Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method

In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved complex variable element-free Galerkin（ICVEFG） method is presented for two-dimensional（2D） elastoplasticity problems. Compared with the previous complex variable moving least-squares approximation, the new approximation has greater computational precision and efficiency. Using the penalty method to apply the essential boundary conditions, and using the constrained Galerkin weak form of 2D elastoplasticity to obtain the system equations, we obtain the corresponding formulae of the ICVEFG method for 2D elastoplasticity. Three selected numerical examples are presented using the ICVEFG method to show that the ICVEFG method has the advantages such as greater precision and computational efficiency over the conventional meshless methods.

Hybrid natural element method for large deformation elastoplasticity problems

We present the hybrid natural element method（HNEM） for two-dimensional elastoplastic large deformation problems. Sibson interpolation is adopted to construct the shape functions of nodal incremental displacements and incremental stresses. The incremental form of Hellinger–Reissner variational principle for elastoplastic large deformation problems is deduced to obtain the equation system. The total Lagrangian formulation is used to describe the discrete equation system.Compared with the natural element method（NEM）, the HNEM has higher computational precision and efficiency in solving elastoplastic large deformation problems. Some numerical examples are selected to demonstrate the advantage of the HNEM for large deformation elastoplasticity problems.

RATE VARIATIONAL EXTREMUM PRINCIPLES FOR FINITE ELASTOPLASTICITY

Dual variational extremum principles for rate problems of classical elastoplasticitv at finite deformation are studied in Updated Lagrangian rate forms. It is proved that the convexity of the variational functionals are closely related to a so-called gap function, which plavs an important role in nonlinear variational problems.

Isotropic Elastoplasticity Fully Coupled with Non-Local Damage

This paper presents a simple damage-gradient based elastoplastic model with non linear isotropic hardening in order to regularize the associated initial and boundary value problem (IBVP). Using the total energy equivalence hypothesis, fully coupled constitutive equations are used to describe the non local damage induced softening leading to a mesh independent solution. An additional partial differential equation governing the evolution of the non local isotropic damage is added to the classical equilibrium equations and associated weak forms derived. This leads to discretized IBVP governed by two algebric systems. The first one, associated with equilibrium equations, is highly non linear and can be solved by an iterative Newton Raphson method. The second one, related to the non local damage, is a linear algebric system and can be solved directly to compute the non local damage variable at each load increment. Two fields, linear interpolation triangular element with additional degree of freedom is terms of the non local damage variable is constructed. The non local damage variable is then transferred from mesh nodes to the quadrature (or Gauss) points to affect strongly the elastoplastic behavior. Two simple 2D examples are worked out in order to investigate the ability of proposed approach to deliver a mesh independent solution in the softening stage.

Modelling of the elastoplastic behaviour of the bio-cemented soils using an extended Modified Cam Clay model

An elastoplastic constitutive model based on the Modified Cam Clay(MCC)model is developed to describe the mechanical behaviour of soils cemented via microbially induced calcite precipitation(MICP).It considers the increase of the elastic stiffness,the change of the yield surface due to MICP cementation and the degradation of calcium carbonate bonds during shearing.Specifically,to capture the typical contraction-dilation transition in MICP soils,the original volumetric hardening rule in the MCC model is modified to a combined deviatoric and volumetric hardening rule.The model could reproduce a series of drained triaxial tests on MICP-treated soils with different calcium carbonate contents.Further,we carry out a parametric study and observe numerical instability in some cases.In combination with an analytical analysis,our numerical modelling has identified the benefits and limitations of using MCCbased models in the simulation of MICP-cemented soils,leading to suggestions for further model development.

Analysis of elastoplasticity and rheology due to mining subsidence

At present, as the easily mining resources are being increasingly depleted, the exploitation of coal under buildings, water-bodies and railways is imminent for the sustainable production. Probability in-tegral method is a general method for mining subsidence in the coal system. Because of poor under-standing of mining subsidence for other sections, the authors suggest probability integral method for the study of coal mining under buildings, water-bodies and railways. Moreover, the calculation result of probability integral method should be corrected by numerical simulation method. Based on practical projects, the impact has been evaluated on the security of Xifeihe left embankment under coal mining. Combining with the results of probability integral method, we propose that the 600 m far from em-bankment is a good rationality. This article provides the basis for the rational exploitation of coal re-source which is a major practical problem under the premise of Water Infrastructure Security. Fur-thermore, it also can be served as a reference for the similar projects, such as mining Xiaolangdi res-ervoir area, mining Yuecheng reservoir and mining the major channels of Middle Route South to North Water Transfer.

Finite Element Simulations on Failure Behaviors of Granular Materials with Microstructures Using a Micromechanics-Based Cosserat Elastoplastic Model

This paper presents a micromechanics-based Cosserat continuum model for microstructured granular materials.By utilizing this model,the macroscopic constitutive parameters of granular materials with different microstructures are expressed as sums of microstructural information.The microstructures under consideration can be classified into three categories:a medium-dense microstructure,a dense microstructure consisting of one-sized particles,and a dense microstructure consisting of two-sized particles.Subsequently,the Cosserat elastoplastic model,along with its finite element formulation,is derived using the extended Drucker-Prager yield criteria.To investigate failure behaviors,numerical simulations of granular materials with different microstructures are conducted using the ABAQUS User Element(UEL)interface.It demonstrates the capacity of the proposed model to simulate the phenomena of strain-softening and strain localization.The study investigates the influence of microscopic parameters,including contact stiffness parameters and characteristic length,on the failure behaviors of granularmaterials withmicrostructures.Additionally,the study examines themesh independence of the presented model and establishes its relationship with the characteristic length.A comparison is made between finite element simulations and discrete element simulations for a medium-dense microstructure,revealing a good agreement in results during the elastic stage.Somemacroscopic parameters describing plasticity are shown to be partially related to microscopic factors such as confining pressure and size of the representative volume element.

A new elastoplastic model for bolt-grouted fractured rock

Complexities in mechanical behaviours of rock masses mainly stem from inherent discontinuities,which calls for advanced bolt-grouting techniques for stability enhancement.Understanding the mechanical properties of bolt-grouted fractured rock mass(BGFR)and developing accurate prediction methods are crucial to optimize the BGFR support strategies.This paper establishes a new elastoplastic(E-P)model based on the orthotropic and the Mohr-Coulomb(M-C)plastic-yielding criteria.The elastic parameters of the model were derived through a meso-mechanical analysis of composite materials mechanics(CMM).Laboratory BGFR specimens were prepared and uniaxial compression test and variable-angle shear test considering different bolt arrangements were carried out to obtain the mechanical parameters of the specimens.Results showed that the anisotropy of BGFR mainly depends on the relative volume content of each component material in a certain direction.Moreover,the mechanical parameters deduced from the theory of composite materials which consider the short fibre effect are shown to be in good agreement with those determined by laboratory experiments,and the variation rules maintained good consistency.Last,a case study of a real tunnel project is provided to highlight the effectiveness,validity and robustness of the developed E-P model in prediction of stresses and deformations.

Unified description of different soils based on the superloading and subloading concepts

Geotechnical engineering often involves different types of geomaterials,such as sandy soil and clayey soil.Existing studies have confirmed that these soils have some common features,i.e.their mechanical behaviors depend not only on the inherent characteristics but also on their initial states.To describe the main mechanical behaviors of different soils within a simple and reasonable constitutive framework is of great significance for the numerical analysis on geotechnical engineering.This paper first introduces a model based on the concepts of superloading and subloading,which considers the“state dependence”(effects of overconsolidation and structure)of soil and only adds two material parameters compared with the Cam-Clay model.Secondly,conventional triaxial tests are systematically carried out on four types of soils(i.e.sand,silty clay,clay,and intermediate soil)with different initial void ratios,and the mechanical similarities and differences of these soils are discussed uniformly.After that,six material parameters of these soils are uniformly determined based on the concepts of superloading and subloading,and then used in constitutive calculations to verify the feasibility.The calculated results show a good agreement with test data,indicating that the model based on the concepts of superloading and subloading has great potential for describing the general mechanical behaviors of different soils within a unified framework.This work is expected to be applied to constitutive selection and parameter determination in the geotechnical numerical analysis of complex soil profiles.

FFT-Based Numerical Method for Nonlinear Elastic

In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic contact is typically simplifed to a linear elastic contact problem, which must be improved in terms of calculation accuracy. Based on the fast Fourier transform, a numerical method suitable for elastoplastic and hyperelastic frictionless contact that can be used for solving two-dimensional and three-dimensional (3D) contact problems is proposed herein. The nonlinear elastic contact problem is converted into a linear elastic contact problem considering residual deformation (or the equivalent residual deformation). Results from numerical simulations for elastic, elastoplastic, and hyperelastic contact between a hemisphere and a rigid plane are compared with those obtained using the fnite element method to verify the accuracy of the numerical method. Compared with the existing elastoplastic contact numerical methods, the proposed method achieves a higher calculation efciency while ensuring a certain calculation accuracy (i.e., the pressure error does not exceed 15%, whereas the calculation time does not exceed 10 min in a 64 × 64 grid). For hyperelastic contact, the proposed method reduces the dependence of the approximation result on the load, as in a linear elastic approximation. Finally, using the sealing application as an example, the contact and leakage rates between complicated 3D rough surfaces are calculated. Despite a certain error, the simplifed numerical method yields a better approximation result than the linear elastic contact approximation. Additionally, the result can be used as fast solutions in engineering applications.

Triaxial elastoplastic damage constitutive model of unreinforced clay brick masonry wall

Due to differences in the properties of composition materials and construction techniques,unreinforced masonry is characterized by low strength,anisotropy,nonuniformity,and low ductility.In order to accurately simulate the mechanical behavior of unreinforced brick masonry walls under static and dynamic loads,a new elastoplastic damage constitutive model was proposed and the corresponding subroutine was developed based on the concrete material constitutive model.In the proposed constitutive model,the Rankine strength theory and the Drucker-Prager strength theory were used to define the tensile and compressive yield surface function of materials,respectively.Moreover,the stress updating algorithm was modified to consider the tensile plastic permanent deformation of masonry materials.To verify the accuracy of the proposed constitutive model,numerical simulations of the brick masonry under monotonic and cyclic uniaxial tension and compression loads were carried out.Comparisons among the numerical and theoretical and experimental results show that the proposed model can properly reflect the masonry material mechanical properties.Furthermore,the numerical models of four pieces of masonry walls with different mortar strengths were established.Low cyclic loadings were applied and the results show that the proposed constitutive model can properly simulate the wall shear failure characteristics,and the force-displacement hysteretic curves obtained by numerical simulation are in good agreement with the tests.Overall,the proposed elastic-plastic damage constitutive model can simulate the nonlinear behavior of unreinforced brick masonry walls very well,and can be used to predict the structural response of masonry walls.

A novel elastoplastic model for Yunnan sandstone under poly-axial loading

The lack of understanding of plastic hardening(softening)laws,especially under anisotropic stress conditions,results in inappropriate geotechnical management.Most of the yielding envelopes do not consider the effect of intermediate principal stress and the influence of Lode's angle.In addition,the application of plastic flow rules regarding yielding surfaces compromises the softening of rock internal friction as well as the influence of Lode's angle on the plastic potential.Moreover,the ductility to brittleness transition in the intermediate principal stress direction still requires a theoretical foundation.In this study,based on poly-axial testing results of Yunnan sandstone,we adopted a failure criterion with the intermediate principal stress proposed by Menétrey and Willam.The proposed new failure envelope was applied to capture the plastic evolution of rock samples.A plastic hardening-softening model is constructed,based on the framework of the plastic theory.The softening envelope is modified to better present the stress drop and considers the deterioration of rock internal friction in the post-peak stage of poly-axial loading.The differential of plastic potential according to the principal stresses is also modified,considering the rotation of Lode's angle in the poly-axial loading tests.The model results were compared with laboratory testing results,which showed great consistency across 9 different loading tests(5 under triaxial stress and 4 under poly-axial stress with 22 stress-strain curves in total).The induced brittleness by the intermediate principal stress is also well captured by the proposed model.

Calibration of an elastoplastic model of sand liquefaction using the swarm intelligence with a multi-objective function

According to post-seismic observations,spectacular examples of engineering failures can be ascribed to the occurrence of sand liquefaction,where a sandy soil stratum could undergo a transient loss of shear strength and even behave as a“liquid”.Therefore,correct simulation of liquefaction response has become a challenging issue in geotechnical engineering field.In advanced elastoplastic models of sand liquefaction,certain fitting parameters have a remarkable effect on the computed results.However,the identification of these parameters,based on the experimental data,is usually intractable and sometimes follows a subjective trial-and-error procedure.For this,this paper presented a novel calibration methodology based on an optimization algorithm(particle swarm optimization(PSO))for an advanced elastoplastic constitutive model.A multi-objective function was designed to adjust the global quality for both monotonic and cyclic triaxial simulations.To overcome computational problem probably appearing in simulation of the cyclic triaxial test,two interrupt mechanisms were designed to prevent the particles from wasting time in searching the unreasonable space of candidate solutions.The Dafalias model has been used as an example to demonstrate the main programme.With the calibrated parameters for the HN31 sand,the computed results were highly consistent with the laboratory experiments(including monotonic triaxial tests under different confining pressures and cyclic triaxial tests in two loading modes).Finally,an extension example is given for Ottawa sand F65,suggesting that the proposed platform is versatile and can be easily customized to meet different practical needs.

Numerical Modeling of the Behaviour of a Road Structure on Compressible Soil: Case of the Road Section at the Beau-Rivage-Djassin Intersection

This document presents a study of the behaviour of a pavement structure on compressible soil and the evaluation of its durability. The objective of this study is to highlight the impact of taking into account the non-linear elastic behaviour of soils and granular materials in the design process. To this end, a numerical modelling of the pavement of the beau-rivage-Djassin crossroads section in Porto-Novo was carried out, based on a compressible soil whose behaviour will be considered elastoplastic. The subgrade soil on the section is made up of several sub-layers. The layer of soft, highly plastic clay was modelled according to a modified Cam Clay behaviour, a model of swelling clay soils. The fine sand layer and the granular layers of the structure are modelled according to Mohr-Coulomb behaviour. The loading is considered to be uniformly distributed according to the assumptions of the Burmister model in the French standard. A first verification with ALIZE allowed to validate the structure on the basis of the rutting deformation at the head of the platform εz = 359.6*10-6 which remains lower than the admissible deformation εz,adm = 360*10-6. The numerical calculation was carried out using the finite element method, the code of which is implemented under the PLAXIS v21 software. A comparative study with the results of the ALIZE design revealed that the numerically calculated strains εz = 585*10-6 are higher than those of ALIZE. These numerical strains, which are higher than the elastic strains, do not meet the validation criteria that the strains under loading must remain below the allowable strains. An evaluation of the pavement durability was carried out and it was found that the pavement would only last under traffic for 3 years before the first fatigue deformations appeared.

Stability analysis of a concrete gravity dam and its foundation

The stability of dams and their foundations is an important problem to which dam engineers have paid close attention over the years. This paper presented two methods to analyze the stability of a gravity dam and its foundation. The direct analysis method was based on a rigid limit equilibrium method which regarded both dam and the rock foundation as undeformable rigid bodies. In this method, the safety factor of potential sliding surfaces was computed directly. The second method, the indirect analysis method, was based on elasto-plastic theory and employs nonlinear finite element method (FEM) in the analysis of stresses and deformation in the dam and its foundation. The determination of the safety degree of the structure was based on the convergence and abrupt the change criterion. The results obtained showed that structures' constituent material behavior played an active role in the failure of engineered structures in addition to the imposed load.

Finite element simulation of elastoplastic fieldnear crack tips and results for a central crackedplate of le-lhp material under tension

The elastoplastic field near crack tips is investigated through finite element simulation.A refined mesh model near the crack tip is proposed. In the mesh refining area, element size continuously varies from the nanometer scale to themicrometer scale and the millimeter scale. Graphics of the plastic zone, the crack tip blunting, and the deformed crack tip elements are given in the paper.Based on the curves of stress and plastic strain, closely near the crack tip, the stresssingularity index and the stress intensity factor,as well as the plastic strain singularity index and the plastic strain intensity factor are determined.Thestress and plastic strainsingular index vary with the load, while the dimensions of the stress and the plastic strain intensity factorsdependon the stress and the plastic strain singularity index, respectively. The singular field near the elastoplastic crack tip is characterized by the stress singularity index and the stress intensity factor, or alternativelythe plastic strain singularity index and the plastic strain intensityfactor.At the end of the paper, following Irwin’s concept of fracture mechanics,σδKσδKcriterion andεδQεδQcriterion are proposed.Besides, crack tip angle criterion is also presented.

A practical constitutive theory based on egg-shaped function in elasto-plastic modeling for soft clay

An exploratory discussion is presented on the application of egg-shaped function in elasto-plastic constitutive analysis for soft clay.Two main tasks of the paper are:1)to propose a complete yield criterion based on egg-shaped function and supplement its definition in the deviatoric section,and then a yield criterion suitable for 3D stress conditions is obtained;2)to elaborate its numerical implementation based on the drained triaxial tests.During the above discussion,a non-associated flow rule is proposed,in which the stress-dilatancy relationship in most classical theory is replaced by a linear dependence between the stress state parameterηand the rotation angleγof the plastic potential surface.Thereafter,isotropic and kinematic hardening behavior is considered by employing the hardening parameter H,which can be expressed as the function of plastic work Wp.Finally,comparisons between numerical results and test data on Taizhou soft clay are made to verify the effectiveness of the proposed model.

T-Splines for Isogeometric Analysis of Two-Dimensional Nonlinear Problems

Nonlinear behaviors are commonplace in many complex engineering applications,e.g.,metal forming,vehicle crash test and so on.This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear problems including general large deformation hyperelastic problems and small deformation elastoplastic problems,to reveal the advantages of local refinement property of T-splines in describing nonlinear behavior of materials.By applying the adaptive refinement capability of T-splines during the iteration process of analysis,the numerical simulation accuracy of the nonlinear model could be increased dramatically.The Bézier extraction of the T-splines provides an element structure for isogeometric analysis that can be easily incorporated into existing nonlinear finite element codes.In addition,T-splines show great superiority of modeling complex geometries especially when the model is irregular and with hole features.Several numerical examples have been tested to validate the accuracy and convergence of the proposed method.The obtained results are compared with those from NURBS-based isogeometric analysis and commercial software ABAQUS.

Characteristics of Deformation and Strength of Concrete in Plane Strain State

The characteristics of deformation and strength of concrete under the plane strain condition are studied experimentally with the triaxial apparatus designed by the authors and are compared with those under the plane stress condition. A formula of stress transformation between plane stress and plane strain conditions is proposed for the elasto-plastic state, and it provides a theoretical basis for simplifying nonlinear analysis and fully using the strength of concrete.

Influence of formation in-situ stress on mechanical heterogeneity of shale through grid nanoindentation

Mechanical heterogeneity is a major characteristic of the organic-rich shale.The relation between mechanical heterogeneity and formation in-situ stress has been seldomly addressed but important to understand hydraulic fracture propagation,wellbore stability,and hydrocarbon flow.In this paper,the grid nanoindentation technique was used to characterize the heterogeneity of the mechanical properties of Longmaxi organic-rich shales from various burial depths and in-situ stress.The measured elastic modulus and hardness of each sample are deconvolved into three phases including soft phase,medium stiff phase and stiff phase according to mineral category.As the burial depth and corresponding in-situ stress increase,the overall elastic modulus and hardness of the sample enhance.Simultaneously,the percentage of soft minerals decreases,and the probability distribution tends to concentrate through 95%confidence interval evaluation which demonstrates weakened heterogeneity.Furthermore,SEM images provide evidence that extended cracking,initiated cracking,crushing and ductile deforming always occur around indentation imprints.This confirms that even under deep buried depth and high in-situ stress,brittle fracture and ductile deformation can exist synchronously.This paper demonstrates the influence of in-situ stress on the heterogeneity of shale micromechanics.