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.

A new thermo-elasto-plasticity constitutive theory for polycrystalline metals

In this study, the behavior of polycrystalline metals at different temperatures is investigated by a new thermo-elasto-plasticity constitutive theory. Based on solid mechanical and interatomic potential, the constitutive equa- tion is established using a new decomposition of the deformation gradient. For polycrystalline copper and magnesium, the stress-strain curves from 77 to 764 K （copper）, and 77 to 870 K （magnesium） under quasi-static uniaxial loading are calculated, and then the calculated results are compared with the experiment results. Also, it is determined that the present model has the capacity to describe the decrease of the elastic modulus and yield stress with the increasing temperature, as well as the change of hardening behaviors of the polycrystalline metals. The calculation process is simple and explicit, which makes it easy to implement into the applications.

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.

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 finite element analysis of squaring circular tube

The flow rule of Prandtl-Reuss was adopted and incremental elasto-plastic finite-element analysis formulation of Coulomb’s friction law combining the finite deformation theory was established, and Lagrangian formulation for simulating the squaring process of circular tube was updated. Incremental Coulomb’s friction law was used in the global stiffness matrix to solve the sliding-sticking state of friction at the boundary contact interface. During the squaring process, the linear factor rmin was adopted to solve the non-linear boundary problems of changing node contact and separation, elasto-plastic transient situation in an element and the non-linear constitutive behavior of material so as to make each reasonable increment of the punch meet the demand of calculation for linear increment. The squaring process of circular tube, load distribution and final shape of work piece after unloading were simulated by this mode and compared with research data. It is known that the circular tube with higher geometrical ratio (R/t) could be pressed into symmetric square tube without collapse. This result can provide reference for the analysis of this process and evaluation and improvement of product defects.

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.

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.

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.

Finite element analysis of elasto-plastic plate bending problems using transition rectangular plate elements

In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results.

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.

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.

A STUDY ON THE EFFECT OF RADIAL INERTIA ON THE ELASTO-PLASTIC COMBINED STRESS WAVE PROPAGATION IN THIN-WALLED TUBES

An in-depth analysis of propagation characteristics ofelasto-plastic combined stress waves in circular thin-walled tubeshas been made. In obtaining the simple-wave solution, however, mostresearches have ignored the influence of the circumferential stressrelated to the radial inertial ef- fect in the tubes. In this paperthe incremental elasto-plastic constitutive relations which areconve- nient for dynamic numerical analysis are adopted, and thefinite-difference method is used to study the evolution adpropagation of elasto-plastic combined stress waves in a thin-walledtube with the radial inertial effect of the tube considered. Thecalculation results are compared with those obtained when the radialinertial effect is not considered. The calculation results show thatthe radial inertial effect of a tube has a fairly great influence onthe propagation of elasto-plastic combined stress waves.

Elasto-plastic analysis of masonry with anisotropic plastic material model

This paper establishes an anisotropic plastic material model to analyze the elasto-plastic behavior of masonry in plane stress state.Being an anisotropic material,masonry has different constitutive relation and fracture energies along each orthotropic axes.Considering the unique material properties of masonry,a new yield criterion for masonry is proposed combining the Hill's yield criterion and the Rankine's yield criterion.The new yield criterion not only introduces compression friction coefficient of shear but also considers yield functions for independent stress state along two material axes of tension.To solve the involved nonlinear equations in numerical analysis,several nonlinear methods are implemented,including Newton-Raphson method for nonlinear equations and Implicit Euler backward mapping algorithm to update stresses.To verify the proposed material model of masonry,a series of tests are operated.The simulation results show that the new developed material model implements successfully.Compared with isotropic material model,the proposed model performs better in elasto-plastic analysis of masonry in plane stress state.The proposed anisotropic model is capable of simulating elasto-plastic behavior of masonry and can be used in related applications.

A new numerical method for determining collapse load-carrying capacity of structure made of elasto-plastic material

Determination of collapse load-carrying capacity of elasto-plastic material is very important in designing structure.The problem is commonly solved by elasto-plastic finite element method(FEM).In order to deal with material nonlinear problem involving strain softening problem effectively,a new numerical method-damped Newton method was proposed.The iterative schemes are discussed in detail for pure equilibrium models.In the equilibrium model,the plasticity criterion and the compatibility of the strains are verified,and the strain increment and plastic factor are treated as independent unknowns.To avoid the stiffness matrix being singularity or condition of matrix being ill,a damping factor α was introduced to adjust the value of plastic consistent parameter automatically during the iterations.According to the algorithm,the nonlinear finite element program was complied and its numerical example was calculated.The numerical results indicate that this method converges very fast for both small load steps and large load steps.Compared with those results obtained by analysis and experiment,the predicted ultimate bearing capacity from the proposed method is identical.

Elasto-plastic constitutive modeling for granular materials

Based on the modified plastic strain energy approach, an elasto-plastic constitutive modeling for sand was proposed. The hardening function between the modified plastic strain energy and a stress parameter was presented, which was independent of stress history and stress paths. The proposed model was related to an isotropically work-hardening and softening, non-associated and elasto-plastic material description. It is shown that the constitutive modeling, the inherent and stress system-induced cross-anisotropic elasticity is also considered. The constitutive model is capable of simulating the effects on the deformation characteristics of stress history and stress path, pressure level and anisotropic strength.

ANALYSIS ON THERMAL ELASTO-PLASTIC ASPERITY CONTACTS OF LAYERED MEDIA

A thermal elasto-plastic asperity contact model is investigated, which takes into account the steady-state heat transfer and the asperity distortion due to thermal elasto-plastic deformations. A hard coating and a soft coating are applied to study the correlations between contact area and contact pressure, average gap and contact pressure, coating thickness and contours of the contact stress distribution, etc. The effects of material properties, coating thickness, frictional coefficient, and the heat input combinations on the stress distribution are investigated and discussed. The frictional heat input increases the maximum value of yon Mises stress. Finally, the appropriate thickness of the hard coating is also discussed. To protect the substrate, one can choose hard coating and the thickness of that is suggested that can be hc=70 Rm.

An elasto-visco-plastic constitutive model of polypropylene incorporating craze damage behavior and its validation

An elasto-visco-plastic constitutive model incorporating the craze damage behavior was developed for the polypropylene(PP), by using the plastic failure model applied for the concrete, to capture the craze yielding and stress-whitening phenomena. In addition, the developed constitutive model was implemented into finite element codes in Abaqus to simulate the tensile deformation. The standard uniaxial tensile tests were carried out. The stress-strain curves from the uniaxial tensile tests show that the stress keeps decreasing after yielding and the yield stress rises with the increasing of the strain rate. It is worth noting that the craze damage is more visible with higher strain rate. The stress-whitening can be seen clearly around the fracture. The uniaxial tensile tests using specially designed specimen with circular holes weakening were performed for the validation of the developed model. The simulation results of the tensile deformation of the hole-weakened specimen suggest that the stress-whitening could be attributed to the equivalent visco-plastic strain. By comparing between the simulation analysis and the experimental results, the proposed model can describe the stress whitening phenomenon with good accuracy.