but is much smaller when compared with horizontal, vertical, and out-of-plane stresses ([Formula: see text]) in the profile, in the salt body, horizontal stress drops and converges to vertical stress and von Mises stress ([Formula: see text]) equals to zero due to isotropic stresses. The results provide scientific insights on stress perturbations and wellbore drilling design near salt structures in the Tarim Basin.

A fracture mechanics analysis of asperity cracking due to sliding contact

Microfracture of surface protrusions residing on contacting surfaces, known as asperities, due to normal and shear surface traction occurs at various scales affecting the durability and performance of many mechanical components. In this study, microfracture of an asperity due to sliding against a rigid asperity was examined using a two-dimensional (plane strain) finite element model and linear elastic fracture mechanics. The effects of the asperity interference depth, sliding friction, crack position, and crack-face friction on the rate, direction, and dominant mode of crack growth were determined by the ranges of the maximum tensile and shear stress intensity factors. The asperity interference depth and sliding friction exhibited the most pronounced effects on the rate and direction of crack growth. A transition from shear to tensile dominant mode of crack growth was encountered with increasing asperity interference depth and/or sliding friction coefficient. Crack mechanism maps revealing the evolution of opening, slip, and stick between the crack faces are presented for a range of crack-face friction coefficient, asperity interference depth, and sliding friction coefficient. The simulation results provide insight into the underlying microfracture mechanics of asperities residing on sliding surfaces that exhibit different friction characteristics.

Numerical modeling of rigid strip shallow foundations overlaying geosythetics-reinforced loose fine sand deposits

This research displays the influence of geogrid inclusions on the bearing capacity of rigid strip shallow foundations overlying sand dunes. An extensive chain of settings—containing plain fill case—is verified by valuing some factors as first geogrid reinforcement depth, vertical spacing between geogrid inclusions, and geogrid extension relative to the footing width on the mobilized bearing capacity. To achieve the research aims, a group of finite element analysis is carried out to assess the studied parameters. For the purpose of validation; two-dimensional plane strain finite element model is implemented completely similar to the previously built experimental model tests using Plaxis code version 8.2. The soil is represented by Mohr-Coulomb soil constitutive model, and the geogrid reinforcement is characterized by tension elastic elements which have only a normal stiffness. Well matching is detected between the physical and numerical model test results. The results designate that geogrid insertion can severely enhance the bearing capacity of rigid strip footing overlaying sand dunes. Additionally, it is revealed that the load-settlement performance can be considerably improved. The effectiveness of the geosynthetics loose fine sand composite increases to the maximum as the optimum values of the assessed parameters are reached.