Modelling the viscoplastic behaviour of Callovo-Oxfordian claystone with consideration of damage effect

In order to evaluate the performance of deep geological disposal of radioactive waste,an underground research laboratory(URL)was constructed by Andra in the Callovo-Oxfordian(COx)claystone formation at the Meuse/Haute-Marne(MHM).The construction of URL induced the excavation damage of host formations,and the ventilation in the galleries desaturated the host formation close to the gallery wall.Moreover,it is expected that the mechanical behaviour of COx claystone is time-dependent.This study presents a constitutive model developed to describe the viscoplastic behaviour of unsaturated and damaged COx claystone.In this model,the unsaturation effect is considered by adopting the Bishop effective stress and the van Genuchten(VG)water retention model.In terms of the viscoplastic behaviour,the nonstationary flow surface(NSFS)theory for unsaturated soils is used with consideration of the coupled effects of strain rate and suction on the yield stress.A progressive hardening law is adopted.Meanwhile,a non-associated flow rule is used,which is similar to that in Barcelona basic model(BBM).In addition,to describe the damage effect induced by suction change and viscoplastic loading,a damage function is defined based on the crack volume proportion.This damage function contains two variables:unsaturated effective stress and viscoplastic volumetric strain,with the related parameters determined based on the mercury intrusion porosimetry(MIP)tests.For the model validation,different tests on COx claystone under different loading paths are simulated.Comparisons between experimental and simulated results indicated that the present model is able to well describe the viscoplastic behaviour of damaged COx claystone,including swelling/shrinkage,triaxial extension and compression,and triaxial creep.

Viscoplastic solutions of time-dependent deformation for tunnels in swelling rock mass considering stress release

Excavation and control of tunneling responses in swelling soft-rock tunnels of Sichuan-Tibet railway under seepage conditions were studied.For this,a fractional viscoplastic(FVP)model for swelling soft rocks was established by introducing Abel dashpot and unsteady viscosity coefficient,considering additional swelling deformation and damage of rock caused by humidity effect.In view of the FVP model,the viscoplastic deformation solutions for rock mass surrounding tunnel under seepage conditions were derived and long-term mechanical responses of swelling rocks upon tunnel excavation were analyzed.Next,a stress release coefficient considering seepage and creep was proposed,based on which control responses considering stress release and failure mechanism of stress release measures were analyzed.The results showed that:(i)The one-dimensional(1D)FVP model has a good application for swelling rock and the three-dimensional(3D)FVP model could well describe the whole creep process of rock mass despite a much higher creep attenuation rate in the first stage of creep;and(ii)An appropriate stress release and deformation of surrounding rocks could effectively reduce the supporting resistance.However,upon a large stress release,the radius of plastic region could increase significantly,and the strength of the surrounding rock mass decreases greatly.The proposed solution could provide a theoretical framework for capturing the excavation and support responses for tunneling in swelling rock mass in consideration of time effect.

A STUDY OF B-P UNIFIED VISCOPLASTIC CONSTITUTIVE MODEL

By combining the Bodner-Partom constitutive model and equivalent stressfunction, finite element methods and program on analyzing non-elastic deformation and stress forthermal viscoplastic material are studied in this paper, and it's the first time that this materialmodel is used in a kind of engineering software-MARC. Thermal viscoplastic behavior of hightemperature alloy GH536 specimen with gap is analyzed by this program. The research results show itis feasible to analyze thermal viscoplastic behavior of specimen or structure by applying B-P model.

An elasto-plastic and viscoplastic damage constitutive model for dilatancy and fracturing behavior of soft rock squeezing deformation

Soft rock squeezing deformation mainly consists of pre-peak damage-dilatancy and post-peak fracture-bulking at the excavation unloading instant,and creep-dilatancy caused by time-dependent damage and fracturing.Based on the classic elastoplastic and Perzyna over-stress viscoplastic theories,as well as triaxial unloading confining pressure test and triaxial unloading creep test results,an elastoplastic and viscoplastic damage constitutive model is established for the short-and long-term dilatancy and fracturing behavior of soft rock squeezing deformation.Firstly,the criteria for each deformation and failure stage are expressed as a linear function of confining pressure.Secondly,the total damage evolution equation considering time-dependent damage is proposed,including the initial damage produced at the excavation instant,in which the damage variable increases exponentially with the lateral strain,and creep damage.Thirdly,a transient five-stages elasto-plastic constitutive equation for the short-term deformation after excavation that comprised of elasticity,pre-peak damage-dilatancy,post-peak brittle-drop,linear strain-softening,and residual perfectly-plastic regimes is developed based on incremental elasto-plastic theory and the nonassociated flow rule.Fourthly,regarding the timedependent properties of soft rock,based on the Perzyna viscoplastic over-stress theory,a viscoplastic damage model is set up to capture creep damage and dilatancy behavior.Viscoplastic strain is produced when the stress exceeds the initial static yield surface fs;the distance between the static yield surface fs and the dynamic yield surface fd determines the viscoplastic strain rate.Finally,the established constitutive model is numerically implemented and field applied to the-848 m belt conveyer haulage roadway of Huainan Panyidong Coal Mine.Laboratory test results and in-situ monitoring results validate the rationality of the established constitutive model.The presented model takes both the transient and time-dependent damage and fracturing into consideration.

Study on the Deformation Behavior of Mg-Gd-Y-Zn-Mn Wrought Magnesium Alloys by Visco-plastic Self-consistent Modeling

The plastic deformation behavior of new Mg-Gd-Y-Zn-Mn magnesium alloys gains great necessity to clarify and understand the mechanism deeply. In the present work,the tensile mechanical property test and visco-plastic self-consistent (VPSC) model are used to investigate the activities of deformation modes of VW84M and VW94M magnesium alloys during the tensile deformation. The results show that the mechanical properties of the above extruded alloys are similar but VW94M has higher strength than VW84M after the same aging process. Compared with the extruded alloys,the as-aged alloys have significantly higher activation of pyramidal slip at the later stage of plastic deformation. In addition,the as-aged VW94M alloy with higher strength has the largest activity of pyramidal slip. In summary,the addition of Gd increases the critical resolved shear stress (CRSS)in each slip system of VW94M,while the increase in the strength and the decrease in the elongation of as-aged alloys are associated with the significant activation of pyramidal slip.

CRACK PROPAGATION IN POLYCRYSTALLINE ELASTIC-VISCOPLASTIC MATERIALS USING COHESIVE ZONE MODELS

Cohesive zone model was used to simulate two-dimensional plane strain crack propagation at the grain level model including grain boundary zones. Simulated results show that the original crack-tip may not be separated firstly in an elastic-viscoplastic polycrystals. The grain interior＇s material properties （e.g. strain rate sensitivity） characterize the competitions between plastic and cohesive energy dissipation mechanisms. The higher the strain rate sensitivity is, the larger amount of the external work is transformed into plastic dissipation energy than into cohesive energy, which delays the cohesive zone rupturing. With the strain rate sensitivity decreased, the material property tends to approach the elastic-plastic responses. In this case, the plastic dissipation energy decreases and the cohesive dissipation energy increases which accelerates the cohesive zones debonding. Increasing the cohesive strength or the critical separation displacement will reduce the stress triaxiality at grain interiors and grain boundaries. Enhancing the cohesive zones ductility can improve the matrix materials resistance to void damage.

Modeling and Numerical Simulation of Yield Viscoplastic Fluid Flow in Concentric and Eccentric Annuli

Numerical solution of yield viscoplastic fluid flow is hindered by the singularity inherent to the Herschel-Bulkley model. A finite difference method over the boundary-fitted orthogonal coordinate system is util- ized to investigate numerically the fully developed steady flow of non-Newtonian yield viscoplastic fluid through concentric and eccentric annuli. The fluid rheology is described with the Herschel-Bulkley model. The numerical simulation based on a continuous viscoplastic approach to the Herschel-Bulkley model is found in poor accordance with the experimental data on volumetric flow rate of a bentonite suspension. A strict mathematical model for Herschel-Bulkley fluid flow is established and the corresponding numerical procedures are proposed. However, only the case of flow of a Herschel-Bulkley fluid in a concentric annulus is resolved based on the presumed flow stnicture by using the common optimization technique. Possible flow structures in an eccentric afinulus are presumed, and further challenges in numerical simulation of the Herschel-Bulkley fluid flow are suggested.

Self-Consistent Model for Pulsed Direct-Current N_2 Glow Discharge

A self-consistent analysis of a pulsed direct-current (DC) N2 glow discharge is presented. The model is based on a numerical solution of the continuity equations for electron and ions coupled with Poisson's equation. The spatial-temporal variations of ionic and electronic densities and electric field are obtained. The electric field structure exhibits all the characteristic regions of a typical glow discharge (the cathode fall, the negative glow, and the positive column). Current-voltage characteristics of the discharge can be obtained from the model. The calculated current-voltage results using a constant secondary electron emission coefficient for the gas pressure 133.32 Pa are in reasonable agreement with experiment.

A VISCOPLASTIC MODEL BASED ON NO-YIELD-SURFACE CONCEPT

The elasticjviscoplastic constitutive equation which describes deformation law of metal materials was suggested based on no-yield-surface concept and thermal activation theory of dislocation. The equation which takes account of effects of strain-rate, strain history, strain-rate history, hardening and temperature has stronger physical basis.Comparison of the theoretical prediction with experimental results of mechanical behaviours of Ti under conditions of uniaxial stress and room temperature shows good consistency.

A nonlinear creep model for surrounding rocks of tunnels based on kinetic energy theorem

The initiating condition for the accelerated creep of rocks has caused difficulty in analyzing the whole creep process.Moreover,the existing Nishihara model has evident shortcomings in describing the accelerated creep characteristics of the viscoplastic stage from the perspective of internal energy to analyze the mechanism of rock creep failure and determine the threshold of accelerated creep initiation.Based on the kinetic energy theorem,Perzyna viscoplastic theory,and the Nishihara model,a unified creep constitutive model that can describe the whole process of decaying creep,stable creep,and accelerated creep is established.Results reveal that the energy consumption and creep damage in the process of creep loading mainly come from the internal energy changes of geotechnical materials.The established creep model can not only describe the viscoelasticeplastic creep characteristics of rock,but also reflect the relationship between rock energy and creep deformation change.In addition,the research results provide a new method for determining the critical point of creep deformation and a new idea for studying the creep model and creep mechanical properties.

GH4169合金多轴热机械粘塑性本构模型及验证

为了更加精确地描述GH4169合金的多轴热机械力学行为,以Chaboche粘塑性本构模型为基础,引入了Lemaitre损伤模型、基于临界面理论的非比例强化因子和粘塑性势函数修正系数,提出建立了一种适用于GH4169合金的多轴热机械疲劳粘塑性本构模型,来描述材料的循环软化、非比例硬化和非玛辛效应,并给出了本构模型各参数的获取方法。采用此本构模型,对GH4169合金的多轴和热机械力学行为进行了模拟研究,结果表明:在20℃时,分别对轴向加载、扭转加载、比例加载、45°非比例加载以及90°非比例加载这5种加载条件下的第200次循环的迟滞回线进行模拟,轴向的应力峰谷值均与试验值结果吻合;在650℃时,模拟比例加载、45°非比例加载和90°非比例加载这3种加载条件下的第200次循环的迟滞回线,结果与试验值基本吻合,证明了建立的模型适用于高温条件;模拟300℃、550℃和650℃这3种温度下的单轴轴向加载和圆形路径加载的迟滞回线,结果与试验值基本吻合;模拟同相位与反相位加载条件下的第200次循环迟滞回线,修正后的本构模型的模拟值与试验值吻合良好。

基于触发式黏塑性元件的黏性土黏弹塑性动本构模型

基于黏性、弹性和塑性元件构造的动本构模型往往存在预测效果较差,不能完全反映黏性土的黏性、弹性、塑性的缺点。通过引入一种触发式的黏塑性元件Ψ,以残余变形为切入点,提出了一个考虑振动稳定和振动衰化现象的黏性土黏弹塑性动本构模型,并通过动三轴试验进行了验证。该动本构模型不但能够描述动荷载作用下黏性土残余应变的发展规律,且能合理地预测动应变的发展情况。结果表明,试样在动荷载作用下,存在元件Ψ的黏滞系数随振动周期增长而衰减的现象,且衰减情况和含水率密切相关。最优含水率是影响振动稳定和振动衰化现象的重要参数,当含水率小于最优含水率时,试样变形表现为振动稳定,此时元件Ψ黏滞系数的变化可以忽略不计;当含水率大于最优含水率时,试样变形表现为振动衰化,此时元件Ψ黏滞系数的变化不可忽略。

A UNIFIED ENERGY APPROACH TO A CLASS OF MICROMECHANICS MODELS FOR COMPOSITE MATERIALS

Several micromechanics models for the determination of composite moduli are investigated in this paper,including the dilute solution,self-consistent method,generalized self-consistent method,and Mori-Tanaka's method.These mi- cromechanical models have been developed by following quite different approaches and physical interpretations.It is shown that all the micromechanics models share a common ground,the generalized Budiansky's energy-equivalence framework.The dif- ference among the various models is shown to be the way in which the average strain of the inclusion phase is evaluated.As a bonus of this theoretical development,the asymmetry suffered in Mori-Tanaka's method can be circumvented and the applica- bility of the generalized self-consistent method can be extended to materials contain- ing microcracks,multiphase inclusions,non-spherical inclusions,or non-cylindrical inclusions.The relevance to the differential method,double-inclusion model,and Hashin-Shtrikman bounds is also discussed.The application of these micromechanics models to particulate-reinforced composites and microcracked solids is reviewed and some new results are presented.

Finite element modelling of the geodynamic processes of the Central Andes subduction zone:A Reference Model

This paper presents preliminary results of three-dimensional thermomechanical finite-element models of a parameter study to compute the current temperature and stress distribution in the subduction zone of the central Andes （16°S-26°S） up to a depth of 400 km, the bottom of the asthenosphere. For this purpose a simulation running over c. 50,000 years will be realized based on the geometry of a generic subduction zone and an elasto-viscoplastic Drucker-Prager rheology. The kinematic and thermal boundary conditions as well as the rheological parameters represent the current state of the study area. In future works the model will be refined using a systematic study of physical parameters in order to estimate the influence of the main parameters （e.g. viscosity, fault friction, velocity, shear heating） on the results of the reference model presented here. The reference model is kept as simple as possible to be able to estimate the influence of the parameters in future studies in the best possible way, whilst minimizing comnutational time.

Effective electroelastic constants for three-phase confocal elliptical cylinder model in piezoelectric quasicrystal composites

A three-phase confocal elliptical cylinder model is proposed to analyze micromechanics of one-dimensional hexagonal piezoelectric quasicrystal （PQC） compos- ites. Exact solutions of the phonon, phason, and electric fields are obtained by using the conformal mapping combined with the Laurent expansion technique when the model is subject to far-field anti-plane mechanical and in-plane electric loadings. The effective elec- troelastic constants of several different composites made up of PQC, quasicrystal （QC）, and piezoelectric （PE） materials are predicted by the generalized self-consistent method. Numerical examples are conducted to show the effects of the volume fraction and the cross-sectional shape of inclusion （or fiber） on the effective electroelastic constants of these composites. Compared with other micromechanical methods, the generalized self- consistent and Mori-Tanaka methods can predict the effective electroelastic constants of the composites consistently.

DISSIPATION-BASED CONSISTENT RATE-DEPENDENT MODEL FOR CONCRETE

An energy-dissipation based viscoplastic consistency model is presented to describe the performance of concrete under dynamic loading. The development of plasticity is started with the thermodynamic hypotheses in order that the model may have a sound theoretical background. Independent hardening and softening and the rate dependence of concrete are described separately for tension and compression. A modified implicit backward Euler integration scheme is adopted for the numerical computation. Static and dynamic behavior of the material is illustrated with certain numerical examples at material point level and structural level, and compared with existing experimental data. Results validate the effectiveness of the model.

Intelligent back analysis of geotechnical parameters for time-dependent rock mass surrounding mine openings using grey Verhulst model

In this paper,we present a new method of intelligent back analysis(IBA)using grey Verhulst model(GVM)to identify geotechnical parameters of rock mass surrounding tunnel,and validate it via a test for a main openings of−600 m level in Coal Mine“6.13”,Democratic People's Republic of Korea.The displacement components used for back analysis are the crown settlement and sidewalls convergence monitored at the end of the openings excavation,and the final closures predicted by GVM.The non-linear relation between displacements and back analysis parameters was obtained by artificial neural network(ANN)and Burger-creep viscoplastic(CVISC)model of FLAC3D.Then,the optimal parameters were determined for rock mass surrounding tunnel by genetic algorithm(GA)with both groups of measured displacements at the end of the final excavation and closures predicted by GVM.The maximum absolute error(MAE)and standard deviation(Std)between calculated displacements by numerical simulation with back analysis parameters and in situ ones were less than 6 and 2 mm,respectively.Therefore,it was found that the proposed method could be successfully applied to determining design parameters and stability for tunnels and underground cavities,as well as mine openings and stopes.

Collective Hamiltonian for Multi-O（4） Model

The collective Bamiltonian up to the fourth order for multi-O（4） model is derived based on the self-consistent collective-coordinate （SCC） method, which is formulated in the framework of the time-dependent Hartree-Bogoliubov （TDHB） theory. The validity of the collective Hamiltonian is checked in the two special cases of the multi-O（4） model： the case where the number of the shells is equal to one （a single j-shell case）, and the case where the Hartree-Bogoliubov equilibrium point is spherical （the spherical case）. The collective Hamiltonian constitutes a good starting point to study nuclear shape coexistence.

3-D consistency dynamic constitutive model of concrete

Based on the consistency-viscoplastic constitutive model,the static William-Warnke model with three-parameters is modified and a consistency-viscoplastic William-Warnke model with three-parameters is developed that considers the effect of strain rates. Then,the tangent modulus of the consistency viscoplastic model is introduced and an implicit backward Elure iterative algorithm is developed. Comparisons between the numerical simulations and experimental data show that the consistency model properly provides the uniaxial and biaxial dynamic behaviors of concrete. To study the effect of strain rates on the dynamic response of concrete structures,the proposed model is used in the analysis of the dynamic response of a simply-supported beam and the results show that the strain rate has a significant effect on the displacement and stress magnitudes and distributions. Finally,the seismic responses of a 278 m high arch dam are obtained and compared by using the linear elastic model,as well as rate-independent and rate-dependent William-Warnke three-parameter models. The results indicate that the strain rate affects the first principal stresses,and the maximal equivalent viscoplastic strain rate of the arch dam. Numerical calculations and analyses reveal that considering the strain rate is important in the safety assessments of arch dams located in seismically active areas.

Comparative Study on Constitutive Modeling of Tantalum and Tantalum Tungsten Alloy

As a model bee metal, tantalum and its alloys have wide applications in defense-related fields. The KHL （Khan, Huang, Liang, 1999） model and the constitutive model proposed by Nemat-Nasser et al （Nemat-Nasser and Kapoor, 2001） for tantalum and its alloys were analyzed and compared with each other. A set of published data recorded during elastic-plastic deformations of tantalum, tantalum alloy containing tungsten of 2.5% （Ta-2.5W）, over a wide range of strains, strain rates, and temperatures were used to correlate the two models. Overall, it can be concluded that KHL model correlates much better with the data than the model used by Nemat-Nasser et al.