Elasto-plastic Finite Element Method Research Articles

Site response analysis: Uncertain motions propagating through uncertain elastoplastic soil

Presented is a stochastic site response analysis of uncertain seismic motions propagating through uncertain elastoplastic soil. Time domain stochastic bedrock motions are simulated from GMPE of Fourier amplitude spectra and Fourier phase derivative. The uncertain motions are directly modeled as a non-stationary random process in the time domain, capturing all the important seismic characteristics. Uncertain heterogeneous parameters for the elastoplastic behavior of soils are also considered and modeled as random fields. Both uncertain motions and uncertain material parameters are discretized in the probabilistic space using orthogonal Hermite polynomial chaos basis. The probabilistic site response is efficiently solved using Galerkin stochastic elastoplastic finite element method, circumventing Monte Carlo simulations. The implication of the presented methodology for site-specific probabilistic seismic hazard analysis is discussed as well.

HTS Tape Mechanical Behavior Sensitivity on Material Properties and Thickness of Material Layers

Multilayer 2G high-temperature superconductor (HTS) tapes undergo various mechanical loading steps as part of a superconducting magnet operation. The mechanical loading steps include cool-down to cryogenic temperatures and Lorentz forces when powering up the magnets. Studying the mechanical behavior of the constituent layers in a HTS tape can reveal the strain or stress level in each layer and help in predicting the probability of mechanical failure or critical current degradation. A detailed finite element method (FEM) -based simulation models enable us to estimate the mechanical behavior in each layer. However, defining the model parameters for material mechanical properties or thickness of each material layer can have consid-erable uncertainty due to variation in manufacturing processes and missing measurements of material properties within these tapes. The material properties in thin layers may not exactly comply with bulk materials of the same kind. In this paper we present a sensitivity analysis for mechanical behavior dependence on material properties variation in the constituent layers of a HTS tape. The results give important insight about the accuracy and reliability of mechanical simulation results and guide the priorities in future material characterization. In addition, we will investigate the effect of the thickness of Hastelloy layer on effective macroscopic mechanical behavior of the tape. A nonlinear elastoplastic FEM model is used for performing the simulations.

Effects of Different Pre-Heating Welding Methods on the Temperature Field, Residual Stress and Deformation of a Q345C Steel Butt-Welded Joint

Heavy plate welding has been widely used in the construction of large projects and structures, in which the residual stress and deformation caused by the welding process are the key problems to address to reduce the stability and safety of the whole structure. Strengthening before welding is an important method to reduce the temperature gradient, control the residual stress and reduce the deformation of welds. Based on the ABAQUS software, the thermal elastoplastic finite element method (FEM) was used to simulate the welding thermal cycle, residual stress and deformation of low-alloy, high-strength steel joints. Based on the finite element simulation, the influences of flame heating and ceramic heating on the temperature field, residual stress distribution and deformation of a Q345C steel butt-welded joint were studied. The results showed that the thermal cycle of the ceramic sheet before welding had little influence on the whole weldment, but had great influence on the residual stress of the weldment. The results show that the maximum temperature and residual stress of the welded parts are obviously weakened under the heating of ceramic pieces, and the residual stress of the selected feature points is reduced by 5.88%, and the maximum temperature of the thermal cycle curve is reduced by 22.67%. At the same time, it was concluded that the weld shapes of the two were basically the same, but the weld seams heated by ceramic pieces had a better weld quality and microstructures through comparing the macro- and micro-structures between the welded parts heated by ceramic pieces and the simulated weld. Heating before welding, therefore, is an effective method to obtain a high weld quality with less residual stress and deformation.

A method to directly estimate the dynamic failure peak ground acceleration of a single-layer reticulated dome

The present paper gives a method to directly estimate the dynamic failure peak ground acceleration of single-layer reticulated domes according to the Chinese earthquake response spectrum. A method given by the Japanese code for seismic design of buildings is presented first, which can be used to estimate the dynamic failure peak ground acceleration of a single-layer dome. However, the existing method cannot be used to calculate the dynamic failure load for a structure in China because of the different codes and methods used for the seismic design of single-layer reticulated domes. Meanwhile, the existing method needs to repeat the finite element method (FEM) elasto-plastic static analysis and FEM nonlinear time–history response analysis to calculate the FEM plasticity adjustment factor and the dynamic ductility index of different domes. Secondly, on this basis, 28 Kiewitt-8 (K8) single-layer reticulated domes with different key structural design parameters are designed using the relevant Chinese specifications, they will be used for the parameter revision of the peak ground acceleration and the dome’s design spectral acceleration, the fitting of the formula to calculate the FEM plasticity adjustment factor, and the statistical analysis of the dynamic ductility index respectively. Thirdly, the peak ground acceleration and the dome’s design spectral acceleration in the existing method are revised according to the Chinese code for the seismic design of buildings. Fourthly, the FEM elasto-plastic static analysis is carried out to get a fitting formula to directly calculate the FEM plasticity adjustment factor with the static safety factor K of the dome. The calculation results of this formula are smaller than that of FEM analysis, which can ensure the safety of the dome. Fifthly, the failure criteria with clear physical meaning are selected from the existing dynamic failure criteria to predict the dynamic failure load of the domes. Then, a FEM nonlinear time–history response analysis is carried out using the FE package ANSYS for the 28 typical domes subjected to 30 different ground motions, and the dynamic failure loads are calculated by the selected failure criteria. It is found that the dynamic failure loads correspond to two different failure modes, one is the local failure caused by the sudden increase of the displacement of the dome’s local node, the other is the global failure caused by the sudden increase of the overall energy of the single-layer reticulated dome. After this, the lower bound failure accelerations with a certain guaranteed rate of those dynamic failure loads are determined using a lognormal distribution. The dynamic ductility index is then revised by the lower bound failure accelerations and the statistical analysis of the dynamic ductility index of the 28 typical domes is conducted to get a lower bound value for it. Finally, a method directly estimating the dynamic failure load of a dome is constructed and verified. The research will provide a new method under a certain degree of reliability to directly estimate the dynamic failure loads of single-layer reticulated shells in the earthquake area of China and contribute to the structural design with more overall confidence.

Numerical modelling for geotechnical assessment of rock mass behaviour and performance of support system for diversion tunnels using optimized Hoek-Brown parameters

Purpose. Empirical and numerical methods play a vital role in assessing rock mass behaviour quantitatively and qualitatively to design underground structures/caverns and support systems. This research aims to assess and evaluate the rock mass be-haviour for safe, stable, efficient, and economical design of support system for underground structures especially tunnels in diverse rock mass conditions. Methods. In this research, such empirical design methods as Rock Mass Rating (RMR), Q-system and GSI were used to characterize and classify the rock mass environment along the tunnel for the preliminary design of twin tunnels and support systems. The geomechanical parameters, Hoek-Brown failure criterion, and its variants for assessing rock mass behaviour were optimized using multiple regression of Stewart, generalized and globalized variant of nonlinear regression method. The rock mass was classified for the selected section A-A. The excavation method and support system for the said section were designed based on the results obtained from empirical modelling. 2D elasto-plastic finite element method (FEM) was used for numerical analysis of rock mass behaviour and performance of the designed supports in section A-A. Findings. The major rock type encountered in the diversion scheme comprises gabbronorite (GN) and Ultramafic Association (UMA). Based on the quantification of RMR, Q-system, and GSI, section A-A’s rock mass ranges from very poor to poor. From the numerical analysis for the said rock mass environment both RMR and Q system support recommendations are equally efficient to support the rock mass surrounding the tunnel. However, keeping in view the yield zone, especially in the crown, the rock bolt’s length should not be less than 5 meters. Based on the analysis of results, both the tunnels are at a safe distance from each other. Originality. In this research, the design input parameters for numerical modeling were optimized by using different techniques to eliminate the chances of error in evaluating rock mass behaviour and designing an optimum support system in the said rock mass environment. Practical implications. The assessment of rock mass behaviour and the design of optimum support systems in heterogenous conditions is quite challenging and requires thorough investigation through different design techniques. This research provides a refined meth-od to be used for the safe, stable, and economical design of tunnels.

Determination of Safety Factor for Rock Mass Surrounding Tunnel by Sudden Change of Equivalent Plastic Strain in Strength Reduction Method

The safety factor of rock mass surrounding tunnel can be determined using the strength reduction method (SRM), furthermore, it is very important to solve the criterion of critical state. For the stability estimation of rock mass surrounding tunnel, there is need to discuss that it is preferable to use the same criteria for the slope stability, such as non-convergence of finite element calculation, penetration of plastic strain and sudden change of horizontal displacement. The safety factor can be determined by sudden change of equivalent plastic strain in relationship between a reduction coefficient of strength parameter and equivalent plastic strain. This method is based on the elasto-plastic finite element method (FEM) and the SRM by ABAQUS and Mohr–Coulomb yield criterion. Simulation results using this method show how a safety factor varies with geometries, friction angles and cohesions for circle and square tunnels. Simulation results also show the safety factor varying with quality change of rock mass, pore water pressure and tunnel depth.

Probabilistic finite element analysis of fatigue life of additively manufactured clasp.

The present study was aimed to develop a probabilistic finite element method (FEM) that predicts the variability in the fatigue life of additively manufactured clasp so that it can be used as a virtual test in the design phase before manufacturing. Titanium alloy (Ti-6Al-4V) clasp with integrated chucking part, which was designed for experimental fatigue test to validate the computational method, was investigated. To predict the lower bound, an initial spherical defect was assumed in the region where stress concentration was predicted. The Smith-Watson-Topper (SWT) method, Bäumel & Seeger rule, elasto-plastic FEM, and zooming FEM were used. The influence of assumed initial defect on the fatigue life was significant, and the large variability in the fatigue life was predicted. This study demonstrated that the proposed practical computational method can simulate the large variability in the fatigue life of titanium alloy clasp, which is useful in its design before manufacturing.

Interaction of Mechanical Heterogeneity and Residual Stress on Mechanical Field at Crack Tips in DMWJs

The interaction between the mechanical heterogeneity and the residual stress in dissimilar metal welded joints (DMWJs) leads to a complex mechanical field of crack tips, which strongly affects stress corrosion cracking (SCC) behaviors. A dual-field coupling model was established by using the user-defined field (USDFLD) and the predefined stress field method based on the elastoplastic finite element method in this study. Thus, the mechanical heterogeneity and the residual stress of the DMWJ are realized. The influence of the interaction between the mechanical heterogeneity and the residual stress on the mechanical field of crack tips at different locations was investigated. The results show that the mechanical heterogeneity causes the stress and strain distribution on both sides of the crack tip asymmetry. And the residual stress affects the magnitude of the stress and strain around the crack tip. The variation trend of the stress and strain along the crack propagation with crack length is basically the same as that of the residual stress. However, the stress and strain distributions are slightly lagging behind the residual stress distribution due to the redistribution of the residual stress caused by the crack propagation. In addition, the stress and strain range of cracks at different positions with crack length are also different.

Experimental evaluation of the local failure criterion and its implementation in a damage mechanics model

Herein, a tensile test for notched round–bar specimens of two types of carbon steel used in nuclear containment vessels was performed. The test results were analyzed using the Bridgman solution and an elastoplastic finite element method. The analyses showed that ductile failures in the tensile state were initiated when the sum of equivalent and mean stresses reached a critical value of the material. A simple analysis of local failure for a nuclear containment was conducted using the failure criterion, and its engineering effectiveness was then discussed. The criterion is consistent with Argon's void nucleation model and can be implemented into the void nucleation term of stress control in the Gurson–Tvergaard (GT) model. The simulation performed using the GT model, which applied the limit value of the sum of equivalent and mean stress obtained from the tensile tests to the void nucleation term, successfully reproduced failure behaviors in the specimens.

Prediction and controlling for welding deformation of propeller base structure

Welding deformation often brings about manufacturing problems such as dimensional inaccuracies during assembly and reduces fabrication efficiency. Prediction and controlling welding deformation can help to improve the quality of welded structures. In this paper, the welding deformation of propeller base structures is predicted by means of numerical approaches and mechanical constraints are proposed to control deformations in welding process. Thermal elasto-plastic finite element method (TEP FEM) is employed to simulate welding process of the base structure. Computed accuracy of welding deformation by TEP FEM analysis is verified by comparing with experimental data of tee joint welding. Results show that welding deformations of the base mainly comprise out-of-plane distortion of ring fringe and radial distortion of cylindrical plate. Exerting mechanical constraints of fixed points at fringe and rigid supports inside cylinder can decrease out-of-plane and radial distortions effectively. The numerical approach adopted in this article can serve as an effective tool to optimize welding process planning in integrated design method.

Analysis of Damage Mechanism of Tunnel Lining Structure under the Coupling Action of Active Fault

To reveal the failure mechanism of tunnel structure under active fault movement, based on the pseudostatic elastoplastic finite element method, the failure modes of the tunnel lining are studied under different movement ratios of strike-slip faults and thrust faults with 45° dip angle by using numerical simulation. The results show that the range of significant lining failure section can be determined according to any direction of the coupling fault movement decomposition direction, and the damage effect is determined by the overall movement amount of the coupling fault. The significant damage area of the lining under the action of the coupling fault is the same as the area of deformation, which mainly manifests as tensile failure. Compressive failure occurs in the boundary area between the fracture zone and the hanging wall and foot wall. The plastic strain is the largest in the area where the arch waist and the arch bottom intersect. The development of tunnel lining plastic zone under coupling fault is from arch top and arch bottom to both sides of the arch waist. The development of the plastic zone under active fault is mainly determined by the form of fault with a large ratio. The research results can provide a reference for the design and safety evaluation of tunnel crossing active faults.

Building an Integrated Drilling Geomechanics Model Using a Machine-Learning-Assisted Poro-Elasto-Plastic Finite Element Method

SummaryThe petroleum industry has long relied on predrilling geomechanics models to generate static representations of the allowable mud weight limits. These models rely on simplifying assumptions such as linear elasticity, a uniform wellbore shape, and generalized failure criteria to predict failure and determine a safe mud weight. These assumptions lead to inaccurate results, and they fail to reflect the effect of different routing drilling events. Thus, this paper’s main objective is to improve the process for predicting the wellbore rock failure while drilling. This work overcomes the limitations by using a new and integrated modeling scheme.Wellbore failure prediction is improved through the use of an integrated modeling scheme that involves an elasto-plastic finite element method (FEM) model, machine learning (ML) algorithms, and real-time drilling data, such as image logs from a logging while drilling (LWD) tool that accurately describes the current shape of the wellbore. Available offset well data are modeled in the FEM code and are then used to train the ML algorithms. The produced integrated model of FEM and ML is used to predict failure limits for new wells. This improved failure prediction can be updated with the occurrence of different drilling events such as induced fractures and wellbore enlargements. The values are captured from real-time data and reflected in the integrated model to produce a dynamic representation of the drilling window.The integrated modeling scheme was first applied to laboratory experimental results to provide a proof of concept and validation. This application showed improvement in rock-failure prediction when compared with conventional failure criteria such as Mohr-Coulomb. Also, offset-well data from wireline logging and drilling records are used to train and build a field-based integrated model, which is then used to show that the model output for a separate test well reasonably matches the drilling events from the test well. Application of this integrated model highlights how the allowable mud-weight limits can vary because drilling progresses in a manner that cannot be captured by the conventional predrilling models.As illustrated by a field case, the improvement in failure prediction through this modeling scheme can help avoid nonproductive time events such as wellbore enlargements, hole cleaning issues, pack-offs, stuck-pipe, and lost circulation. This efficiency is to be achieved by a real-time implementation of the model where it responds to drilling events as they occur. Also, this model enables engineers to take advantage of available data that are not routinely used by drilling.

NUMERICAL SIMULATION OF LATERALLY LOADED PILE GROUPS ADJACENT TO A SLOPE

This paper is a numerical study based on a number of numerical model tests of pile groups, subjected to static lateral loading. Tests were conducted on single, (2x1), and (2x3) pile groups at three-diameter (3D) spacing. The model piles studied is concrete piles with 25 cm diameter and 10m length founded in loose sand (Dr=25%). The model is developed to study the effect of the number of piles in group on its lateral capacity on level ground and adjacent to a slope of inclination (3H:2V). The behavior of the piles was analyzed using a 3-D elasto-plastic finite element method (FEM) computer program Plaxis 3D ver. 2020, which represents a realistic model to simulate the problem. The response of the piles in the group was compared with the response of the single pile. It was found that the behavior of laterally loaded pile group depends largely on the arrangement of piles in group with respect to direction of load. In case of a slope it was found that the behavior of pile groups depends on the distance of lead row of pile groups from the slope crest (B/D) and arrangement of piles in group corresponding to load direction. &nbsp

Effect of Specimen Thickness and Stress Intensity Factor Range on Plasticity-Induced Fatigue Crack Closure in A7075-T6 Alloy.

Fatigue crack growth experiments are performed using A7075-T6 compact tension (CT) specimens with various thicknesses t (1–21 mm). The stress intensity factor at the crack opening level Kop is measured, and the effects of t and the stress intensity factor range ΔK on Kop are investigated. In addition, the change in Kop value due to specimen surface removal is investigated. Furthermore, we clarify that the radius of curvature of the leading edge of the fatigue crack decreases as t becomes thinner. Using the three-dimensional elastoplastic finite element method, the amount of plastic lateral contraction (depression depth d) at the crack tip after fatigue loading is calculated quantitatively. The following main experimental results are obtained: In the region where ΔK is 5 MPam1/2 or higher, the rate of fatigue crack growth da/dN at a constant ΔK value increases as t increases from 1 to 11 mm. The da/dN between t = 11 and 21 mm is the same. Meanwhile, in the region where ΔK is less than 5 MPam1/2, the effect of t on da/dN is not observed. The effects of t and ΔK on the da/dN–ΔK relationship are considered physically and quantitatively based on d.

Analysis and research on the bearing capacity of geocell reinforced cushion subgrade in liyu expressway

This paper takes the filling roadbed of the Lipu-Yulin Expressway (Liyu Expressway) project in the Guangxi Zhuang Autonomous Region as the backup project. Numerical simulation research is conducted by employing the general finite-element analysis software ABAQUS. The three-dimensional numerical models of the unreinforced soil embankment and reinforced embankment are formulated and the subgrade’s ultimate bearing capacity is calculated and solved by the elastoplastic finite element method. Effects of planar and three-dimensional reinforcement, i.e., geotextile and geocell, on the ultimate bearing capacity of the foundation are calculated and analysed. Simultaneously, the strength and deformation characteristics of geocells and geotextiles under embankment loads are studied. Research results show that the enhanced bearing capacity of geocell-reinforced foundation in this paper is increased by about 30%, which is greater than that of the planar reinforced material. This research results in this paper provide reference and theoretical basis for designing and analysing geocell-reinforced embankment in actual engineering practices.

Bearing capacity of ring footings placed on dense sand underlain by a loose sand layer

The ultimate bearing capacity of a ring footing on loose sand deposit, with an inclusion of a dense sand layer on its top, has been determined numerically in a bound form by following the finite element limit analysis (FELA). The friction angles ϕ1 and ϕ2 were varied from 40° to 46° and 30° to 36° for the top dense sand and the bottom loose sand respectively. The Mohr-Coulomb’s yield criterion has been assumed to be applicable. The bearing capacity has been found to increase quite extensively with an increase in the thickness of the dense sand layer thickness up to a certain optimal thickness before attaining a constant value. The magnitude of has been found to lie generally between 1.5 and 4.7, and the corresponding maximum value of the bearing capacity with an inclusion of the dense sand layer varies in a wide range of 2.32–82.45 times the corresponding value for an unimproved loose sand deposit; the parameters and refer to the inner and outer radii of the ring, respectively. Similar to a ring footing on homogeneous sand deposit, the bearing capacity for different chosen combinations of internal friction angles of the two sand layers, tends to become maximum generally for a value of closer to 0.25. For the validation, the results for a ring footing on two-layered sand deposit were also determined by using the displacements based elastoplastic finite element (EP-FE) method. The results from the FELA were found to compare well with (i) the obtained solutions based on the EP-FE method, and (ii) the published results by using experiments and the method of stress characteristics.

Dependence of bonding strength and variations in residual stress on interface wedge angles and bonding temperature conditions

AbstractResidual stress can considerably weaken systems with ceramics-to-metal joints. Herein, we investigate the dependence of bonding strength and residual stress variation of a ceramics-to-metal joint system on the interface wedge angle and bonding temperature condition. First, disparity between large-scale displacement models with varying work-hardening parameters was confirmed using thermal elastoplastic Finite Element Method (FEM) analysis. Each interface wedge shape was set to a plane surface to compare FEM results to experimental results related to the effect of the interface wedge angle on the practical bonding strength. The experimental results were specifically for a system consisting of Si3N4-WC/TiC/TaC bonded to Ni plate. The effects of the wedge angle of the metal side on residual stress near the interface edge were numerically predicted using FEM models. The interface wedge angles for this model, φ1 and φ2, were defined using the configuration angle between the interface and free surfaces of both materials. The numerical results showed that the stress σr on the free surface of the ceramic side was concentrated near the interface edge at which discontinuity in the stress state is generated. Dependence of the residual stress variation on both the wedge angle and temperature conditions can be predicted. It was confirmed that the bonding strength improves with decreasing residual stress in geometrical conditions. Therefore, residual stress appears to be a predominant factor affecting bonding strength. The observed fracture pattern showed that the fracture originated near the interface edges, after which small cracks propagated on the ceramic side. The residual stress is presumed to dominate bonding strength as the fracture occurred near the interface edge of the ceramic side. Results showed that the maximum bonding strength appears at the geometrical condition where the fracture pattern changes to φ2 lower than 90° of joint bonded at 980 °C. Therefore, the optimum interface wedge angle depends on a combination of materials and bonding temperature conditions, because the weak point of the bonded joint system will affect the stiffness balance of both materials and the adhesion power of the bonded interface.

Influence of Both Soil Properties and Geometric Parameters on Failure Mechanisms and Stability of Two-Layer Undrained Slopes

The stability of the two-layer undrained clay slopes should be given considerable attention since they are commonly observed in nature and in manmade structures, and they traditionally have low stability. Therefore, with the elastoplastic finite element method, this paper thoroughly explores the influence of the soil strength parameter cu, slope angle β, and slope depth ratio DH on the slope stability and failure mechanisms by the wide-ranging parametric changes. The aims of this study are also to find the critical strength ratio (cu2/cu1)crit and the maximum values of the stability number Nc that were observed in the parametric studies. Numerical results are displayed in the form of charts to give Nc and (cu2/cu1)crit as a function of cu, β, and DH. Moreover, influences of DH and β on Nc and failure mechanisms are examined in this study. The results of numerical analysis demonstrate that cu2/cu1 significantly affects both the critical failure mechanism and the stability of the two-layer undrained slope. Improved knowledge of the location of the critical failure mechanism allows for accurately estimating the stability of the two-layer undrained slopes for future strengthening measurements to preserve stability.

Study on Crack Closure Considering Welding Residual Stress Under Constant Amplitude Loading and Overloading

Welding residual stress in the engineering structure has a non-negligible influence on crack propagation, and crack closure is a significant factor affecting the crack propagation. Based on the elastoplastic finite element method and crack closure theory, we studied crack closure and residual compressive stress field of butt-welded plates under constant amplitude loading and overloading regarding the stress ratio, maximum load, overload ratio, and number of overloads. The results show that the welding residual tensile stress can decrease the crack closure because of a decrease in the residual compressive stress in the wake zone, but the effect is gradually reduced with increased stress ratio or maximum load. And the combined effect of welding residual tensile stress and overload can produce a stronger retardation effect on crack propagation.

Mechanical Characteristics Generated by Solidification Crack During High Strength Steel Welding

A multiscale method was developed to elaborate weld solidification crack mechanical field. A sequential thermo-mechanical finite element method (FEM) of butt-joint was performed to provide both of geometry and loading condition of submoel. Then mechanical behaviours generated by impurity was achieved by submodelling with embedded solidification cracks in terms of elasto-plastic FEM. The solidification initial cracks were geometrical discontinuity in nature and modelled as mechanical property discontinuity. Results show that additive stress and back stress are built-up at impurity-weld matrix interface. The developed modelling method was validated by solidification crack tests, X-ray tests together with fractography. The underlying mechanisms in suppression solidification cracking by adjustment of alloy contents in flux cored wire aiming to diminish the impurity size and improve the ductility of weld metal were revealed by developed method. Results show that, given a 9 percent increase of the weld metal ductility, a 29.6 percent decrease of the additive stress is achieved; and the longitudinal oriented impurity readily propagates crossing section rather than along impurity longitudinal tip. The susceptibility to cracking is distance-dependent, heavily on fields near to impurity and little on far field.