Elastic-plastic Large Deformation Research Articles

Three-dimensional J-integral evaluation for finite strain elastic–plastic solid using the quadratic tetrahedral finite element and automatic meshing methodology

In this paper, the three-dimensional J-integral for finite deformation problems is critically concerned when it is computed by the domain integral method for the quadratic tetrahedral finite element. When a cracked body undergoes a large elastic–plastic deformation, the domain independent property is not guaranteed. Evaluation procedures that guarantee the domain independent property by including the terms involving the spatial derivatives of the strain energy density, etc., are proposed. The proposed methodology includes a way to compute such derivatives by adopting the concept of superconvergent patch recovery method. Finally, numerical examples demonstrate that proposed procedures can guarantee the domain independent property.

The Algorithm of Solving the Problem of Large Elastic-Plastic Deformation by FEM

The paper is devoted to development and numerical implementation for a numerical method for investigation of stress-strain state of the solids with large elastic-plastic deformations. Calculation algorithm is based on the linearized equation of virtual work, defined to actual state. The arc-length method is used. A spatial discretization is based on the finite element method. The developed algorithm of investigation of large elastic-plastic deformations is tested on the solution of the necking of circular bar problem and a conical shell subjecting to a constant ring load.

Mathematical modeling of large elastic-plastic deformations

The paper is devoted to development and numerical implementation for a method for investigation of stress-strain state of the solids with large elastic-plastic deformations. Calculation algorithm is based on the linearized equation of virtual work, defined to actual state. The arc-length method is used. A spatial discretization is based on the finite element method. The developed algorithm of investigation of large elastic-plastic deformations is tested on the solution of the necking of circular bar.

Ultimate strength and collapse process of cable-stayed arch bridges

A new type of cable-supported bridge, the cable-stayed arch bridge, is proposed. This new bridge is a combination of a cable-stayed bridge and an arch bridge, and the girder is supported by both stay cables and arch ribs. Its static behavior, sectional forces and deflections, under the design load are compared with those of conventional cable-stayed bridges and arch bridges. Elastic-plastic large deformation analysis is then conducted to clarify the progressive collapse process and the ultimate strength. It is found that the cable-stayed arch bridge has smaller sectional forces and deformation under the design load and also has sufficient ultimate strength. The cable-stayed arch bridge is modified by inclining the arch planes 15 degrees from the vertical axis, which increases ultimate strength.

Formation of the Stress Field in the Vicinity of a Single Defect under Shock (Impulse) Loading

The formation of residual stresses in the vicinity of a single defect of continuity in the process of intense impulse loading surface with considerable distance from the defect is examined. Modeling is carried out within the framework of large elastic-plastic deformation. In the vicinity of the defect there is level of stress, leading to its elimination.

Hydrogen in metals: A coupled theory for species diffusion and large elastic–plastic deformations

We have formulated a thermo-mechanically coupled-theory which accounts for diffusion of hydrogen and large elastic–plastic deformations of metals. Our theory accounts for the trapping of hydrogen — and places this notion, and the notion of an equilibrium between hydrogen residing in normal interstitial lattice sites and hydrogen trapped at microstructural defects — within a thermodynamically-consistent framework. We have numerically implemented the theory in a finite element program, and the numerical implementation is verified by comparing simulation results from an analysis of hydrogen transport near a plastically-blunting crack-tip, against similar previously published results in the literature.The numerically-implemented theory should be of utility in the analysis of hydrogen diffusion in elastic–plastically-deforming solids, an analysis which is an essential prerequisite for theoretical and numerical efforts aimed at modeling the integrity of structural components used for hydrogen gas storage and distribution.

Computer Simulation of Sandwich Sheet Metal Forming

Large elastic-plastic deformations of sandwich composite sheets are computer simulated. Within a framework of the shell theory, the elastic-plastic constitutive relation for transversely anisotropic sandwich sheet taking into account of the Bauschinger effect is discussed. Results of the computer simulation of a hemispherical punch stretching operation are demonstrated.

A ductile–brittle fracture model for material ductile damage in plastic deformation based on microvoid growth

The fracture of ductile solids has frequently been observed to result from the large growth and coalescence of microscopic voids, a process enhanced by the superposition of hydrostatic tensile stresses on a plastic deformation field. The ductile growth of voids is treated here as a problem in continuum plasticity. In this paper, a ductile–brittle fracture criterion derived from a microvoid mechanical model is proposed for microdamage and fracture of metallic material under large elastic–plastic deformation and has been proved to be effective in the analysis of metal forming process. Using this criterion, the analyses of microdamage and ductile–brittle fracture for tensile specimens in complex stress-states have been carried out. The results from these analyses on damage development and fracture are in good agreement with the experimental ones, and from microview point are reasonable for cracked specimens.

A Cahn–Hilliard-type theory for species diffusion coupled with large elastic–plastic deformations

We develop a unified framework of balance laws and thermodynamically consistent constitutive equations which couple Cahn–Hilliard-type species diffusion with large elastic–plastic deformations of a body, and account for the swelling and phase segregation caused by the diffusing species.A potential, technologically important, area of application of the theory is in the chemo-mechanical analysis of the evolution of large stresses which develop because of the volume changes associated with the diffusion of lithium ions in the active electrode particles of lithium-ion batteries during charge–discharge cycles.

Stability Analysis of Slope Based on Finite Element Method

Based on the finite element software as calculation tool, Mohr-Coulomb yield criterion and Drucker-Prager yield criterion were converted to equivalent area circle yield criterion, the elastic-plastic large deformation finite element method (FEM) was adopted, at the same time strength reduction technology combined with convergence criterion, catastrophe criterion and plastic zone penetrability criterion was used, and the problem of 2-D slope stability was analysed. Then based on finite element reduction strength method and three criterions, the homogeneous slope safety factors were calculated. The results showed that equivalent area circle D - P yield criterion was suitable for slope stability analysis and that strength reduction technology could be applied in simple homogeneous side slope stability analysis.

A new surface parameterization method based on one-step inverse forming for isogeometric analysis-suited geometry

In an attempt to construct an isogeometric analysis-suited geometry for isogeometric analysis, a new surface parameterization method using the one-step inverse forming (SPIA) is proposed. Initial generation of watertight analysis-suitable geometry (NURBS surfaces) with complex shapes can be a significant bottleneck for isogeometric analysis because computer-aided design models often include ambiguities such as gaps and overlaps. Most of traditional surface parameterization techniques are based on geometric method and limited to finite meshes, while SPIA is a physics-based method using sheet metal forming technique with large elastic–plastic deformation and robust enough and rapid to deal with the finite elements mesh with over 100,000 nodes within 2 min without the necessity to simplify the meshes. Using Coons surface parameterization, global mesh parameterization, and NURBS reconstruction, we can rebuild new computer-aided design models with errors under any tolerance to which isogeometric analysis can be applied. The NURBS surfaces after reconstruction are also used for computer-aided manufacturing.

The Research of Cold Roll Forming Numerical Simulation of Involutes Spline on ANSYS

According to the large deformation elastic-plastic FEM and contact theory, Through the cold roll forming numerical simulation of involutes spline by the finite element software ANSYS, studied with the key techniques of numerical simulation of the large displacements, large rotations, large elastic-plastic deformation under the highly complex nonlinear and the action of friction.

Soundness Diagnosis Of A Steel Bridge Pier Repaired By Heating/Pressing

In order to diagnose the soundness of a steel bridge pier, repaired by heating/pressing, a series of experiments and analyses were conducted. A virgin specimen was first locally buckled by cyclic bending loads and subsequently corrected by heating/pressing. The corrected specimen was again subjected to the same loading experiment as the virgin specimen. In addition, loading experiments were simulated by elastic-plastic large deformation analysis. It was confirmed that heating temperatures should be kept below the A1 transformation temperature (around 700 °C within the general structural steel) to prevent changes to its mechanical properties. It was ideal for the imperfection, which was the residual deformation in the panel, to be controlled within the acceptance of the initial deflection. Further, it was found that correcting the residual deformation opposite the mode of local buckling of the panel was an effective method for maintaining the maximum strength of the repaired pier, equivalent to that of the virgin specimen.

The Analysis to the Forming Process of Welded Pipe by Non-Linear Finite Element Method

Understanding the mechanism of the forming of the welded pipe may help the engineer to design the shape of forming rollers and forming technology. It is hard to study the forming process of the welded pipe by both the method of experiment and numerical modeling because of too much nonlinear factors included in the forming process such as elastic-plastic large deformation and non linear contact. Although many research works have been conducted in this field by the method of experiment or numerical modeling, but few of the works deal with the whole forming process of the welded pipe. The main difficulties in the numerical modeling are of huge computational labor time, witch has been over the ability of the hardware and software of the computer. The whole process of roll forming of welded pipe has been simulated by nonlinear finite element method with ANSYS and LS-DYNA solver, the distribution of both stresses and strains have been got successfully. Mapping meshes and the rigid models for rollers have been used in the analysis in order to decrease the number of the elements. Numerical results and parameter study have shown that the forming rollers of both the level and vertical are the key factors to the forming process. It is believe that the method used in the paper can also be used to study the forming process of both cage roll forming and flexible forming.

3D FINITE ELEMENT MODELLING OF CHIP FORMATION PROCESS FOR MACHINING INCONEL 718: COMPARISON OF FE SOFTWARE PREDICTIONS

Many efforts have been focused on the development of Finite Element (FE) machining models due to growing interest in solving practical machining problems in a computational environment in industry. Most of the current models are developed under 2D orthogonal plane strain assumptions, or make use of either arbitrary damage criterion or remeshing techniques for obtaining the chip. A complete understanding of the material removal process together with its effects on the machined parts and wear behaviour of the cutting tools requires accurate 3D computational models to analyze the entire physical phenomenon in materials undergoing large elastic-plastic deformations and large temperature changes as well as high strain rates. This work presents a comparison of 3D machining models developed using commercially available FE softwares ABAQUS/Explicit© and DEFORM™3D Machining. The work material is chosen as Inconel 718, a difficult-to-cut nickel-based alloy material. Computational results of temperature, strain and stress distributions obtained from the FE models for the effect of cutting speed are presented in comparison with results obtained from experimental tests. In addition, modified material model for Inconel 718 with flow softening is compared with the Johnson-Cook model. The predictions of forces and chip formation are improved with the modified material model.

Introducing/reproducing of welding distortion and residual stress in analysis for elastic-plastic behaviors of steel plates under compressive loads

A series of analyses was carried out to elucidate treatment of welding imperfection for simulating elastic-plastic behaviors of steel plates under compressive loads. A thermal elastic-plastic analysis based on infinitesimal deformation theory was carried out on a single-pass butt-welding of thin steel plates to predict welding distortion and welding residual stress. The obtained welding distortion and welding residual stress were introduced into an elastic-plastic large deformation analysis as initial imperfection. However, it was elucidated that welding distortion and welding residual stress could not be reproduced precisely due to unbalanced force caused by the difference between both analysis theories. Therefore, it should be confirmed whether the introduced welding distortion and welding residual stress were reproduced with high accuracy. Consequently, if welding distortion and welding residual stress cannot be reproduced, the treatment such as the convergence calculation method applied in this study should be done for precise elucidation of the elastic-plastic behavior of plates under compressive loads.

Effects of welding residual stress on compressive behavior and ultimate strength of corroded plate

This study examined the effects of welding residual stress on the compressive behavior and the ultimate strength of the corroded plate. First, welding residual stress was obtained by the thermal elastic-plastic analysis. Then, the change of welding residual stress and the deflection due to the volume loss was investigated by using a newly developed program based on FEM. Finally, the effects of welding residual stress on the compressive behavior and the ultimate strength of the corroded plate were investigated by the elastic-plastic large deformation analysis. As results, the beginning point of the reduction of the initial stiffness with welding residual stress was earlier than that without welding residual stress. Such effect was observed significantly in the case that the volume was lost in the region which has compressive residual stress. Furthermore, the ultimate strength of the corroded plate was reduced by welding residual stress regardless of the plate length, the corroded regions and the reduction of the thickness. The effect of welding residual stress on the ultimate strength became small with the decrease of the thickness.

A new model for simulation of cold roll-forming of tubes by using spline finite strip method

A new model, called object model, for the simulation of cold roll-forming of tubes is presented. The model inherits the advantages of old models and is the embodiment of forming process that the strip is rolled step by step from feed rollers to last rolling pass. The elastic-plastic large deformation spline finite strip method based on updated Lagrangian method has been developed by improving the stiffness and transition matrix. Combined theory formulas and new analytical model, the forming process of a tube has been simulated successfully as an example. The analytical results are submitted and indicate that the proposed simulation method and new model are applicable.

Fracture of metallic glasses at notches: Effects of notch-root radius and the ratio of the elastic shear modulus to the bulk modulus on toughness

The Anand–Su theory for large elastic–plastic deformations of metallic glasses is modified to account for the strongly nonlinear and eventually softening dilatational volumetric elastic response of these materials. Using this theory, we have conducted finite-element simulations of fracture initiation at notch tips in a representative metallic glass under Mode-I, plane-strain, small-scale-yielding conditions. We show that our theory predicts three important experimentally observed phenomena: (a) fracture initiates ahead of the notch root, where the mean normal stress reaches a maximum value; (b) the fracture toughness increases linearly with the square-root of the notch-tip radius; and (c) the fracture toughness decreases as the ratio of the elastic shear modulus to the bulk modulus increases.

Effect of Correction by Heating/Pressing on Mechanical Behaviour of Steel Structural Members

A series of experiments was carried out to investigate the effects of correction by heating/pressing on the mechanical behaviour of steel members. Compressive experiments for virgin cruciform column specimens were carried out and local buckling was generated. After the buckling deformation was corrected by heating/pressing, compressive experiments were carried out again. In the case of the corrected specimens, the ultimate strength was almost the same compared to that of the virgin specimens. Though only one kind of deformation mode occurred in the virgin specimens, various deformation modes occurred in the corrected ones. To determine the dominant factors affecting the compressive behaviour of cruciform columns corrected by heating/pressing, the experiment was simulated by elastic-plastic large deformation analysis. It was determined that the dominant factors were both residual imperfection and increase of yield stress due to large plastic deformations caused by buckling and its correction.