Coupled viscoplasticity damage constitutive model for concrete materials

A coupled viscoplasticity damage constitutive model for concrete materials is developed within the framework of irreversible thermodynamics. Simultaneously the Hehnholtz free energy function and a non-associated flow potential function are given, which include the internal variables of kinematic hardening, isotropic hardening and damage. Results from the numerical simulation show that the model presented can describe the deformatioa properties of the concrete without the formal hypotheses of yield criterion and failure criteria, such as the volume dilatancy under the compression, strain-rate sensitivity, stiffness degradation and stress-softening behavior beyond the peak stress which are brought by damages and fractures. Moreover, we could benefit from the application of the finite element method based oi1 this model under complex loading because of not having to choose different constitutive models based on the deformation level.

SYMMETRIC FORMULATION OF TANGENTIAL STIFFNESSES FOR NON-ASSOCIATED VISCOPLASTICITY WITH AN IMPLICIT TIME INTEGRATION SCHEME

A numerical scheme is presented which enables the use of symmetric equation solvers in tangential stiffness programs for non-associated viscoplastic materials.

THE PARAMETRIC VARIATIONAL PRINCIPLE FOR PERZYNA MODEL IN VISCOPLASTICITY

This paper presents the parametric variational principle for Perzyna model which is one of the main constitutive relations of viscoplasticity.The principle,by which the potential energy function is minimized under a constrained condition transformed by the constitutive relations of viscoplasticity, is free from the bound of Drucker's postulate of plastic flow and consequently suitable for solving the nonassociated plastic flow problems. Furthermore, the paper has proven the presented principle and discussed the creep problem.

A unified viscoplasticity constitutive model based on irreversible thermodynamics

A unified viscoplasticity constitutive model for metal materials is developed within the framework of irreversible thermodynamics, and an expression for the Helmholtz free energy function involving the parameters reflecting kinematic hardening and isotropic hardening is given. At the same time a non-associated flow potential function including the corresponding state variables is also given, from which the flow equation and the evolution equations of the internal state variables are derived. Thus, a general theoretical framework constructing a unified viscoplasticity constitutive model is given. Compared with the typical unified viscoplasticity constitutive models, the presented model evidently satisfies the irreversible thermodynamics laws. Moreover, this method not only provides a new theoretical foundation for further development of the unified viscoplasticity constitutive model, but also gives a new theoretical framework for the stress-strain analysis of more materials.

Development of a unified viscoplasticity constitutive model based on classical plasticity theory

The traditional unified viscoplasticity constitutive model can be only applied to metal materials.The study of the unified constitutive theory for metal materials has discovered the correlation between the classical plasticity theory and the unified viscoplasticity constitutive model,thus leading to the con-cepts of the classic plastic potential and yield surface in the unified constitutive model.Moreover,this research has given the continuous expression of the classical plastic multiplier and presented the corresponding constructive method,which extends its physical significance and lays down a good foundation for the application of the unified constitutive theory to the material analysis in more fields.This paper also introduces the unified constitutive model for metal materials and geo-materials.The numerical simulation indicates that the construction should be both reasonable and practical.

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.

Enhancing the elastoplastic damage constitutive model for clayey rocks: Incorporating anisotropy, saturation, time-dependent, and debonding effects

This paper introduced a novel microstructure-based constitutive model designed to comprehensively characterize the intricate mechanical behavior of anisotropic clay rocks under the influence of water saturation.The proposed model encompasses elastoplastic deformation,time-dependent behavior,and induced damage.A two-step homogenization process incorporates mineral compositions and porosity to determine the macroscopic elastic tensor and plastic yield criterion.The model also considers interfacial debonding between the matrix and inclusions to capture rock damage.The application of the proposed model is demonstrated through an analysis of Callovo-Oxfordian clayey rocks,specifically in the context of radioactive waste disposal in France.Model parameters are determined,followed by numerical simulations of various laboratory tests including lateral decompression tests with constant mean stress,triaxial compression tests under different water saturation conditions,and creep tests.The numerical results are compared with corresponding experimental data to assess the efficacy of the proposed model.

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.

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.

Limit analysis of viscoplastic thick-walled cylinder and spherical shell under internal pressure using a strain gradient plasticity theory

Plastic limit load of viscoplastic thick-walled cylinder and spherical shell subjected to internal pressure is investigated analytically using a strain gradient plasticity theory. As a result, the current solutions can capture the size effect at the micron scale. Numerical results show that the smaller the inner radius of the cylinder or spherical shell, the more significant the scale effects. Results also show that the size effect is more evident with increasing strain or strain-rate sensitivity index. The classical plastic-based solutions of the same problems are shown to be a special case of the present solution.

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.

VISCO-ELASTIC (PLASTIC) EFFECTS AND FAILURE BEHAVIOR OF PUR FOAMED PLASTICS

The viscous effects and failure behavior of PUR foamed plastics are investigated by the cycling loading and preloading experiments. On the basis of static and dynamic compressive experiments, the SEM analysis is given for the PUR foamed plastics specimens

Phenomenological behavior of rock salt:On the influence of laboratory conditions on the dilatancy onset

Recently,stress-based dilatancy criteria have become essential tools to design underground facilities in salt formations such as gas storage caverns.However,these criteria can depend critically on the volumetric strain measurements used to deduce the dilatancy onset.Results from conventional triaxial compression tests can show different volumetric behavior depending on the loading conditions,as well as on the measurement techniques.In order to obtain a quantitative understanding of this problem,an experimental program was carried out and the testing procedure was investigated numerically under homogeneous and heterogeneous stress states.The experimental results showed that the deviatoric stress corresponding to the dilatancy onset was significantly dependent on the measurement techniques.With a heterogeneous stress state,the simulation results revealed that the strain measurements at different scales (referred to as local,hybrid or global) can provide different volumetric results with moderate to significant deviations from the idealized behavior,and hence different onsets of dilatancy.They also proved that,under low confinement,tensile stresses can take place within the compressed specimen,leading to a great deviation of the dilatancy onset from the idealized behavior.From both experimental and numerical investigations,the difference in sensitivity to the measurement techniques between the deviatoric and the volumetric behaviors is explained by the relatively small values of the volumetric strain.The non-ideal laboratory conditions have more impact on this strain than on the deviatoric one.These findings can have implications for the interpretation of the dilatancy behavior of rock salt,and hence on the geomechanical design aspects in salt formations.

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.

Rheology elasticity determined by deformation of stretchable molecular trains

The average stretching direction,local rotation angular,and stretching ratio parameters of molecular trains were used to express the rheology deformation.Based on this micro geometrical deformation,the macro deformation of medium was expressed.Then,using intrinsic elasticity concept,the stress-strain relation was obtained.In this theoretic formulation,the response functions of extension ratio and rotation angular were used to express the rheology feature of medium.For medium composed by incompressible molecular trains,the local rotation angular divides rheology deformation into three kinds:viscoelastic deformation or elasticity enhancement,viscoplastic deformation or elasticity degenerate and constant elasticity range.These results explain the experimental features of rheology deformation well.

CYCLIC VISCOPLASTIC DESCRIPTION FOR THE MEAN STRAIN EFFECT

A viscoplastic constitutive model incorporating the cyclic deformation be-havior with mean strain is presented. In the model,a memory parameter q of strainamplitude is proposed,the evolution equations of back stresses are formulated,an ap-propriate defini

Impact Buckling and Post-Buckling of Elasto-Viscoplastic Cylindrical Shell Under Torsion

The dynamic torsional buckling and post-buckling of elasto-plastic circular cylindrical shell is studied. By the usage of the Bodner-Partom constitutive relation, the present visco-plastic problem is treated as an orthotropic elastic problem. Based on the nonlinear large deflection shell therory, the governing dynamic buckling equation is solved by the Runge-Kutta method, and the critical buckling stress is determined by the B-R criterion. The present paper is mainly focused on the imperfection sensitivity, the strain rate sensitivity, and the dynamic post-buckling characters for the shell loaded dynamically with a constant shear strain rate. Numerical results show that the critical shear stress and imperfection sensitivity will increase with the increase of strain rate. It is found that the elastic buckling stress is more sensitive to imperfection than the visco-plastic buckling. The present research also reveals some dynamic post-buckling characters for the cylindrical shell, and it is shown that the shell will vibrate with the amplitude proportional to the strain rate in elastic buckling but improportional to the strain rate in visco-plastic buckling. An interesting phenomenon is found that when the strain rate is sufficiently high, there is no dynamic visco-plastic buckling occurrence and the shell produces a harmonic oscillation with a very small amplitude.

Research on rheologic characteristics of soil based on endo-chronic theory

Rheologic characteristics of soil are very important in soil mechanics. Almost every aspect of research on soil mechanics deals with rheologic characteristics of soil. Although more than half century has passed, study on rheologic characteristics of soil only made a very small progress, which was due to the two facts: (1 ) the complexity of rheologic characteristics of soil; (2) the research methods based on experimental fOrmulas. Based on thermodynamic theory and endo-chronic theory, a new intrinsic constitutive equation for rheologic characteristic of soil was developed, which combined with two groups of internal state variables and their correlative intrinsic time. The new intrinsic constitutive equation did very well in predict essential features of the rheologic behavior of soil, with which the dilatancy of soil during the rheologic process could be described.

Viscoplastic Torsional Buckling of Cylindrical Shell

The Bodner-Partom constitutive equation is used to study the viscoplastic torsional buckling of perfect cylindrical shell. By treating the viscoplastic shell as an orthotropic shell at each moment and neglecting the inertia term, the critical torque is determined from a set of homogeneous linear equations. The strain rate sensitivity is mainly discussed in the present paper.

Modelling of temperature and strain rate dependent behaviour of pearlitic steel in block braked railway wheels

Block braked railway wheels are subjected to thermal and rolling contact loading.The thermal loading results in high temperatures and thermal stresses which cause slow time dependent processes such as creep,relaxation and static recovery of the wheel material.At the same time,the rolling contact loading implies a very fast mechanical load application.This paper is focused on material modeling of pearlitic steel for a wide range of loading rates at elevated temperatures.The starting point is a viscoplasticity model including nonlinear isotropic and kinematic hardening.The Delobelle overstress function is employed to capture strain rate dependent response of the material.The model also includes static recovery of the hardening to capture slower viscous(diffusion dominated)behaviour of the material.Experiments for the pearlitic wheel steel ER7 in terms of cyclic strain-controlled uniaxial tests with hold-time,uniaxial ratchetting tests including rapid cycles and biaxial cyclic tests with tension/compression and torsion are used to calibrate the material model.These experiments were performed under isothermal conditions at different temperatures.In the ratchetting tests,higher loading rates are obtained and these have been used to calibrate the high strain rate response of the viscoplasticity model.The paper is concluded with a numerical example of a block braked wheel where the importance of accounting for the viscoplasticity in modelling is highlighted.