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.

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.

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.

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.

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.

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.

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.

Shear viscosity of aluminum studied by shock compression considering elasto-plastic effects

The strength always exists before the material melts. In this paper, the viscoelastic-plastic model is applied to improve the finite difference method, and the numerical solutions for the disturbance amplitude damping behavior of the sinusoidal shock front in a flyer-impact experiment are obtained. When the aluminum is shocked to 101 GPa, the effect of elasto-plasticity on the zero-amplitude point of the oscillatory damping curve is the same as that of viscosity when η= 700 Pa.s, and the real shear viscosity coefficient of the shocked aluminum is determined to be about 2800±100 Pa.s. Comparing the experiment data with the numerical results of the viscoelastic-plastic model, we find that the aluminum is close to melting at 101 GPa.

Geotechnical particle finite element method for modeling of soilstructure interaction under large deformation conditions

The possibilities of the particle finite element method(PFEM)for modeling geotechnical problems are increasingly evident.PFEM is a numerical approach to solve large displacement and large strain continuum problems that are beyond the capabilities of classical finite element method(FEM).In PFEM,the computational domain is reconfigured for optimal solution by frequent remeshing and boundary updating.PFEM inherits many concepts,such as a Lagrangian description of continuum,from classic geomechanical FEM.This familiarity with more popular numerical methods facilitates learning and application.This work focuses on G-PFEM,a code specifically developed for the use of PFEM in geotechnical problems.The article has two purposes.The first is to give the reader an overview of the capabilities and main features of the current version of the G-PFEM and the second is to illustrate some of the newer developments of the code.G-PFEM can solve coupled hydro-mechanical static and dynamic problems involving the interaction of solid and/or deformable bodies.Realistic constitutive models for geomaterials are available,including features,such as structure and destructuration,which result in brittle response.The solutions are robust,solidly underpinned by numerical technology including mixedfield formulations,robust and mesh-independent integration of elastoplastic constitutive models and a rigorous and flexible treatment of contact interactions.The novel features presented in this work include the contact domain technique,a natural way to capture contact interactions and impose contact constraints between different continuum bodies,as well as a new simplified formulation for dynamic impact problems.The code performance is showcased by the simulation of several soil-structure interaction problems selected to highlight the novel code features:a rigid footing insertion in soft rock,pipeline insertion and subsequent lateral displacement on over-consolidated clay,screw-pile pull-out and the dynamic impact of a free-falling spherical penetrometer into clay.

3D contaminant migration model with consolidation dependent transport coefficients

Soil consolidation would induce variations of its transport coefficients such as hydraulic conductivity and diffusion coefficient. This paper presents a study of the influence of barrier consolidation on transport coefficients, and a 3D transport model based on mixture theory is proposed for describing the liners that involve circular defects in the geomembrane. The elastoplastic ALPHA model is revised by using the spatially mobilized plane （SMP） criterion for simulating the deformation of the soils. Then, the 3D model coupling the nonlinear consolidation and contaminant advection-diffusion is solved using the finite element software ABAQUS. The results show that the importance of reducing the defect size in the geomembrane and the liner porosity to control the contaminant concentration increase