SUPER-ELASTIC CONSTITUTIVE MODEL CONSIDERING PLASTICITY AND ITS FINITE ELEMENT IMPLEMENTATION

Based on the experimental results of super-elastic NiTi alloy, a three-dimensional super-elastic constitutive model including both of stress-induced martensite transformation and plasticity is constructed in a framework of general inelasticity. In the proposed model, transformation hardening, reverse transformation of stress-induced martensite, elastic mismatch between the austenite and martensite phases, and temperature-dependence of transformation stress and elastic modulus of each phase are considered. The plastic yielding of martensite occurred under high stress is addressed by a bilinear isotropic hardening rule. Drucker-Prager-typed transformation surfaces are employed to describe the asymmetric behavior of NiTi alloy in tension and compression. The prediction capability of the proposed model is verified by comparing the simulated results with the correspondent experimental ones. Based on backward Euler＇s integration, a new expression of consistent tangent modulus is derived. The proposed model is then implemented into a finite element package ABAQUS by user-subroutine UMAT. Finally, the validity of such implementation was verified by some numerical samples.

RECRYSTALLIZATION-INDUCED PLASTICITY IN 18Ni MARAGING STEEL UNDER ELASTIC STRESS

An approach to study the recrystallization-induced plasticity(RIP)phenomenon in the 18Ni maraging steel under the elastic stress has been made by the analysis of dynamic behaviour at elevated temperatures,the phenomenological analysis of dynamic strain feature curves,the confirmation of phase transformation point and TEM observation of RIP processing itself.

Flow stress model considering the transformation-induced plasticity effect and the inelastic strain recovery behavior

On the basis of continuum mechanics and the Mori-Tanaka mean field theory, a micro-mechanical flow stress model that considered both the transformation-induced plasticity （TRIP） effect and the inelastic strain recovery behavior of TRIP multiphase steels was presented. The relation between the volume fraction of constituent phases and plastic strain was introduced to characterize the transformation-induced plasticity effect of TRIP steels. Loading-unloading-reloading uniaxial tension tests of TRIP600 steel were carried out and the strain recovery behavior after unloading was analyzed. From the experimental data, an empirical elastic modulus expression is extracted to characterize the inelastic strain recovery. A comparison of the predicted flow stress with the experimental data shows a good agreement. The mechanism of the transformation-induced plasticity effect and the inelastic recovery effect acting on the flow stress is also discussed in detail.

On Elastic-plasticity Dynamic Analysis for Complicated Hiuh-rise Buildinus

介绍复杂高层建筑结构弹塑性动力分析方法，并结合工程实例，说明用工程常用软件PKPM、ANSYS对复杂高层建筑进行弹塑性动力分析的可行性和必要性。

Study on magneto-elastic-plastic deformation characteristics of ferromagnetic rectangular plate with simple supports

In this paper, the magnetic-elastic-plastic deformation behavior is studied for a ferromagnetic plate with simple supports. The perturbation formula of magnetic force is first derived based on the perturbation technique, and is then applied to the analysis of deformation characteristics with emphasis laid on the analyses of modes, symmetry of deformation and influences of incident angle of applied magnetic field on the plate deformation. The theoretical analyses offer explanations why the configuration offer- romagnetic rectangular plate with simple supports under an oblique magnetic field is in-wavy type along the x-direction, and why the largest deformation of the ferromagnetic plate occurs at the incident angle of 45°for the magnetic field. A numerical code based on the finite element method is developed to simulate quantitatively behaviors of the nonlinearly coupled multi-field problem. Some characteristic curves are plotted to illustrate the magneto--elastic-plastic deflections, and to reveal how the deflections can be influenced by the incident angle of applied magnetic field. The deformation characteristics obtained from the numerical simulations are found in good agreement with the theoretical analyses.

ELASTIC-PLASTIC FINITE ELEMENT ANALYSIS OF THREE-DIMENSIONAL CONTACT-IMPACT AT RAIL JOINT

Using the finite element code ANSYS/LS-DYNA, a dynamic finite element modelwith an elastic-linear-kinematic-hardening plastic material is established to analyzeelastic-plastic stresses in the railhead in the impact process of wheel and rail occurring at thegap of rail joint. The model is based on the discrete elastic support condition of the rails, whichis suitable for the actual situation of wheel/track rolling contact. In the analysis the influencesof axle load, yield stress and tangent modulus of rail material on the stresses and strains areinvestigated in detail. The distribution of stresses and strains in the jointed railhead are given.It is found that the axle load, yield stress and tangent modulus of rail material greatly affect thestresses and strains in the railhead during impacting. The study provides a reliable method anduseful datum for the further research on fatigue and wear of railhead and improving the rail jointmode.

GENERAL FORM OF MATCHING EQUATION OF ELASTIC-PLASTIC FIELD NEAR CRACK LINE FOR MODE I CRACK UNDER PLANE STRESS CONDITION

Crack line field analysis method has become an independent method for crack elastic-plastic analysis, which greatly simplifies the complexity of crack elastic-plastic problems and overcomes the corresponding mathematical difficulty. With this method, the precise elastic-plastic solutions near crack lines for variety of crack problems can be obtained. But up to now all solutions obtained by this method were for different concrete problems, no general steps and no general form of matching equations near crack line are given out. With crack line analysis method, this paper proposes the general steps of elastic plastic analysis near crack line for mode I crack in elastic-perfectly plastic solids under plane stress condition, and in turn given out the solving process and result for a specific problem.

Elastic-plastic contact force history and response characteristics of circular plate subjected to impact by a projectile

A new elastic-plastic impact-contact model is proposed in this paper. By adopting the principle of minimum acceleration for elastic-plastic continue at finite deformation, and with the aid of finite difference method, the proposed model is applied in the problem of dynamic response of a clamped thin circular plate subjected to a projectile impact centrally. The impact force history and response characteristics of the target plate is studied in detail. The theoretical predictions of the impact force and plate deflection are in good agreements with those of LDA experimental data. Linear expressions of the maximum impact force/transverse deflection versus impact velocity are given on the basis of the theoretical results.

CRACK INITIATION AND STEADY PROPAGATION OF ELASTIC-PLASTIC MATERIALS IN PLANE STRESS CONDITION

The crack tip stress-strain fields of the elastic-plastic cracked specimens have been analyzed using finite element calculations.The crack initiation and steady propagation behaviours have also been investigated by means of slip line pattern etching technique and mechanical tests. The results show that there are HRR near field and distant field in the crack tip region,and the later depends on the specimen configuration.The crack initiation behaviour is controlled by a single parameter J.In contrast,the steady crack propagation is affected by the distant strain field and can not be described by single parameter only.

Elastic-plastic analysis of antiplane crack near crack surface region

The elastic-plastic stress distribution and the elastic-plastic boundary con- figuration near a crack surface region are significant but hard to obtain by means of the conventional analysis. A crack line analysis method is developed in this paper by consid- ering the crack surface as an extension of the crack line. The stresses in the plastic zone, the length, and the unit normal vector of the elastic-plastic boundary near a crack surface region are obtained for an antiplane crack in an elastic-perfectly plastic solid. The usual small scale yielding assumptions are not needed in the analysis.

A NOVEL METHOD FOR MEASURING AND CHARACTERIZING DYNAMIC FRACTURE-INITIATION TOUGHNESS OF ELASTIC-PLASTIC MATERIALS

The characterization and testing methods of the dynamic fractureinitiation toughness of elas- tic-plastic materials under tensileimpact are studied. By using the self-designed bar-bar tensile impactappa- ratus, a novel test method for studying dynamicfracture-initiation ahs been proposed based on the one-di- mensionaltest principle. The curve of average load v. s. displacement (P-δ)is smooth until unstable crack propagation, and the kinetic energywhich does not contribute to the crack growth can be removed fromtotal work done by external-force to the specimen.

Harten-Lax-van Leer-contact(HLLC)approximation Riemann solver with elastic waves for one-dimensional elastic-plastic problems

A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver is built with elastic waves （HLLCE） for one-dimensional elastic-plastic flows with a hypo- elastic constitutive model and the von Mises＇ yielding criterion. Based on the HLLCE, a third-order cell-centered Lagrangian scheme is built for one-dimensional elastic-plastic problems. A number of numerical experiments are carried out. The numerical results show that the proposed third-order scheme achieves the desired order of accuracy. The third-order scheme is used to the numerical solution of the problems with elastic shock waves and elastic rarefaction waves. The numerical results are compared with a reference solution and the results obtained by other authors. The comparison shows that the pre- sented high-order scheme is convergent, stable, and essentially non-oscillatory. Moreover, the HLLCE is more efficient than the two-rarefaction Riemann solver with elastic waves （TRRSE）

A NEW APPROACH OF PREDICTING BIFURCATION POINTS OF ELASTIC-PLASTIC BUCKLING OF PLATES AND SHELLS

The paper proposes a new approach of predicting the bifurcation points of elastic-plastic buckling of plates and shells,which is obtained from the natural combination of the Lyaponov's dy- namic criterion on stability and the modified adaptive Dynamic Relaxation(maDR)method developed recently by the authors.This new method can overcome the difficulties in the applications of the dy- namic criterion.Numerical results show that the theoretically predicted bifurcation points are in very good agreement with the corresponding experimental ones.The paper also provides a new means for further research on the plastic buckling paradox of plates and shells.

The acoustoelastic effect on Rayleigh waves in elastic-plastic deformed layered rocks

On the basis of the acoustoelastic theory for elastic-plastic materials, the influence of statically deformed states including both the elastic and plastic deformations induced by applied uniaxial stresses on the Rayleigh wave in layered rocks is investigated by using a transfer matrix method. The acoustoelastic effects of elastic plastic strains in rocks caused by static deformations, are discussed in detail. The Rayleigh-type and Sezawa modes exhibit similar trends in acoustoelastic effect： the acoustoelastic effect increasing rapidly with the frequency-thickness product and the phase velocity change approaching a constant value for thick layer and high frequency limit. Elastic-plastic deformations in the Castlegate layered rock obviously modify the phase velocity of the Rayleigh wave and the cutoff points for the Sezawa modes. The investigation may be useful for seismic exploration, geotechnical engineering and ultrasonic detection.

Seismic elastic-plastic time history analysis and reliability study of quayside container crane

Quayside container crane is a kind of huge dimension steel structure,which is the major equipment used for handling container at modern ports.With the aim to validate the safety and reliability of the crane under seismic loads,besides conventional analysis,elastic-plastic time history analysis under rare seismic intensity is carried out.An ideal finite element（FEM） elastic-plastic mechanical model of the quayside container crane is presented by using ANSYS codes.Furthermore,according to elastic-plastic time history analysis theory,deformation,stress and damage pattern of the structure under rare seismic intensity are investigated.Based on the above analysis,the established reliability model according to the reliability theory,together with seismic reliability analysis based on Monte-Carlo simulation is applied to practical analysis.The results show that the overall structure of the quayside container crane is generally unstable under rare seismic intensity,and the structure needs to be reinforced.

ELASTIC-PLASTIC CONSTITUTIVE RELATION OF PARTICLE REINFORCED COMPOSITES

In this paper, a systematic approach is proposed to obtain the macroscopic elastic-plastic constitutive relation of particle reinforced composites (PRC). The strain energy density of PRC is analyzed based on the cell model, and the analytical formula for the macro-constitutive relation of PRC is obtained. The strength effects of volume fraction of the particle and the strain hardening exponent of matrix material on the macro-constitutive relation are investigated, the relation curve of strain versus stress of PRC is calculated in detail. The present results are consistent with the results given in the existing references.

Elastic-plastic solution to stamping thin strip on elastic foundation

An analytical method was proposed to solve the mechanical problems of stamping a thin strip on an elastic foundation. The thin strip was divided into four parts according to its deformation and contact with the punch and the elastic foundation, especially an elastic-plastic part was considered in the deflection of the thin strip. Analytical solutions were derived individually for each part and two models were established with the help of elastic and plastic large deflection theories. Compatibility conditions between the neighboring parts of the thin strip constructed the non-linear equation group. Solutions were carried out by programming with a software. The deformation shape, the membrane force, and the moment and shear force of the deformed thin strip were obtained. The results of the two models were compared. The study shows that the method is effective.

Interaction of underwater explosion bubble with complex elastic-plastic structure

Considering the elastic-plasticity of the structure, the combination of boundary element method and finite element method （FEM） is employed to present the calculation method for solving the complex coupled dynamic problem of bubble, elastic-plastic structure and the free surface, and the complete three-dimensional calculation program is developed as well. The error between the calculated result and the experimental result is within 10%. Taking a surface ship for example, the three-dimensional calculation program is extended to engineering filed. By employing the program, the response of the ship under the bubble loading is analyzed. From the stress-time history curves of typical elements of the structure, it can be seen that the pressure reaches its maximum when the bubble collapses and this validates that the pressure generated by the bubble collapse and the jet can cause serious damage on the ship structure. From the dynamic process of the interaction between the three-dimensional bubble and the ship, the low order vertical mode of the ship is provoked and the ship presents whip-shaped motion. And the ship does elevation and subsidence movement with the expansion and shrinkage of the bubble. Some rules and conclusions which can be applied to the engineering problems are obtained from the analysis in this paper.

On the yield functions in Lagrangian stress space of elastic-plastic materials with internal constraints

In the present paper it is shown that the elastic range in the second Piola-Kirchhoff stress space can be chosen in a hyperplane which is through the origin of Lagrangian stress space and perpendicular to the normal of the constraint manifold at the plastic configuration, if the determinate stress response of the elastic-plastic material with simple internal constraints with some condition is correctly chosen, otherwise, it is in general in a hypersurface and the normal flow rule by Ⅱ yushin＇s postulate will have an indeterminate part. The choice of deterrninate stress response is probable because of its indeterminacy. Therefore the yield function should be a function of the second Piola-Kirchhoff stress lying in the hyperplane so that it is more simple and the back stress as the geometric center of the elastic range in general is inside the elastic range. Finally some examples are concerned.

PATH-INDEPENDENT J-INTEGRAL AND ITS DUAL FORM IN ELASTIC-PLASTIC SOLIDS WITH FINITE DISPLACEMENTS

In this paper, based on energy variational principles of elastic-plastic solids, the path-independent J-integral and its dual form in elastic-plastic solids with finite displacements are presented. Whose testification is given there after.