Elasto-plastic Finite Element Method Research Articles

Deformation Prediction of Plate Line Rolling Forming Based on Inherent Strain Method

Inherent strain method has been widely used as a forecasting and computing method for welding deformation of large complicated structures and further applied to the research of line heating forming. Mechanical forming is a common ship-hull plate forming method, for which deformation prediction still depends mainly on elastoplastic finite element method. This paper researched the application of inherent strain method to plate line rolling forming, a common mechanical forming method, and then compared the results of inherent strain method and elastoplastic finite element method, proving the applicability of inherent strain method, providing a method for fast, accurate forecasting of distortion in plate line rolling and formation of automation equipment.

Effect of main layer thickness on the response of multi layer bonded steel butt joint under Charpy impact test

The numerical analysis of the main layer thickness on the impact response of the steel butt joint bonded by multi-layer under the Charpy impact test is investigated using the elasto-plastic finite element method (FEM). The results obtained from numerical simulation show that both the elastic strain and plastic strain occurred at the point near the upper or lower surface decreased significantly when the main layer thickness increased from 0.1 mm to 0.4 mm. The value of the normal stress Sx and the von Mises equivalent stress Seqv is increased first when the main layer thickness increased and then it decreased significantly when the main layer thickness is greater than 0.2 mm. There is a strong value fluctuation for stress Seqv at the point 0.5 mm away from the upper surface when the main layer thickness is greater than 0.2 mm.

Numerical analysis of the adherends with similar thickness on weld-bonded single lap aluminium joint

The effect of the adherend with similar thickness varied from 1 mm to 3 mm on the stress distribution in weld-bonded single lap aluminium joint was investigated using elasto-plastic finite element method (FEM). The results from the numerical simulation show that all the values of the peak stresses along the mid-bondline at the points near the both ends of the lap zone as well as the ones in the region of the nugget are increased when the adherend thickness increased. It is suggested that the adherend thickness of 2 mm to 2.5 mm be appropriate to optimize the stress distribution in the weld-bonded single lap aluminium joint.

Geomechanical Modeling of Stress and Fracture Distribution during Contractional Fault-Related Folding

Understanding and predicting the distribution of fractures in the deep tight sandstone reservoir are important for both gas exploration and exploitation activities in Kuqa Depression. We analyzed the characteristics of regional structural evolution and paleotectonic stress setting based on acoustic emission tests and structural feature analysis. Several suites of geomechanical models and experiments were developed to analyze how the geological factors influenced and controlled the development and distribution of fractures during folding. The multilayer model used elasto-plastic finite element method to capture the stress variations and slip along bedding surfaces, and allowed large deformation. The simulated results demonstrate that this novel Quasi-Binary Method coupling composite failure criterion and geomechanical model can effectively quantitatively predict the developed area of fracture parameters in fault-related folds. High-density regions of fractures are mainly located in the fold limbs during initial folding stage, then gradually migrate from forelimb to backlimb, from limbs to hinge, from deep to shallow along with the fold uplift. Among these factors, the fold uplift and slip displacement along fault have the most important influence on distributions of fractures and stress field, meanwhile the lithology and distance to fault have also has certain influences. When the uplift height exceeds approximately 55 percent of the total height of fold the facture density reaches a peak, which conforms to typical top-graben fold type with large amplitude and high-density factures in the top. The overall simulated results match well with core observation and FMI results both in the whole geometry and fracture distribution.

DISCUSSION OF SAFETY FACTOR DEFINITIONS AND COMPUTATION METHODS FOR GEOTECHNICAL STRUCTURES

Taking common geotechnical problems, such as the bearing capacity of soil foundations and slope stability, as examples, two different definitions for the safety factor of structures, i.e. the ratio of limit load to allowable load and that of the available strength to required strength, are discussed. It is noted that the first definition is valid only for certain types of structures, whereas the second can be used for any type of structures. When both definitions can be employed, the proper choice depends on the characteristics as well as the loading environment of a specific structure, and different values for the required safety factor should be specified to reach the same level of reliability when a different safety factor definition is adopted. Moreover, the available methods for the computation of safety factors are reviewed, including the classical methods such as the slip line method, the limit analysis method, and the limit equilibrium method; as well as the modern methods such as the ordinary elasto-plastic finite element method, the strength reduction finite element method, and the finite element limit analysis method. The advantages and disadvantages of each method are discussed, and some suggestions are also presented with regard to their applications.

Plane stress problems using hysteretic rigid body spring network models

In this work, a discrete numerical scheme is presented capable of modeling the hysteretic behavior of 2D structures. Rigid Body Spring Network (RBSN) models that were first proposed by Kawai (Nucl Eng Des 48(1):29–207, 1978) are extended to account for hysteretic elastoplastic behavior. Discretization is based on Voronoi tessellation, as proposed specifically for RBSN models to ensure uniformity. As a result, the structure is discretized into convex polygons that form the discrete rigid bodies of the model. These are connected with three zero length, i.e., single-node springs in the middle of their common facets. The springs follow the smooth hysteretic Bouc–Wen model which efficiently incorporates classical plasticity with no direct reference to a yield surface. Numerical results for both static and dynamic loadings are presented, which validate the proposed simplified spring-mass formulation. In addition, they verify the model’s applicability on determining primarily the displacement field and plastic zones compared to the standard elastoplastic finite element method.

Real time bolt preload monitoring using piezoceramic transducers and time reversal technique—a numerical study with experimental verification

Bolted joints are ubiquitous structural elements, and form critical connections in mechanical and civil structures. As such, loosened bolted joints may lead to catastrophic failures of these structures, thus inspiring a growing interest in monitoring of bolted joints. A novel energy based wave method is proposed in this study to monitor the axial load of bolted joint connections. In this method, the time reversal technique was used to focus the energy of a piezoelectric (PZT)-generated ultrasound wave from one side of the interface to be measured as a signal peak by another PZT transducer on the other side of the interface. A tightness index (TI) was defined and used to correlate the peak amplitude to the bolt axial load. The TI bypasses the need for more complex signal processing required in other energy-based methods. A coupled, electro-mechanical analysis with elasto-plastic finite element method was used to simulate and analyze the PZT based ultrasonic wave propagation through the interface of two steel plates connected by a single nut and bolt connection. Numerical results, backed by experimental results from testing on a bolted connection between two steel plates, revealed that the peak amplitude of the focused signal increases as the bolt preload (torque level) increases due to the enlarging true contact area of the steel plates. The amplitude of the focused peak saturates and the TI reaches unity as the bolt axial load reaches a threshold value. These conditions are associated with the maximum possible true contact area between the surfaces of the bolted connection.

Incremental elastoplastic FEM for simulating the deformation process of suction caissons subjected to cyclic loads in soft clays

This paper presents an incremental elastoplastic finite element method (FEM) to simulate the undrained deformation process of suction caisson foundations subjected to cyclic loads in soft clays. The method is developed by encoding the total-stress-based bounding surface model proposed by the authors in the ABAQUS software package. According to the model characteristics, elastoplastic stress states associated with the incremental strains of each iteration are determined using the sub-incremental explicit Euler algorithm, and the state parameters describing the cyclic accumulative rates of strains are updated by setting state variables during the calculations. The radial fallback method is also proposed to modify the stress states outside the bounding surface to the surface during determination of the elastoplastic stress states. The stress reversals of soil elements are judged by the angle between the incremental deviatoric stress and the exterior normal vector at the image stress point on the bounding surface to update the mapping centre and state variables during cyclic loading. To assess the general validity of the method, the reduced scale model tests and centrifuge tests of suction caissons subjected to cyclic loads are simulated using the method. Predictions are in relative good agreement with test results. Compared with the limit equilibrium and quasi-static methods, the method can not only determine the cyclic bearing capacity, but can also analyse the deformation process and the failure mechanisms of suction caisson under cyclic loads in soft clays.

A Screening Method for Prevention of Ratcheting Strain Derived From Movement of Temperature Distribution

In this paper, we simplify the existing method and propose a screening method to prevent thermal ratcheting strain in the design of practical components. The proposed method consists of two steps to prevent the continuous accumulation of ratcheting strain. The first step is to determine whether all points through the wall thickness are in the plastic state. This is based on an equivalent membrane stress, which comprises the primary stress and the secondary membrane stress. When the equivalent stress exceeds the yield strength in some regions of the cylinder, the axial lengths of these regions are measured for the second step. The second step is to determine whether the accumulation of the plastic strain saturates. For this purpose, we define the screening criteria for the length of the area with full section yield state. When this length is sufficiently small, residual stress is generated in the direction opposite to the plastic deformation direction. As a result of residual stress, further accumulation of the plastic deformation is suppressed, and finally shakedown occurs. To validate the proposed method, we performed a set of elastoplastic finite element method (FEM) analyses, with the assumption of elastic perfectly plastic material. Not only did we investigate about the effect of the axial length of the area with full section yield state but also we investigated about effects of spatial distribution of temperature, existence of primary stress, and radius thickness ratio.

Effect of cutter tip angle on cutting characteristics of acrylic worksheet subjected to punch/die shearing

This paper aims to describe the effect of tool geometry on cutting characteristics of a 1.0 mm thickness acrylic worksheet subjected to a punch/die shearing. A set of side-wedge punch and side-wedge die which had the edge angle of 30°, 60° and/or 90° was prepared and used for cutting off the worksheet. A load cell and a CCD camera were installed in the cutting system to investigate the cutting load resistance and the side-view deformation of the worksheet. From experimental results, it was revealed that a cracking pattern at a sheared zone was remarkably affected by the edge angle of cutting tool. A cracking direction was almost coincident to the edge angle when considering the punch/die edge angle of 30°, while any matching of them was not observed in case of the punch/die edge angle of 60°, 90°. By using the 30° side-wedge tool, a flat-smooth sheared surface was generated. When combing the punch edge angle of 90° and the die edge angle of 60°, the cracking profile was characterized by the both edge angles for each part (die and punch). Carrying out an elasto-plastic finite element method analysis of cutter indentation with a few of symmetric and asymmetric punch/die edges, the stress distribution and deformation flow at the sheared zone were discussed with the initiation of surface cracks

Growth and residual stresses in the bonded compliant seal of planar solid oxide fuel cell: Thickness design of window frame

Bonded compliant seal (BCS) is a new sealing method for planar solid oxide fuel cell. The BCS design uses a thin foil to bond the cell and window frame, which generates a multilayer structure. However, the high temperature bonding generates large residual stresses that greatly affect the fracture. This paper presents a numerical method and neutron diffraction measurement to study the residual stress, and effect of window frame thickness has been discussed. A grain boundary diffusion model incorporated with a power-law creep constitutive model is developed to calculate the growth stress in the oxide film. Then, the thermal elasto-plastic finite element method is applied to calculate the thermal stress. A neutron diffraction experiment is performed to measure the through-thickness stresses. A good agreement is found between the calculation results and the neutron diffraction measurements. Compressive stress is generated in the oxide scale because of the substrate constraint. Furthermore, a competition exists between the generation of growth stress and the creep relaxation in the oxide layer. The residual stresses in the oxide layer decrease with the decrease in the substrate thickness. The thicknesses of the window frame and foil are designed to be 500 and 50μm, respectively.

Macro-element method with water absorption and discharge functions for vertical drains

When simulating the vertical drain method using a soil–water coupled finite element analysis, a macro-element method can be used as a means of approximately applying the water absorption function of drains to individual elements. In this paper, the discharge function of vertical drains was added to the method by treating the water pressure in the drain as an unknown and adding a continuity equation for the drains to the governing equations. By extending the method in this way, the analytical results came to exhibit the well-resistance phenomenon automatically, depending on the analytical conditions. Numerical analyses were conducted after incorporating the proposed macro-element method into a quasi-static soil–water coupled elasto-plastic finite element method based on the finite deformation theory. The main conclusions are as follows: (1) the proposed method enables highly accurate approximations for problems involving material and/or geometrical nonlinearity and multilayered grounds; (2) the proposed macro-element method is capable of reproducing various phenomena that occur when the vacuum consolidation method is applied to a clayey ground containing a middle sand layer; (3) by following the formulation used in this paper, it is unnecessary to match the mesh division width to the drain arrangement and spacing. In addition, it is possible to obtain solutions that are minimally affected by the mesh size.

Stability and reinforcement analysis of rock slope based on elasto-plastic finite element method

The rigid body limit equilibrium method (RBLEM) and finite element method (FEM) are two widely used approaches for rock slope’s stability analysis currently. RBLEM introduced plethoric assumptions; while traditional FEM relied on artificial factors when determining factor of safety (FOS) and sliding surfaces. Based on the definition of structure instability that an elasto-plastic structure is not stable if it is unable to satisfy simultaneously equilibrium condition, kinematical admissibility and constitutive equations under given external loads, deformation reinforcement theory (DRT) is developed. With this theory, plastic complementary energy (PCE) can be used to evaluate the overall stability of rock slope, and the unbalanced force beyond the yield surface could be the identification of local failure. Compared with traditional slope stability analysis approaches, the PCE norm curve to strength reduced factor is introduced and the unbalanced force is applied to the determination of key sliding surfaces and required reinforcement. Typical and important issues in rock slope stability are tested in TFINE(a three-dimensional nonlinear finite element program), which is further applied to several representatives of high rock slope’s stability evaluation and reinforcement engineering practice in southwest of China.

Numerical and experimental studies of single-stroke bumper forming using high-strength steel and laminate sheets

This work is to assess whether car bumpers can be formed using single-stroke pressing instead of conventional double-stroke pressing. Some basic characteristics of the car bumper forming process are also clarified. An incremental elasto-plastic finite-element method is used to simulate a bumper forming process using high-strength steel and laminate sheets under the plane strain condition. Simulations clearly demonstrate the processes involved in single-stroke forming. A three-layer steel/polymer/steel laminate developed for vibration-damping in an automobile bumper is also tested to demonstrate how shear defects occur between the two skin steel layers along the entire length of the laminate sheet in simulation. The springback phenomenon resulting from the elastic recovery is observed in simulations of the final bumper shape. Accordingly, experiments for high-strength steel sheet were performed to verify the numerical simulation and to investigate how process geometry conditions affect the springback angle, which is an essential consideration when assessing and controlling the final bumper shape in practice. This work improves understanding of the bumper forming processes used in the automotive industry.

3-D elasto-plastic spectral element application to evaluate the stability of large-scale landslides

This research deals with the computational accuracy impact factors of elasto-plastic spectral element applications to slope stability. It contains three categories of impact factors: 1) modelling domain related parameters, 2) spectral parameters, and 3)X elasto-plastic parameters. Each category has many accuracy impact factors. The modelling domain and elasto-plastic related impact factors can be equally applied to the elasto-plastic finite element method, however spectral corrections can only be applied for spectral element applications. This work presents a numerical evaluation of all three impact factors to the stability factor of a slope in three representative theoretical domains of slope angle, of 26.26°, 36.69°, and 45°. In addition, the study focuses on spectral element applications to slope stability evaluation, because it is a new and reliable approach in slope stability modelling. It has several benefits over the existing modelling methods to apply for slope stability modelling: 1) geometric flexibility of the finite elements, 2) high computational efficiency, 3) reliable spectral accuracy, and 4) high numerical stability.

Effect of Chamfer Angle on the Stress Distribution in Weld-Boded Single Lap Aluminum Joint

The effect of the outer chamfered angle at the free end of adherend on the stress distribution in weld-bonded single lap aluminum joint was investigated using elasto-plastic finite element method (FEM). The results from the numerical simulation showed that the peak stress along the bondline at the end of lap zone decreases when the adherend is chamfered on the outside and it is decreased greatly as the chamfer angle decreased. Compared to the results from the normal joint, a 15 degree chamfer angle may be appropriate to optimize the stress distribution in the weld-bonded single lap aluminum joint.

Numerical Analysis of Multi-Layer on the Stress Distribution in Adhesively Bonded Single Lap Aluminum Joint

The effect of dual adhesives to form multi-layer on the stress distributed in adhesively bonded single lap aluminum joint was investigated using elasto-plastic finite element method (FEM). The results from the numerical simulation showed that the values of the peak stress along the bondline are influenced evidently when there is a multi-layer formed by a middle layer with higher elastic modulus adhesive and two layers with lower elastic modulus adhesive.

Comparison of Rigid-Plastic and Elastoplastic Finite Element Predictions of a Tensile Test of Cylindrical Specimens

In this paper, finite element predictions of a tensile test of cylindrical specimens obtained by rigid-plastic and elastoplastic finite element methods are compared in terms of tensile load-elongation curve and deformed shape. The flow stress curve used for this study is obtained by a scheme of obtaining flow stress at large strain from tensile test of cylindrical specimen using rigid-plastic finite element method. The two predictions are compared in a quantitative manner and discussed not only to find some similarity but also to distinguish the elastoplastic finite element method from the rigid-plastic finite element method.

A new numerical method for determining collapse load-carrying capacity of structure made of elasto-plastic material

Determination of collapse load-carrying capacity of elasto-plastic material is very important in designing structure. The problem is commonly solved by elasto-plastic finite element method (FEM). In order to deal with material nonlinear problem involving strain softening problem effectively, a new numerical method-damped Newton method was proposed. The iterative schemes are discussed in detail for pure equilibrium models. In the equilibrium model, the plasticity criterion and the compatibility of the strains are verified, and the strain increment and plastic factor are treated as independent unknowns. To avoid the stiffness matrix being singularity or condition of matrix being ill, a damping factor α was introduced to adjust the value of plastic consistent parameter automatically during the iterations. According to the algorithm, the nonlinear finite element program was complied and its numerical example was calculated. The numerical results indicate that this method converges very fast for both small load steps and large load steps. Compared with those results obtained by analysis and experiment, the predicted ultimate bearing capacity from the proposed method is identical.

Numerical elastoplastic analysis of the shear stress distribution in the adhesive layer for single-lap joints

The purpose of this paper was to investigate the stress distribution of adhesive single-lap joint loaded in the elastic and elastoplastic range. The stress variation across the adhesive length was achieved both analytically and numerically. A two-dimensional finite element solution presented a detailed picture of the stress behavior in a single-lap joint loaded in the elastic and elastoplastic range. After the finite element results matched very well with results obtained from analytic solution in the elastic range, it was decided that adhesive plasticity needed to be added to the finite element models in order to make them as accurate as possible. The residual stresses after elastic-plastic loading were calculated. The results obtained from numerical analysis showed that the residual stress was important as the joint strength can be increased by residual stresses. In addition, the effect of the adhesive length, thickness of adhesive, and thickness of adherends on the shear distribution of the adhesive was examined numerically by using elastoplastic finite element method. The target was to change the geometry of the joint and study its effects on the stress distribution in the adhesive.