An improved strain-softening constitutive model of granite considering the effect of crack deformation

This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results.The improved model assumes that total strain is a combination of plastic,elastic,and crack strains.The constitutive relationship between the crack strain and the stress was further derived.The evolutions of mechanical parameters,i.e.strength parameters,dilation angle,unloading elastic modulus,and deformation parameters of crack,with the plastic strain and confining pressure were studied.With the increase in plastic strain,the cohesion,friction angle,dilation angle,and crack Poisson's ratio initially increase and subsequently decrease,and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease.The increasing confining pressure enhances the strength and unloading elastic modulus,and decreases the dilation angle and Poisson's ratio of the crack.The theoretical triaxial compressive stress-strain curves were compared with the experimental results,and they present a good agreement with each other.The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.

A thermodynamics-based three-scale constitutive model for partially saturated granular materials

A three-scale constitutive model for unsaturated granular materials based on thermodynamic theory is presented.The three-scale yield locus,derived from the explicit yield criterion for solid matrix,is developed from a series of discrete interparticle contact planes.The three-scale yield locus is sensitive to porosity changes;therefore,it is reinterpreted as a corresponding constitutive model without phenomenological parameters.Furthermore,a water retention curve is proposed based on special pore morphology and experimental observations.The features of the partially saturated granular materials are well captured by the model.Under wetting and isotropic compression,volumetric compaction occurs,and the degree of saturation increases.Moreover,the higher the matric suction,the greater the strength,and the smaller the volumetric compaction.Compared with the phenomenological Barcelona basic model,the proposed three-scale constitutive model has fewer parameters;virtually all parameters have clear physical meanings.

A viscoelastic-plastic constitutive model with Mohr-Coulomb yielding criterion for sea ice dynamics

A new viscoelastic-plastic （VEP） constitutive model for sea ice dynamics was developed based on continuum mechanics. This model consists of four components： Kelvin-Vogit viscoelastic model, Mohr-Coulomb yielding criterion, associated normality flow rule for plastic rehololgy, and hydrostatic pressure. The numerical simulations for ice motion in an idealized rectangular basin were made using smoothed particle hydrodynamics （SPH） method, and compared with the analytical solution as well as those based on the modified viscous plastic（VP） model and static ice jam theory. These simulations show that the new VEP model can simulate ice dynamics accurately. The new constitutive model was further applied to simulate ice dynamics of the Bohai Sea and compared with the traditional VP, and modified VP models. The results of the VEP model are compared better with the satellite remote images, and the simulated ice conditions in the JZ20-2 oil platform area were more reasonable.

Review on cyclic plasticity of magnesium alloys:Experiments and constitutive models

Fatigue analysis has always been a concern in the design and assessment of Mg alloy structure components subjected to cyclic loading,and research on the cyclic plasticity is fundamental to investigate the corresponding fatigue failure.Thus,this work reviews the progress in the cyclic plasticity of Mg alloys.First,the existing macroscopic and microscopic experimental results of Mg alloys are summarized.Then,corresponding macroscopic phenomenological constitutive models and crystal plasticity-based models are reviewed.Finally,some conclusions and recommended topics on the cyclic plasticity of Mg alloys are provided to boost the further development and application of Mg alloys.

ON PLASTIC ANISOTROPY OF CONSTITUTIVE MODELFOR RATE-DEPENDENT SINGLE CRYSTAL

An algorithm for single crystals was developed and implemented to simulate plastic anisotropy using a rate-dependent slip model. The proposed procedure was a slightly modified form of single crystal constitutive model of Sarma and Zacharia. Modified Euler method, together with Newton-Raphson method was used to integrate this equation which was stable and efficient. The model together with the developed algorithm was used to study three problems. First, plastic anisotropy was examined by simulating the crystal deformation in tension and plane strain compression, respectively. Secondly, the orientation effect of some material parameters in the model and applied strain rate on plastic anisotropy for single crystal also is investigated. Thirdly, the influence of loading direction on the active slip system was discussed.

Strain localization of Mohr-Coulomb soils with non-associated plasticity based on micropolar continuum theory

To address the problems of strain localization, the exact Mohr-Coulomb (MC) model is used based on second-order cone programming (mpcFEM-SOCP) in the framework of micropolar continuum finite element method. Using the uniaxial compression test, we focused on the earth pressure problem of rigid wall segment involving non-associated plasticity. The numerical results reveal that when mpcFEM-SOCP is applied, the problems of mesh dependency can be effectively addressed. For geotechnical strain localization analysis involving non-associated MC plasticity, mpcFEM-SOCP in conjunction with the pseudo-time discrete scheme can improve the numerical stability and avoid the unreasonable softening issue in the pressure-displacement curves, which may be encountered in the conventional FEM. It also shows that the pressure-displacement responses calculated by mpcFEM-SOCP with the pseudo-time discrete scheme are higher than those calculated by mpcFEM-SOCP with the Davis scheme. The inclination angle of shear band predicted by mpcFEM-SOCP with the pseudo-time discrete scheme agrees well with the theoretical solution of non-associated MC plasticity.

Constitutive equation and processing map of equiatomic NiTi shape memory alloy under hot plastic deformation

In order to describe the deformation behavior and the hot workability of equiatomic NiTi shape memory alloy (SMA) during hot deformation, Arrhenius-type constitutive equation and hot processing map of the alloy were developed by hot compression tests at temperatures ranging from 500 to 1100 °C and strain rates ranging from 0.0005 to 0.5 s?1. The results show that the instability region of the hot processing map increases with the increase of deformation extent. The instability occurs in the low and high temperature regions. The instability region presents the adiabatic shear bands at low temperatures, but it exhibits the abnormal growth of the grains at high temperatures. Consequently, it is necessary to avoid processing the equiatomic NiTi SMA in these regions. It is preferable to process the NiTi SMA at the temperatures ranging from 750 to 900 °C.

INVESTIGATION ON GRADIENT-DEPENDENT NONLOCAL CONSTITUTIVE MODELS FOR ELASTO-PLASTICITY COUPLED WITH DAMAGE

Firstly, typical) gradient-dependent nonlocal inelastic models were briefly reviewed. Secondly, based on the principle of ‘gradient-dependent energy dissipation', a gradient-dependent constitutive model for plasticity coupled with isotropic damage was presented in the framework of continuum thermodynamics. Numerical scheme for calculation of Laplacian term of damage field with the numerical results obtained by FEM calculation was proposed. Equations have been presented on the basis of Taylor series for both 2-dimensional and 3-dimensional cases, respectively. Numerical results have indicated the validity of the proposed gradient-dependent model and corresponding numerical scheme.

Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.

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.

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.

INVESTIGATION ON ELASTO-PLASTIC CONSTITUTIVE MODEL COUPLED WITH DAMAGE FOR LOCALIZATION PHENOMENA

On the basis of existing plasticity-based damage model for plasticity coupled with damage for localization analysis, constitutive parameter identification was carried out through a series of numerical tests at local level.And then improvements were made on the expressions of the evolution laws of damage. Strain localization phenomena were simulated with a typical double-notched specimen under tensions. Numerical results indicate the validity of the proposed theory.

CONSTITUTIVE MODELLING OF NONPROPORTIONAL CYCLIC PLASTICITY

A multiplicative hardening function and a unified evolution rule of the hardening factors are proposed.The hardening factor f_1 is introduced to describe cyclic hardening with respect to the plastic strain range,while f_2 and f_3 describe,respectively,instantaneous and hereditary additional hardening with respect to the nonproportionality of the plastic strain path.Two material dependent memory parameters α_1 and α_3 are introduced to keep the memory of the largest cyclic and additional hardening in the previous plastic deformation history.Different hardening mechanisms are then embedded into a thermomechanically consistent constitutive equation through the hardening function.The constitutive response of 304 and 316 stainless steels subjected to biaxial nonproportional cyclic loading is analyzed and the proposed model is critically verified by comparing the results with experimental results obtained by Tanaka et al.,and Ohashi et al.

Rheological constitutive model of rock mass based on viscoplastic theory

With many major projects under construction,more and more attention is paid to rheological mechanical properties of rock mass,and extensive researches are carried out for rheological constitutive modeling of rock mass.Based on viscoplastic theory,a new rheological constitutive model is proposed.The rationality and validity of proposed model are verified through the creep test data.The results show that the rheological constitutive model based on viscoplastic theory is able to simulate the typical creep curves of rock mass and the identified parameters are reasonable.Therefore,the rheological constitutive model could be used to describe the rheological mechanical behaviour of rock mass.

Effect of hydrostatic stress on yield function and plastic constitutive relations

A new yield function taking effect of hydrostatic stress into account is presented through establishing and solving the functional equation satisfied by the yield function, and its characteristic is simple in form and strong in generality. In order to reveal its availability, a comparison is made between the results obtained with it and the experimental results of grey cast iron has be done, both seem to be in good agreement. At the same time, taking the yield function obtained here as a potential function, a new associative plastic constitutive equation taking effect of hydrostatic stress into account is built, and the plastic volume change ratio of plastic deformation is given.

A FRACTURE-ENERGY-BASED ELASTO-SOFTENING-PLASTIC CONSTITUTIVE MODEL FOR JOINTS OF GEOMATERIALS

On the basis of plasticity and fracture mechanics for quasi-brittle materials, this article presented a constitutive model for gradual softening behavior of joints of geomaterials. Corresponding numerical tests are carried out at the local level. Characteristics of the model proposed are 1) plastic softening and dilatancy behavior are directly related to the fracture process of joint, and much less material and model parameters are required compared with those proposed by references; 2) the process of decohesion coupled with frictional sliding at both micro-scale and macro-scale is described.

An elasto-plastic constitutive model of moderate sandy clay based on BC-RBFNN

Application research of neural networks to geotechnical engineering has become a hotspot nowadays.General model may not reach the predicting precision in practical application due to different characteristics in different fields.In allusion to this,an elasto-plastic constitutive model based on clustering radial basis function neural network(BC-RBFNN) was proposed for moderate sandy clay according to its properties.Firstly,knowledge base was established on triaxial compression testing data;then the model was trained,learned and emulated using knowledge base;finally,predicting results of the BC-RBFNN model were compared and analyzed with those of other intelligent model.The results show that the BC-RBFNN model can alter the training and learning velocity and improve the predicting precision,which provides possibility for engineering practice on demanding high precision.

A CONSTITUTIVE MODEL FOR CREEP-PLASTICITY INTERACTION BASED ON DISLOCATION DYNAMICS

A glide-plus-climb micromechanism of dislocation evolution with the formation of subgrains is pro- posed for modelling of the creep-plasticity interaction (CPI). The long-range internal stress can be divided into the resistance for dislocation climb in subgrain boundaries and that for dislocation glide within grains or subgrains. Their evolution equations are then derived based on dislocation dynamics. Furthermore, a unified constitutive model for CPI is developed from Orowan's formula. Theoretical calculations on the basis of this model show a very good agreement between the model prediction and experimental results of benchmark tests for 2 1/4 Cr -1 Mo steel at 600℃.

ELASTIC－PLASTIC CONSTITUTIVE MODELS BASED ON THE MULTIPLICATION PROCESSES OF DEFORMED GRAINS

According to the characteristics of micro-deformation of polycrystalline metal,the author divides grains intothree kinds and proposes a new conceplion of deformed grains.multiplication,from which some explicit elastic-Plastic constitutive equations can be deduced and some experimental results can be explained quantitativelv,It shows that the macro-yield,rate-correlativity work hardening and other phenomena are all closely related to the kinetic process of grains deformation.

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.