Three-dimensional Elasto-plastic Model Research Articles

Reduced T-shaped soil domain for nonlinear dynamic soil-bridge interaction analysis

The one-directional three-component wave propagation in a T-shaped soil domain (1DT-3C) is a numerical modeling technique, in a finite element scheme, to investigate dynamic soil-structure interaction (SSI) coupled with seismic site effects, under the assumption of vertical propagation of three-component seismic motion along a horizontal multilayered soil. A three-dimensional elasto-plastic model is adopted for soils, characterized using their shear modulus reduction curve.In this research, the 1DT-3C wave propagation modeling technique is proposed as an efficient tool for bridge design to take into account directly the spatial variability of seismic loading. This approach, in the preliminary phase of bridge study and design, allows the reduction of the soil domain and the easier definition of boundary conditions, using geotechnical parameters obtained with only one borehole investigation for each pier. This leads to a gain in modeling and computational time.

An investigation on static and fatigue life evaluation of grooved adhesively bonded T-joints

Adhesively bonded joints with T-shaped configurations are widely used in bonded components of engineering structures used in industries such as automotive, aircraft, and marine. In this paper, static strength and fatigue life of two T-joint configurations of flat and grooved types were evaluated. For this purpose, firstly, the effect of the specimen configuration of the bonded T-joints on the stress field has been calculated using the finite element method. For this purpose, a three-dimensional elastoplastic model is used for simulation. Then, static failure load of these joint types was examined under four loading rates of 1, 10, 50, and 100 mm/min. Also, fatigue tests were performed under maximum fatigue loads of 40%, 60% and 80% of average static failure loads. Results indicated that the average static failure load of grooved specimens was 37.3%, 26.5%, 14.4%, and 9.3% higher than that of the flat type T-joints under 1, 10, 50, and 100 mm/min loading rates, respectively. Moreover, fatigue life cycles of grooved T-joints were 40.2%, 25.3%, and 11.6% longer than that of the flat bonded specimens under 40%, 60%, and 80% maximum fatigue loads, respectively. It was also concluded that, under high fatigue loads, the groove effect can be ignored on improving the fatigue life.

On the bending angle of aluminum-copper two-layer sheets in laser forming process

The purpose of this paper is to numerically and experimentally investigate with optimized parameters laser thermal bending of aluminum-copper two-layer sheet. Due to the fact that laminated sheets have more ductility and lower manufacturing costs, in this article, the thermal bending behavior of this type of sheet is investigated. For this purpose, the optimal model is obtained using the Taguchi and finite element methods, with respect to the cost functions and the defined levels for the parameters. The effective parameters of the laser forming process such as the scanning speed, the laser beam power, and the laser beam diameter on the aluminum-copper two-layer sheet are optimally determined and subsequently the laser thermal bending of the aluminum-copper two-layer sheet is obtained by experimental tests. The Taguchi method is used to optimize the simulations required for the analysis. The Taguchi method with its own algorithm reduced the number of experiments to 9 design points. These experiments are simulated by the finite element method with a three-dimensional elastoplastic model. Then, to verify the numerical results of these optimized parameters, the samples are fabricated and the effect of optimal parameters on the behavior of this type of the aluminum-copper two-layer sheet is evaluated under experimental tests. The results showed that the laser beam power has a direct relation and the laser beam diameter and scanning speed have an inverse relation with the final bending angle.

Analysis of deformation and failure characteristics of soft and broken surrounding rocks of super-large section tunnel constructed using benching tunneling method

The benching tunneling method can overcome the problems of insufficient working space and low construction efficiency in the soft and broken surrounding rock tunnel with super large section, but the design and construction theory and method are under developing. In order to solve the problem of insufficient basis for the design of the large-section bench method in the weak and broken surrounding rock, a three-dimensional elastoplastic model was established. The deformation and fracturing of the surrounding rock outside the tunnel excavation profile and in front of the tunnel face were used as indicators to analyze the deformation and failure characteristics of the weak and broken surrounding rock under benching tunneling method. The calculation results show that the grade of surrounding rock worsens (grade IV-V). Depending on the initial support design conditions, instability of the supporting structure or the tunnel face may occur. In the condition that grade of surrounding rock does not lose stability, the leading deformation accounts for a larger proportion of the whole deformation, indicating that the leading deformation is the key to the stability control in the benching tunneling method. When the tunnel face is unstable, the surrounding rock within 4.5m in front of the tunnel and 1.5m above the arch collapses, and the deformation and damage develop from the vault down to the foot of the wall.

Stability control measures of soft and broken surrounding rocks of super-large section tunnel constructed using benching tunneling method

The tunnel face of the super-large section tunnel constructed using benching tunneling method tends to loss stability in the stratum with very poor surrounding rock grade (grade V). Therefore it is necessary to employ advanced support or optimize bench construction parameters to improve the stability of tunnel construction. In order to determine the stability control measures for the super-large section tunnel constructed using benching tunneling method in soft and broken surrounding rock, a three-dimensional elastoplastic model is established. Taking the extrusion displacement of tunnel face and the failure zone of surrounding rock as indices, the influences of bench height, bench length, circulating footage and other construction parameters and the construction of advanced large pipe shed on tunnel stability were analyzed. The calculation results show that when the tunnel is constructed using benching tunneling method, the surrounding rock within 4.5m in front of the tunnel face and 1.5m above the arch collapses, and the failure develops from the arch top down to the arch foot. The measures such as shortening the circulating footage, shortening the length of the bench and reducing the height of the upper bench have little effect on the stability of the tunnel, and the maximum difference among the strength reduction coefficients of the surrounding rock is 0.1 when the tunnel losses stability. The advanced large pipe shed can significantly improve the stability of benching tunneling method construction. The deformation and failure of the tunnel mainly concentrates in the side wall area, which gradually develops from the arch foot to the wall foot, and the depth of the surrounding rock failure zone is very limited.

RETRACTED: An investigation on fatigue behavior of AA2024 aluminum alloy sheets in fuselage lap joints

The purpose of this paper is to estimate the fatigue life of AA2024 aluminum alloy sheets in riveted joints under the influence of cyclic loading. First, the factors affecting the plastic equivalent strain resulting from the riveting process have been identified using the finite element method. For this purpose, a three-dimensional elastoplastic model is used for simulation. The relevant geometrical parameters such as the rivets shank length, the rivets shank diameter, and dimensional tolerances as well as pattern of where the rivets are and the material of the riveted joints are determined and subsequently the fatigue life of the aluminum joint is obtained by experimental tests. Then the fatigue life of the riveted joints is calculated using the Paris equation. To prove the validity of the analytical results, numerical modeling and experimental tests are performed on AA2024 aluminum alloy sheets in riveted joints. Numerical analysis has been performed using linear fracture mechanics and boundary element method (BEM) for the fatigue crack growth of AA2024 aluminum alloy sheets in riveted joints. Finally, the results of the analytical method for fatigue life are compared with experimental tests and numerical method that results in acceptable achievements.

Fatigue performance prediction of Al-alloy 2024 plates in riveted joint structure

The purpose of this paper is to estimate the fatigue life of 2024 aluminum plates in riveted joints under the influence of cyclic loading. First, the factors affecting the plastic equivalent strain resulting from the riveting process have been identified using the finite element method. For this purpose, a three-dimensional elastoplastic model is used for simulation. The relevant geometrical parameters such as the rivets shank length, the rivets shank diameter, and dimensional tolerances as well as pattern of where the rivets are and the material of the rivet joints are determined and subsequently the fatigue life of the aluminum joint is obtained by experimental tests. Then the fatigue life of the riveted joints is calculated using multiple site damage (MSD). To prove the validity of the analytical results, numerical modeling and experimental tests are performed on 2024 aluminum plates in riveted joints. Numerical analysis has been performed using linear fracture mechanics and boundary element method (BEM) for the fatigue crack growth of 2024 aluminum plates in riveted joints. Finally, the results of the analytical method for fatigue life are compared with experimental tests and numerical method that results in acceptable achievements.

Consistent Three-Dimensional Elasto-Plastic Model to Study Unsaturated Soil Behavior with Considerations of Coupled Hydro-Mechanical Hysteresis

This paper presents a consistent three-dimensional elasto-plastic model to study unsaturated soil behavior with consideration of coupled hydro-mechanical hysteresis. The model was first formulated under isotropic conditions with special consideration to the non-linearity of the hydraulic behavior. Only one yield curve is used to represent the yielding of both mechanical and hydraulic behaviors (i.e., the occurrence of plastic water content changes and mechanical strains). Later, the model is extended to general three-dimensional stress conditions. It was formulated in a way that a smooth transition between the saturated and unsaturated soil states is guaranteed. The model provides consistent predictions for different soil phases that is considered a significant limitation in many existing models. One of the characteristic features of the proposed model is the ability to represent the hydro-mechanical coupling during shearing. Moreover, the model is able to represent the degree of saturation increase or decrease during shearing that is closely related to the soil’s contractive or dilative behavior, respectively. The model is validated through the prediction of several hydro-mechanical behavioral features. The paper also compares the model predictions with published experimental results performed under different loading conditions. The response of the model is satisfactory in relation to both mechanical and hydraulic behaviors.

Numerical investigation on the rolling contact wear and fatigue of laser dispersed quenched U71Mn rail

The influences of laser dispersed quenching (LDQ) technology on the rolling contact wear and fatigue of U71Mn rail were investigated numerically. Firstly, based on the improved Abdel Karim-Ohno’s material model, a three-dimensional elasto-plastic model with of LDQ rail was established, and the moving load method was used to apply the equivalent contact load. Subsequently, combined with the ductility exhaustion theory and Smith-Watson-Topper fatigue assessment method, the rolling contact wear and fatigue performances of U71Mn rail were investigated, respectively. The results show that the LDQ treatment has little effect on fatigue crack initiation life, but can significantly improve wear resistance of rails.

A three dimensional model of multicellular aggregate compression.

Multicellular aggregates are an excellent model system to explore the role of tissue biomechanics, which has been demonstrated to play a crucial role in many physiological and pathological processes. In this paper, we propose a three-dimensional mechanical model and apply it to the uniaxial compression of a multicellular aggregate in a realistic biological setting. In particular, we consider an aggregate of initially spherical shape and describe both its elastic deformations and the reorganisation of the cells forming the spheroid. The latter phenomenon, understood as remodelling, is accounted for by assuming that the aggregate undergoes plastic-like distortions. The study of the compression of the spheroid, achieved by means of two parallel, compressive plates, needs the formulation of a contact problem between the living spheroid itself and the plates, and is solved with the aid of the augmented Lagrangian method. The results of the performed numerical simulations are in qualitative agreement with the biological observations reported in the literature and can also be used to estimate quantitatively some fundamental aggregate mechanical parameters.

A hyperbolic augmented elasto-plastic model for pressure-dependent yield

A three-dimensional elasto-plastic model for the deformation and flow of granular materials which generalises the plastic potential model and contains an additional term analogous to that appearing in the double-shearing model is presented. It is shown that for planar flows the resulting system of first-order partial differential equations is hyperbolic. This is in distinct contrast to both the non-associated plastic potential and double-shearing models, which fail to be hyperbolic. The ill-posedness of the Cauchy problem for the planar double-shearing model is due to the presence of the rotation rate of the principal axes of stress while that of the non-associated plastic potential model is due to distinct quasi-static spatial stress and velocity characteristics. The present model attains well-posedness by replacing the planar rotation rate of the principal stress axes by the vector intrinsic spin of a Cosserat continuum and using it to ensure identical spatial stress and velocity characteristics. Flows in which the intrinsic spin vector is constant in both space and time correspond to flows in an ordinary continuum. The model governing such flows is embedded into a Cosserat model in such a way that the characteristic structure is preserved.

Prediction of the Lüders band in fine grained steel strips under uniaxial tension

Abstract The Luders band and the other regions outside the Luders band in fine grained steel strips are treated as two phases in equilibrium in the present paper. The discontinuities of stress and deformation gradient across interfaces between the Luders band and the other regions are considered, and the continuities of traction and displacements across interfaces and the Maxwell relation are imposed. The governing equations for two-phase piecewise-homogeneous deformations are obtained. The analysis is reduced to finding the minimum value of the loading at which governing equations have a unique, real, physically acceptable solution. As an illustration, the trilinear stress–strain response under uniaxial tension for fine grained steel used by other authors is applied to calibrate the three-dimensional elastoplastic model, the Maxwell stress, the inclined angle of the Luders band, the kinking angle of the strip and the strain and stress in the Luders band are predicted numerically. The predictions are in reasonable agreement with experimental measurements. The analysis also explains why the Luders band can spread along the length of the displacement-controlled specimen under the constant Maxwell stress plateau as observed in experiments.

A Three-Dimensional Elastoplastic Model for Unsaturated Compacted Soils with Hydraulic Hysteresis

This paper presents a three-dimensional elastoplastic model for predicting the hydraulic and stress-strain-strength behaviour of unsaturated soils. The model is generalized using the transformed stress method to three-dimensional stress states by assuming that the shapes of the failure surface and the yield surface in the deviatoric plane of the average skeleton stress space are given by the SMP criterion. Hydraulic hysteresis in the water-retention behaviour is modeled as an elastoplastic process with the elastic region of the saturation degree decreasing with increasing suction in the Sr-log s plane. The effect of void ratio on the water-retention behaviour is studied using test data obtained from controlled-suction triaxial tests on unsaturated compacted clay. The effect of change in degree of saturation on the stress-strain-strength behaviour and the effect of change in void ratio on the water-retention behaviour are taken into consideration in the model, in addition to the effect of suction on the hydraulic and mechanical behaviour. Model predictions of the stress-strain and water-retention behaviour are compared with those obtained from triaxial tests on unsaturated soil along isotropic compression, triaxial compression and triaxial extension stress paths with or without variation in suction. The comparisons indicate that the model has well predicting capabilities to reproduce the hydraulic and mechanical behaviour of unsaturated soils under three-dimensional stress states.

An anisotropic hardening elastoplastic model for clays and sands and its application to FE analysis

The Sekiguchi–Ohta model is extended to be a unified three-dimensional elastoplastic model for clays, silts and sands by introducing a transformed stress tensor σ ̃ ij and a new hardening parameter H. The model can describe the negative and positive dilatancy of soils with an initially stress-induced anisotropy in three-dimensional (3D) stress. An elastoplastic constitutive tensor is derived for the application of the proposed model to finite element (FE) analyses. A FE analysis example for a test embankment is given and the result demonstrates that the proposed model can predict reasonably the deformation of anisotropically consolidated clay and sand layers under embankment loading.

Three‐dimensional elasto‐plastic model for unsaturated compacted soils with different initial densities

AbstractThis paper presents an elasto‐plastic model for unsaturated compacted soils and experimental results obtained from a series of suction‐controlled triaxial tests on unsaturated compacted clay with different initial densities. The initial density dependency of the compacted soil behaviour is modelled by establishing experimental relationships between the initial density and the corresponding yield stress and thereby between the initial density and the location and slope of normal compression line. The model is generalized to three‐dimensional stress states by assuming that the shapes of the failure surface and the yield surface in the deviatoric plane are given by the extended SMP criterion. A considerable number of the isotropic compression, triaxial compression and extension tests on unsaturated compacted clay with different initial densities were performed using a suction‐controllable triaxial apparatus, to measure the stress–strain–volume change in different stress paths and wetting paths. The model has well‐predicting capabilities to reproduce the mechanical behaviour of specimens compacted under different conditions not only in isotropic compression but also in triaxial compression and triaxial extension. Copyright © 2003 John Wiley & Sons, Ltd.

An Elasto-Plastic Model for Unsaturated Soil in Three-Dimensional Stresses

A three-dimensional elasto-plastic model for unsaturated soil is presented, using a transformed stress tensor based on the Extended SMP criterion. The influences of suction on the mechanical behavior of unsaturated soil are taken into account in the model by using a parameter named suction stress σ0(s), which is added to net stress to form an effective stress, and associating a yield stress and model parameters with it. The proposed model needs few material parameters, which can be easily determined from the results of ordinary tests, for example, oedometer and direct shear tests or triaxial test. It can predict the stress-strain-strength behavior of unsaturated soil under the conditions of three-dimensional stresses and constant or variable suction. A considerable number of triaxial compression and extension tests on unsaturated compacted kaolin were performed by using a suction-controlled triaxial apparatus, to measure the stress-strain behavior under different stress paths with constant and decreasing suction. The prediction of the proposed model shows good agreement with the measured behavior of unsaturated soil not only in triaxial compression but also in triaxial extension under the conditions of constant suction and reduction in suction, which may induce an irrecoverable volumetric compression (collapse).