NONLINEAR AND ELASTO-PLASTICITY CONSOLIDATION MODELS OF UNSATURATED SOIL AND APPLICATIONS

The non-linear constitutive model suggested by the authors and the Alonso's elasto-plasticity model of unsaturated soil modified by the authors are introduced into the consolidation theory of unsaturated soil proposed by CHEN Zheng-han, and the non-linear and the elasto-plasticity consolidation models of unsaturated soil are obtained. Programs related to the two consolidation models are designed, and a 2-D consolidation problem of unsaturated sail is solved using the programs, the consolidation process and the development of plastic;one under multi-grade bad are studied. The above research develops the consolidation theory of unsaturated soil to a new level.

Measurement of length-scale and solution of cantilever beam in couple stress elasto-plasticity

Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ0 〈〈 H 〈〈 E, where σ0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.

ELASTO-PLASTICITY ANALYSIS BASED ON COLLOCATION WITH THE MOVING LEAST SQUARE METHOD

A meshless approach based on the moving least square method is developed for elasto-plasticity analysis,in which the incremental formulation is used.In this approach,the dis- placement shape functions are constructed by using the moving least square approximation,and the discrete governing equations for elasto-plastic material are constructed with the direct collo- cation method.The boundary conditions are also imposed by collocation.The method established is a truly meshless one,as it does not need any mesh,either for the purpose of interpolation of the solution variables,or for the purpose of construction of the discrete equations.It is simply formu- lated and very efficient,and no post-processing procedure is required to compute the derivatives of the unknown variables,since the solution from this method based on the moving least square approximation is already smooth enough.Numerical examples are given to verify the accuracy of the meshless method proposed for elasto-plasticity analysis.

INVERSE ASYMPTOTIC SOLUTION METHOD FOR FINITEDEFORMATION ELASTO-PLASTICITY

The development of modern mechanics in recent years has made many importantprogresse in the concepts and methods for nonlinear large deforntation mechanics([1],[2],[3]etc.). The presenl paper is aimed to show how the natural co-moving systemmethod and Stokes-Chen,s decomposition theorem can be effectively appliedasymptotically to solving problems of finite defomation elasto-plasticity by inverseasymptotic method for enyineering design purpose. Rigid punch problem is exanipfifiedin the paper.

The complex variable reproducing kernel particle method for elasto-plasticity problems

On the basis of reproducing kernel particle method(RKPM),using complex variable theory,the complex variable reproducing kernel particle method(CVRKPM) is discussed in this paper.The advantage of the CVRKPM is that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is formed.Then the CVRKPM is applied to solve two-dimensional elasto-plasticity problems.The Galerkin weak form is employed to obtain the discretized system equation,the penalty method is used to apply the essential boundary conditions.And then,the CVRKPM for two-dimensional elasto-plasticity problems is formed,the corresponding formulae are obtained,and the Newton-Raphson method is used in the numerical implementation.Three numerical examples are given to show that this method in this paper is effective for elasto-plasticity analysis.

DESIGN OPTIMIZATION FOR TRUSS STRUCTURES UNDER ELASTO-PLASTIC LOADING CONDITION

In this paper, a method for the design optimization of elasto-plastic truss structures is proposed based on parametric variational principles （PVPs）. The optimization aims to find the minimum weight/volume solution under the constraints of allowable node displacements. The design optimization is a formulation of mathematical programming with equilibrium constraints （MPECs）. To overcome the numerical difficulties of the complementary constraints in optimization, an iteration process, comprising a quadratic programming （QP） and an updating process, is employed as the optimization method. Furthermore, the elasto-plastic buckling of truss mem- bers is considered as a constraint in design optimization. A combinational optimization strategy is proposed for the displacement constraints and the buckling constraint, which comprises the method mentioned above and an optimal criterion. Three numerical examples are presented to show the validity of the methods proposed.

Elasto-plastic constitutive model of aluminum alloy foam subjected to impact loading

A multi-parameter nonlinear elasto-plastic constitutive model which can fully capture the three typical features of stress-strain response, linearity, plasticity-like stress plateau and densification phases was developed. The functional expression of each parameter was determined using uniaxial compression tests for aluminum alloy foams. The parameters of the model can be systematically varied to describe the effect of relative density which may be responsible for the changes in yield stress and hardening-like or softening-like behavior at various strain rates. A comparison between model predictions and experimental results of the aluminum alloy foams was provided to validate the model. It was proved to be useful in the selection of the optimal-density and energy absorption foam for a specific application at impact events.

TIME DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR DYNAMIC ANALYSES IN SATURATED PORO-ELASTO-PLASTIC MEDIUM

A time-discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium is proposed.As compared with the existing discontinuous Galerkin finite element methods,the distinct feature of the proposed method is that the continuity of the displacement vector at each discrete time instant is automatically ensured,whereas the discontinuity of the velocity vector at the discrete time levels still remains.The computational cost is then obviously reduced, particularly,for material non-linear problems.Both the implicit and explicit algorithms to solve the derived formulations for material non-linear problems are developed.Numerical results show a good performance of the present method in eliminating spurious numerical oscillations and providing with much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain.

EFFECTIVE NUMERICAL METHODS FOR ELASTO-PLASTIC CONTACT PROBLEMS WITH FRICTION

Several effective numerical methods for solving the elasto-plastic contact problems with friction are pres- ented.First,a direct substitution method is employed to impose the contact constraint conditions on condensed finite ele- ment equations,thus resulting in a reduction by half in the dimension of final governing equations.Second,an algorithm composed of contact condition probes and elasto-plastic iterations is utilized to solve the governing equation,which distinguishes two kinds of nonlinearities,and makes the solution unique.In addition,Positive-Negative Sequence Modifica- tion Method is used to condense the finite element equations of each substructure and an analytical integration is intro- duced to determine the elasto-plastic status after each time step or each iteration,hence the computational efficiency is en- hanced to a great extent.Finally,several test and practical examples are pressented showing the validity and versatility of these methods and algorithms.

Stability and reinforcement analysis of rock slope based on elasto-plastic finite element method

The rigid body limit equilibrium method(RBLEM) and finite element method(FEM) are two widely used approaches for rock slope's stability analysis currently. RBLEM introduced plethoric assumptions; while traditional FEM relied on artificial factors when determining factor of safety(FOS) and sliding surfaces. Based on the definition of structure instability that an elasto-plastic structure is not stable if it is unable to satisfy simultaneously equilibrium condition, kinematical admissibility and constitutive equations under given external loads, deformation reinforcement theory(DRT) is developed. With this theory, plastic complementary energy(PCE) can be used to evaluate the overall stability of rock slope, and the unbalanced force beyond the yield surface could be the identification of local failure. Compared with traditional slope stability analysis approaches, the PCE norm curve to strength reduced factor is introduced and the unbalanced force is applied to the determination of key sliding surfaces and required reinforcement. Typical and important issues in rock slope stability are tested in TFINE(a three-dimensional nonlinear finite element program), which is further applied to several representatives of high rock slope's stability evaluation and reinforcement engineering practice in southwest of China.

STATIONARY DISCONTINUITY AND FLUTTER INSTABILITY OF WAVE PROPAGATION IN ELASTO-PLASTIC SATURATED POROUS MEDIA

In the present work a model based on the Biot theory for simulating coupled hydrodynamic behavior mi saturated porous media is utilized with integration of the inertial coupling effect between the solid-fluid phases of the media into the model. The non-associated Drucker-Prager criterion to describe nonlinear constitutive behavior of pressure dependent elasto-plasticity for the media is particularly considered. With no consideration of compressibility of solid grains and the pore fluid, the discontinuity and instability of the wave propagation in saturated porous media axe analyzed for the plane strain problems in detail. The critical conditions of stationary discontinuity and flutter instability in the wave propagation are given. The results and conclusions obtained by the present work will provide some bases or clues for overcoming the difficulties in numerical modeling of wave propagation in the media subjected to dynamic loading.

A meshfree method and its applications to elasto-plastic problems

Standard finite element approaches are still ineffective in handling extreme material deformation, such as cases of large deformations and moving discontinuities due to severe mesh distortion. Among meshfree methods developed to overcome the ineffectiveness, Reproducing Kernel Particle Method (RKPM) has demonstrated its great suitability for structural analysis.This paper presents applications of RKPM in elasto-plastic problems after a review of meshfree methods and an introduction to RKPM. A slope stability problem in geotechnical engineering is analyzed as an illustrative case. The corresponding numerical simulations are carried out on an SGI Onyx3900 supercomputer. Comparison of the RKPM and the FEM under identical conditions showed that the RKPM is more suitable for problems where there exists extremely large strain such as in the case of slope sliding.

FINITE DEFORMATION ELASTO-PLASTIC THEORY AND CONSISTENT ALGORITHM

By using the logarithmic strain, the finite deformation plastic theory, corresponding to the infinitesimal plastic theory, is established successively. The plastic consistent algorithm with first order accuracy for the finite element method (FEM) is developed. Numerical examples are presented to illustrate the validity of the theory and effectiveness of the algorithm.

A CONDENSED METHOD FOR LINEAR COMPLEMENTARY EQUATIONS OF ELASTO-PLASTIC PROBLEMS

This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations.The present methodcuts down computing time enormously and greatly, promotes the efficiency of the elasto-plastic andlysis for large scale structures.

Modeling texture evolution during rolling process of AZ31 magnesium alloy with elasto-plastic self consistent model

To gain a better understanding about texture evolution during rolling process of AZ31 alloy, polycrystalline plasticity model was implemented into the explicit FE package, ABAQUS/Explicit by writing a user subroutine VUMAT. For each individual grain in the polycrystalline aggregate, the rate dependent model was adopted to calculate the plastic shear strain increment in combination with the Voce hardening law to describe the hardening response, the lattice reorientation caused by slip and twinning were calculated separately due to their different mechanisms. The elasto-plastic self consistent （EPSC） model was employed to relate the response of individual grain to the response of the polycrystalline aggregate. Rolling processes of AZ31 sheet and as-cast AZ31 alloy were simulated respectively. The predicted texture distributions are in aualitative a^reement with experimental results.

Dynamic Buckling of Elasto-Plastic Cylindrical Shells Under Axial Fluid-Solid Impact Load

The dynamic buckling of elasto-plastic cylindrical shells under axial fluid-solid impact is investigated theoretically. A simplified liquid- gas- structure model is given to approximately imitate the problem. The basic equation of the structure is derived from a minimum principle in dynamics of elasto-plastic continua at finite deformation, and the flow theory of plasticity is employed. The liquid is incompressible and the gas is compressed adiabatically. A number of numerical results are presented and the characteristics of the buckling behavior under fluid-solid impact are illustrated.

Elasto-plastic Analysis of Circular Tunnels in Jointed Rock Masses Satisfy the Hoek-Brown Failure Criterion

The relationship between the Hoek-Brown parameters and the mechanical response of circular tunnels is il-lustrated. Closed-form and approximate solutions are given for the extent of the plastic zone and the stress and dis-placement fields under axisymmetrical and asymmetric stress conditions. For the same rock masses and under axisym-metrical stress conditions,the radius of the plastic zone in terms of Hoek-Brown criterion is generally an approximation of the radius in terms of the Mohr-Coulomb criterion. The radius in terms of the Hoek-Brown criterion is larger under low stress conditions. For poor quality rock masses (GSI<25),measures (such as grouting,setting rock bolts,etc.) that improve the GSI of rock masses are effective in improving the stability of tunnels. It is not advisable to improve the sta-bility of the tunnels by providing a small support resistance p through shotcrete,except for very poor quality jointed rock masses. Without reference to the quality of the rock mass,the disturbance factor D should not less than 0.5. Meas-ures which disturb rock masses during tunnel construction should be taken carefully when the tunnel depth increases.

ELASTO-PLASTIC COUPLED ANALYSIS OF BURIED STRUCTURE AND SOIL MEDIUM BY PERTURBATIONAL SEMI-ANALYTIC METHOD

In this paper, an effective numerical method for physically nonlinear interaction analysis is studied, in which the elasto-plastic problem of coupled analysis between the structure and medium may be transformed into several linear problems by means of the perturbation technique, then, the finite strip method and finite layer method are used to analyze the underground structure and rock medium, respectively, for their corresponding linear problems, so the purpose of simplifying the calculation can be achieved. This kind of method has made use of the twice semi-analytical technique: the perturbation and semi-analytic solution function to simplify 3-D nonlinear coupled problem into 1-D linear numerical one. In addition, this method is a new advance of semi-analytical method in the application to nonlinear problems by means of combinating with the analytical perturbation method, and it is also a branch of the perturbational numerical method developed in last years.

Slope analysis based on local strength reduction method and variable-modulus elasto-plastic model

Employing an ideal elasto-plastic model,the typically used strength reduction method reduced the strength of all soil elements of a slope.Therefore,this method was called the global strength reduction method(GSRM).However,the deformation field obtained by GSRM could not reflect the real deformation of a slope when the slope became unstable.For most slopes,failure occurs once the strength of some regional soil is sufficiently weakened; thus,the local strength reduction method(LSRM)was proposed to analyze slope stability.In contrast with GSRM,LSRM only reduces the strength of local soil,while the strength of other soil remains unchanged.Therefore,deformation by LSRM is more reasonable than that by GSRM.In addition,the accuracy of the slope's deformation depends on the constitutive model to a large degree,and the variable-modulus elasto-plastic model was thus adopted.This constitutive model was an improvement of the Duncan–Chang model,which modified soil's deformation modulus according to stress level,and it thus better reflected the plastic feature of soil.Most importantly,the parameters of the variable-modulus elasto-plastic model could be determined through in-situ tests,and parameters determination by plate loading test and pressuremeter test were introduced.Therefore,it is easy to put this model into practice.Finally,LSRM and the variable-modulus elasto-plastic model were used to analyze Egongdai ancient landslide.Safety factor,deformation field,and optimal reinforcement measures for Egongdai ancient landslide were obtained based on the proposed method.

Elasto-plastic analysis of the surrounding rock mass in circular tunnel based on the generalized nonlinear unified strength theory

The present paper aims to establish a versatile strength theory suitable for elasto-plastic analysis of underground tunnel surrounding rock. In order to analyze the effects of intermediate principal stress and the rock properties on its deformation and failure of rock mass, the generalized nonlinear unified strength theory and elasto-plastic mechanics are used to deduce analytic solution of the radius and stress of tunnel plastic zone and the periphery displacement of tunnel under uniform ground stress field. The results show that: intermediate principal stress coefficient b has significant effect on the plastic range,the magnitude of stress and surrounding rock pressure. Then, the results are compared with the unified strength criterion solution and Mohr–Coulomb criterion solution, and concluded that the generalized nonlinear unified strength criterion is more applicable to elasto-plastic analysis of underground tunnel surrounding rock.