Elastoplasticity

This paper presents an adaptive incremental approach capable of handling elastoplastic contact problems with friction. Using the finite element method (FEM), the problem is formulated as an incremental convex programming model (ICPM) under the inequality contact constraints and friction conditions. The Lagrange multiplier approach is adopted for imposing the contact constraints. The classical Coulomb's law of friction is used for simulating the friction conditions throughout the contact interface. The incremental constitutive relations based on the Prandtl-Reuss equations and von Mises yield criterion are adopted to simulate the elastoplastic response. The adopted model advantage is that the model gets rid of the inclusion of any artificial element or intervene user defined parameters such as penalty values and the number of load steps. Numerical examples for the frictional contact having advancing and receding nature under normal load are presented. Illustrated examples prove the capability of the incremental procedure to investigate the sequence of different events during monotonic application of external load. Variations of the contact pressure, relative tangential displacement (RTD), tangential stress over the contact area and equivalent stress within the domain with the coefficient of friction are presented to validate the model. Good agreement has been found with published results. RÉSUMÉ Cet article présente une approche progressive adaptative capable de gérer les problèmes de contact avec frottement élasto-plastiques. Utilisation de la méthode des éléments finis (FEM), le problème est formulé comme un modèle de programmation convexe incrémentale (CIMP) sous les contraintes de contact de l'inégalité et conditions de frottement. L'approche des multiplicateurs de Lagrange est adoptée pour imposer les contraintes de contact. La loi de Coulomb classique de frottement est utilisé pour simuler les conditions de frottement dans l'interface de contact. Les relations constitutives supplémentaires basés sur les équations de Prandtl-Reuss et von Mises critère de rendement sont adoptées pour simuler la réponse élasto-plastique. L'avantage du modèle adopté est que le modèle se débarrasse de l'inclusion de tout élément artificiel ou intervenir les paramètres définis par l'utilisateur tels que les valeurs de pénalité et le nombre de prises en charges. Des exemples numériques pour le contact de friction ayant entrants et sortants nature sous une charge normale sont présentés. Exemples illustrés prouvent la capacité de la procédure incrémentale à rechercher la séquence d'événements différents lors de l'application monotone de charge externe. Les variations de la pression de contact, le déplacement tangentiel relatif (RTD), contrainte tangentielle sur la surface de contact et la contrainte équivalente au sein du domaine avec le coefficient de frottement sont présentés pour valider le modèle. Un bon accord a été trouvé avec les résultats publiés.

A new elasto-plastic model for unsaturated soils incorporating the effect of evolving fabric anisotropy is presented. The model is formulated in terms of mean net stress, deviator stress and suction and reduces to the Barcelona Basic Model for an isotropic material. Model simulations are performed and compared against experimentally observed behaviour from constant suction triaxial tests on isotropically and anisotropically compacted kaolin samples along a variety of stress paths. Simulations indicate an improvement in the prediction of the size and shape of the yield surface compared to the Barcelona Basic Model. In addition, the deformation generated during shearing are better predicted than in the Barcelona Basic Model, even though experimentally observed strains are still grossly over-estimated. Further refinement to model assumptions are required to improve predictions of experimental data and the reformulation of the model in terms of average skeleton stresses, instead of net stresses, might help in this respect as outlined in Al-Sharrad (2013).

This work extends existing multiphase-fluid SPH frameworks to cover solid phases, including deformable bodies and granular materials. In our extended multiphase SPH framework, the distribution and shapes of all phases, both fluids and solids, are uniformly represented by their volume fraction functions. The dynamics of the multiphase system is governed by conservation of mass and momentum within different phases. The behavior of individual phases and the interactions between them are represented by corresponding constitutive laws, which are functions of the volume fraction fields and the velocity fields. Our generalized multiphase SPH framework does not require separate equations for specific phases or tedious interface tracking. As the distribution, shape and motion of each phase is represented and resolved in the same way, the proposed approach is robust, efficient and easy to implement. Various simulation
results are presented to demonstrate the capabilities of our new multiphase SPH framework, including deformable bodies, granular materials, interaction between multiple fluids and deformable solids, flow in porous media, and dissolution of deformable solids.

An automatic time increment selection scheme for numerical analysis of long-term response of geomaterials is presented. The scheme is simple, rational and stable. Governed by a simple empirical expression, it can adaptively adjust the time increments depending on the strain rate-dependent temporal history of the material response. The proposed expression requires only a few parameters whose selection is a trivial task since they have a small effect on accuracy but have a significant effect on computational efficiency. This generalization has been made possible because of the enforcement of certain predefined control criteria to avoid extreme conditions. If any of the control criteria is satisfied, the computation is restarted by going a few time steps back to ensure the smoothness of the computed responses and time increments are again continuously adjusted through the governing equation provided. Performance of the automatic time increment selection scheme is investigated through finite element analyses of the long-term consolidation response of clay under different geotechnical profiles and loading conditions. Both elastic and elasto-viscoplastic constitutive relations are considered, including the consideration of the destructuration effects of geomaterials. Numerical results show that the performance of the automatic time increment selection scheme is reasonably excellent. While offering reasonable accuracy of the numerical solution, it can ensure temporal stability at optimal computational efficiency. In addition to the Euler implicit method, the automatic time increment selection scheme also performs well even when the explicit fourth-order Runge-Kutta method is employed for the integration of time derivatives. © 2010 Taylor & Francis.

http://www.tandfonline.com/doi/abs/10.1080/17486020903576226#.UruWKPuA_5M

This paper presents a new method for selecting parameter values in elasto-plastic models for unsaturated soils under isotropic stress states. The proposed method is an improvement over more traditional calibration approaches as it explicitly takes into account experimental yielding behaviour when defining the unsaturated normal compression surface. This is achieved by “enriching” measured yield stresses with corresponding values of specific volume (estimated from the observed elastic and virgin responses), which generates experimental points that can be interpolated together with virgin compression data. The proposed methodology is general and independent of the chosen mathematical forms of normal compression surface, elastic law and constitutive variables. The validity of the method is demonstrated by calibrating a reference model from a set of constant suction isotropic compression tests. Both improved and traditional calibration approaches are employed to select model parameter values which are then used to predict yield curves in the mean net stress–suction plane. Because of the incorporation of yielding data in the interpolation of the normal compression surface, the improved calibration method produces a more accurate prediction of yield stresses at different suctions compared with the standard method. Due to its generality and limited subjectivity, the proposed method provides an unbiased tool to compare strengths and weaknesses of different constitutive models.

Suction anchors are subjected to inclined, quasi-horizontal or quasi-vertical loadings. The type of the structure and depth of water govern the inclination of the load. Under this load condition, suction anchor experiences a combination of horizontal and vertical translations, and rotation. Therefore the soil's reaction to this load condition can be idealized as horizontal and vertical loadings, together with a moment. The magnitude and combination of the reactions depend on the load inclination, soil property and the point at which the load is applied. The behavior of the suction anchor subjected to the combined V-H-M loading is elaborated in this paper. This is to observe the effects of soil properties on the failure mechanism and ultimate capacity of the foundation. This was achieved by applying the pure horizontal and vertical displacements, and rotation and their combinations to the foundation, on V-H, V-M and H-M spaces and the yield-locus created for each space. The general purpose finite element program DIANA was used for this study. Non-linear analysis was conducted using a simplified elastic-perfectly-plastic model with Von-Mises yield criterion for saturated and consolidated clay. © 2009 Elsevier Ltd. All rights reserved.

http://www.sciencedirect.com/science/article/pii/S095183390900015X 
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An exact analytical elasto-plastic solution for thick-walled cylinder made of functionally graded materials (FGMs) subjected to combined pressure and thermal loading is presented in this paper. It is assumed that the cylinder is bonded at both ends, the material is radially graded and complies with the elastic perfectly plastic behavior. The relations in determining the plastic zone radius as well as the radial, circumferential, longitudinal and effective stresses in both elastic and plastic zones are obtained for any combined loading condition. Moreover, using ABAQUS/Explicit software, the functionally graded (FG) cylinder is simulated in every respect. Comparison of the present theoretical results with those from a finite element simulation illustrates the accuracy of the present analysis.

Seven teams took part in a benchmarking exercise on selection of parameter values for the Barcelona BasicModel (BBM) from experimental data on an unsaturated soil. All teams were provided with experimental results from tests performed on a compacted soil in order to determine values for the ten BBM soil constants and an initial value for the hardening parameter. The coordinating team then performed simulations (at stress point level) with the 7 different sets of parameter values, in order to explore the implications of the differences in parameter values and hence to investigate the robustness of existing BBM parameter value selection procedures. The major challenge was found to be selection of values for the constants λ(0), r, β, N(0) and pc and an initial value for the hardening parameter p0(0), with the various teams proposing significantly different values for some of these key parameters. A key lesson emerging from the exercise is the importance of choosing a method for selecting values for the parameters β and pc which places the main emphasis on attempting to optimise the match to the experimental spacing of normal compression lines at different values of suction.

The paper presents a soil water retention model that takes into account the effects of void ratio and hydraulic hysteresis on the variation of degree of saturation. Based on a modified form of van Genuchten equation, the model defines two bounding surfaces, i.e. a main drying surface and a main wetting surface, which delimit the region of admissible soil states in the space of degree of saturation, suction and void ratio. Suction and void ratio are then combined into a single auxiliary variable, named scaled suction, and the main surfaces are recast as main curves in the plane of degree of saturation and scaled suction. The effects of both suction and void ratio on the drying/wetting behaviour of the soil are simply incorporated by relating degree of saturation to scaled suction. The soil is dried when the scaled suction is increased and is wetted when the scaled suction is decreased. The model assumes that, inside the region of admissible soil states, the derivative of degree of saturation with respect to the scaled suction depends on the distance of the soil state from the main curves. This assumption ensures a smooth transition of the drying and wetting paths towards their respective main curves. Interestingly, the derivative of degree of saturation with respect to scaled suction can be integrated in a closed form and all wetting and drying paths can therefore be described by two explicit equations (one for drying paths and one for wetting paths), where different wetting or drying paths are characterized by different values of the integration constant. The integration of the model in a closed form facilitates its implementation into numerical codes. The model requires seven parameters, whose values can be obtained from a single drying-wetting test. Predictions are validated against two different data sets published in the literature, which shows the capability of the model to capture the behaviour observed during laboratory tests on fine grained soils.

This paper presents the finite element (FE) analysis of the consolidation of the foundation of an embankment constructed over soft clay deposit which shows significant time dependent behaviour and was improved with prefabricated vertical drains. To assess the capability of a simple elastic viscoplastic (EVP) model to predict the long term performance of a geotechnical structure constructed on soft soils, a well documented (Leneghans) embankment was analyzed to predict its long term behaviour characteristics. Two fully coupled two dimensional (2D) plane strain FE analyses have been carried out. In one of these, the foundation of the embankment was modelled with a relatively simpler time dependent EVP model and in the other one, for comparison purposes, the foundation soil was modelled with elasto-plastic Modified Cam-clay (MCC) model. Details of the analyses and the results are discussed in comparison with the field performance. Predictions from the creep (EVP) model were found to be better than those from Elasto-plastic (MCC) analysis. However, the creep analysis requires an additional parameter and additional computational time and resources. © 2011 Taylor & Francis.
http://www.tandfonline.com/doi/abs/10.1080/17486025.2011.578667#.Uruek_uA_5M

An exact analytical elasto-plastic solution for thick-walled cylinder made of functionally graded materials (FGMs) subjected to combined pressure and thermal loading is presented in this paper. It is assumed that the cylinder is bonded at both ends, the material is radially graded and complies with the elastic perfectly plastic behavior. The relations in determining the plastic zone radius as well as the radial, circumferential, longitudinal and effective stresses in both elastic and plastic zones are obtained for any combined loading condition. Moreover, using ABAQUS/Explicit software, the functionally graded (FG) cylinder is simulated in every respect. Comparison of the present theoretical results with those from a finite element simulation illustrates the accuracy of the present analysis.

This work investigates the effect of initial and induced fabric anisotropy on the mechanical behaviour of unsaturated compacted kaolin by performing a programme of suction controlled laboratory tests. A triaxial compaction technique is proposed to produce soil samples with different degrees of initial fabric anisotropy. The results from a first set of tests are interpreted to analyse yielding during stress path loading and behaviour at critical state. The results show different patterns of behaviour for the anisotropically compacted samples compared to the isotropically compacted ones.

The paper presents a physically-based constitutive model for unsaturated soils that considers the bonding effect of water menisci at inter-particle contacts. A bonding factor has been used to represent the magnitude of the equivalent bonding stress, defined as the bonding force per unit cross-sectional area. The average skeleton stress is employed to represent the effect of average fluid pressures within soil pores. Based on an empirical relationship between the bonding factor f and the ratio e/es (where e and es are void ratios at unsaturated and saturated states, respectively, at the same average skeleton stress), we propose an elasto-plastic constitutive model for isotropic stress states, and then extend this model to triaxial stress states within the framework of critical state soil mechanics. Because only one yield surface is needed in the proposed model, a relatively small number of parameters are required. Comparisons between experimental data and model results show that, in most cases, the proposed model can reasonably capture the important features of unsaturated soil behavior.

This paper deals with the particular integral formulation for two (2D) and three (3D) dimensional elastoplastic analyses. The elastostatic equation is used for the complementary solution. The particular integrals for displacement, stress and traction rates are derived by introducing the concept of global shape function to approximate an initial stress rate term of the inhomogeneous equation. The Newton-Raphson algorithm for the plastic multiplier is used to solve the system equation. The developed program is integrated with the pre- and post-processor.
The numerical results of the load-displacement response for six examples of application are compared with their analytical solutions and those by other BEM programs. The results of evolution of plastic region and deformed shape with increasing load are also given to demonstrate the validity and accuracy of the present formulation.

The phenomenon of excess pore water pressure increase or stagnation and continuing large ground deformation in soft sensitive clay following the completion of construction of embankment is simulated for a case study at Saint Alban, Quebec, Canada. The present model employs an updated Lagrangian finite element framework and is combined with an automatic time increment selection scheme. The simulation based on an elasto-viscoplastic constitutive model considers soil-structure degradation effect. It is shown that without consideration for the microstructural degradation effect, it is not possible to reproduce the field responses of soft sensitive clay even during the construction of the embankment. When the soil-structure degradation effect is considered, the present model can offer reasonably accurate prediction for the consolidation behavior of soft sensitive clay, including the so-called anomalous pore water pressure generation and continuing large deformation even after the end of construction, which has been posing numerous uncertainties on the long-term performance of earth structures. © 2013 John Wiley & Sons, Ltd.

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