A DEM investigation on simple shear behavior of dense granular assemblies

A micromechanical investigation on simple shear behavior of dense granular assemblies was carried out by discrete element method.Three series of numerical tests were performed to examine the effects of initial porosity,vertical stress and particle shape on simple shear behavior of the samples,respectively.It was found that during simple shear the directions of principal stress and principal strain increment rotate differently with shear strain level.The non-coaxiality between the two directions decreases with strain level and may greatly affect the shear behavior of the assemblies,especially their peak friction angles.The numerical modelling also reveals that the rotation of the principal direction of fabric anisotropy lags behind that of the major principal stress direction during simple shear,which is described as fabric hyteresis effect.The degrees of fabric and interparticle contact force anisotropies increase as particle angularity increases,whereas the orientations of these anisotropies have not been significantly influenced by particle shape.An extended stress–dilatancy relationship based on ROWE-DAVIS framework was proposed to consider the non-coaxiality effect under principal stress rotation.The model was validated by present numerical results as well as some published physical test and numerical modelled data.

Anisotropic characteristics of granular materials under simple shear

The discrete element method was used to investigate the microscopic characteristics of granular materials under simple shear loading conditions. A series of simple tests on photo-elastic materials were used as a benchmark. With respect to the original experimental observations, average micro-variables such as the shear stress, shear strain and the volumetric dilatancy were extracted to illustrate the performance of the DEM simulation. The change of anisotropic density distributions of contact normals and contact forces was demonstrated during the course of simple shear. On the basis of microscopic characteristics, an analytical approach was further used to explore the macroscopic behaviors involving anisotropic shear strength and anisotropic stress-dilatancy. This results show that under simple shear loading, anisotropic shear strength arises primarily due to the difference between principal directions of the stress and the fabric. In addition, non-coaxiality, referring to the difference between principal directions of the strain rate and the stress, generates less stress-dilatancy. In particular, the anisotropic hardening and anisotropic stress-dilatancy will reduce to the isotropic hardening and the classical Taylor’s stress-dilatancy under proportional loading.

Simple shear extrusion versus equal channel angular pressing:A comparative study on the microstructure and mechanical properties of an Mg alloy

Two severe plastic deformation(SPD)techniques of simple shear extrusion(SSE)and equal channel angular pressing(ECAP)were employed to process an extruded Mg-6Gd-3Y-1.5Ag(wt%)alloy at 553 K for 1,2,4 and 6 passes.The microstructural evolutions were studied by electron back scattered diffraction(EBSD)analysis and transmission electron microscopy(TEM).The initial grain size of 7.5μm in the extruded alloy was reduced to about 1.3μm after 6 SPD passes.Discontinuous dynamic recrystallization was suggested to be operative in both SSE and ECAP,with also a potential contribution of continuous dynamic recrystallization at the early stages of deformation.The difference in the shear strain paths of the two SPD techniques caused different progression rate of dynamic recrystallization(DRX),so that the alloys processed by ECAP exhibited higher fractions of recrystallization and high angle grain boundaries(HAGBs).It was revealed that crystallographic texture was also significantly influenced by the difference in the strain paths of the two SPD methods,where dissimilar basal plane texture components were obtained.The compression tests,performed along extrusion direction(ED),indicated that the compressive yield stress(CYS)and ultimate compressive strength(UCS)of the alloys after both SEE and ECAP augmented continuously by increasing the number of passes.ECAP-processed alloys had lower values of CYS and UCS compared to their counterparts processed by SSE.This difference in the mechanical responses was attributed to the different configurations of basal planes with respect to the loading direction(ED)of each SPD technique.

Prediction of Buckling of Plain Knitted Fabric Sheets Subjected to Simple Shear in Wale Direction

Knitted fabric is very different from woven fabric due to its more complicated knitting structures. The buckling of knitted fabric sheets subjected to simple shear in the wale direction is investigated analytically in consideration of the large deformation of fabric sheet in critical configuration. The theory on instability of finite deformation is applied to the analysis. All the stress boundary conditions of knitted fabric sheet are satisfied. An equation to determine the buckling direction angle is derived. It is shown that there are two possible buckling modes, flexural mode and barreling mode. The buckling condition equations for the flexural mode and barreling mode are also obtained respectively. Numerical illustrations reveal that only the flexural mode can actually occur and the barreling mode cannot, which agrees with the experimental observations. For a permitted buckling mode on margin boundaries, the critical value of shear amount and the buckling direction angle can be determined.

ANALYSIS OF SIMPLE SHEAR ENDOCHRONIC EQUATIONSFOR FINITE PLASTIC DEFORMATION

Jaumann rate, generalized Jaumann rate,Fu rate and Wu rate were incorporated into endochronic equations for finite plastic deformation to analyze simple shear finite deformation. The results show that an oscillatory shear stress and normal stress response to a monotonically increasing shear strain occurs when Jaumann rate objective model is adopted for hypoelastic or endochronic materials. The oscillatory response is dependent on objective rate adopted,independent on elastoplastic models. Normal stress is unequal to zero during simple shear finite deformation.

Simple shear endochronic equations for finite plastic deformation

The endochronic equations proposed by Valanis (1980) were extended to a finite deformation range. Jaumanns rate, Fus rate and Wus rate were incorporated into the endochronic equations to analyze simple shear finite deformation. Incremental equations and numerical solutions are deduced for three endochronic objective models. The results show that an oscillatory shear stress response to a monotonically increasing shear strain occurs when the Jaumanns rate objective model is employed for endochronic materials. The oscillatory response is dependent on the adopted objective rate. Compared with the Jaumanns rate, the Fus rate and the Wus rate satisfy the restrictions to elastic-plastic constitutive relations and are in agreement with the experimental results.

Technical Development of Simple Shear Deformation Experiments Using a Deformation-DIA Apparatus

Technical developments for simple shear deformation experiments at high pressures were made. The newly designed cell assembly can be compressed by deformation-DIA apparatuses with the MA 6-6 system, which consists of six second-stage tungsten carbide anvils （with a truncated edge length of 5 mm） and the anvil guide. Deformation of samples was barely observed during the compression process, showing that the shear strain of the deformed samples can be measured by the rotation of a strain marker. Simple shear deformation experiments on anhydrous and hydrous oli- vine aggregates were conducted under upper mantle conditions （pressures of 5.2-7.6 GPa and temperatures of 1 473-1 573 K）, and sample deformation with a shear strain of 7=0.8-1.2 was successfully achieved at a shear strain rate of 4.0×10^-5-7.5×10^-5 s^-1. The present study extended the pressure range of simple shear deformation experiments in the deformation-DIA apparatus from 3 GPa in an early study to 7.6 GPa at high temperatures.

Macro- and micromechanical evaluation of cyclic simple shear test by discrete element method

Direct simple shear tests are considered to be simple laboratory tests that are capable of imposing a cyclic loading that is analogous to that induced by earthquakes. A realistic evaluation of the test results demands a profound micromechanical investigation of specimens. Three-dimensional discrete element method models of a stacked-ring simple shear test were constructed, in which monotonic and cyclic loadings were applied under constant-volume conditions, and good agreement between the monotonic and cyclic macromechanical behaviors was noted. Micromechanical properties of specimens that were subjected to a cyclic loading are discussed in terms of lateral and intermediate principal stress development, fabric anisotropy, and principal stress rotation. The stress and strain states inside the specimen were investigated and it was shown that despite the uniform stress distribution inside the specimen, the volumetric strain distributes non-uniformly during loading and the non-uniformity grows with cycling, which leads to localized zones of dilative and contractive behavior.

Velocity profiles and energy fluctuations in simple shear granular flows

Rheology analysis of granular flows is important for predicting geophysical hazards and designing industrial processes. Using a discrete element method, we simulate simple shear flows in 3D under a constant confining pressure of 10 kPa. The inertial number proposed by the GDR MiDi group in France is adopted to distinguish rheology regimes, Both translational and angular velocity profiles are investigated, and both fluid-like and solid-like behavior modes are observed in the flows. The maximum angular velocity occurs near the localized deformation area. We also investigate the energy characteristics of the flows and find that at very small shearing speed, the mean kinetic energy density ek is close to zero, while the mean elastic energy density ec is much greater. At large shearing speed, ek increases. The fluctuating parts of the two types of energy increase with increasing shear speed. Thus, the mean energy density ratio ek/ec can be used in addition to the inertial number to distinguish flow regimes. These results provide insights from energetics into the rheological properties of granular flows.

Assessment of liquefaction potential based on shear wave velocity:Strain energy approach

Liquefaction assessment based on strain energy is significantly superior to conventional stress-based methods.The main purpose of the present study is to investigate the correlation between shear wave velocity and strain energy capacity of silty sands.The dissipated energy until liquefaction occurs was calculated by analyzing the results of three series of comprehensive cyclic direct simple shear and triaxial tests on Ottawa F65,Nevada,and Firoozkuh sands with varying silt content by weight and relative densities.Additionally,the shear wave velocity of each series was obtained using bender element or resonant column tests.Consequently,for the first time,a liquefaction triggering criterion,relating to effective overburden normalized liquefaction capacity energy(WL=s’c)to effective overburden stresscorrected shear wave velocity(eVs1)has been introduced.The accuracy of the proposed criteria was evaluated using in situ data.The results confirm the ability of shear wave velocity as a distinguishing parameter for separating liquefied and non-liquefied soils when it is calculated against liquefaction capacity energy(WL=s’c).However,the proposed WL=s’c-Vs1 curve,similar to previously proposed cyclic resistance ratio(CRR)-Vs1 relationships,should be used conservatively for fields vulnerable to liquefaction-induced lateral spreading.

Geometry and kinematics of brittle deformation in the Central Cameroon Shear Zone (Kékem area): Implication for gold exploration within the Central Africa Fold Belt in Cameroon

The Central Africa Fold Belt(CAFB)is a collision belt endowed with gold deposits in Eastern Cameroon area mined for about 50 years.However,favorable areas for gold exploration are poorly known.This paper presents(1)the kinematics of the brittle deformation in the Kékem area in the SW portion of the Central Cameroon Shear Zone and(2)constraints gold mineralization events with respect to the collisional evolution of the CAFB.The authors interpret that the conjugate ENE to E and NNW to NW trending lineament corresponds to the synthetic(R)and the antithetic(R’)shears,which accompanied the dextral slip along the NE to ENE striking shear.The latter coincides with the last 570-552 Ma D3 dextral simple shear-dominated transpression,which is parallel to the BétaréOya shear zone hosting gold deposits.Gold mineralizations,which mainly occurred during the last dextral shearing,are disseminated within quartz veins associated to Riedel’s previous structures reactivated due to late collisional activities of the CAFB as brittle deformation.Gold mineralizations occurred mainly during the 570-552 Ma D3 event.The reactivation,which might be due to dextral simple shear during mylonitzation,plausibly remobilized the early gold deposits hosted in syn-compressional rocks and/or possibly focused deep-sourced fluid mixed with those released by dehydration.Therefore,the Central Cameroon Shear Zone where Kékem is located,and which shows similar petrographical and structural features to those controling Batouri gold district,is a target area for gold exploration in Cameroon.

Influence of strain rate on grain refinement and texture evolution under complex shear stress conditions

The effects of different complex shear stress conditions on grain refinement and texture evolution of Mg-13Gd-4Y-2Zn-0.5Zr alloy were investigated.With increasing strain rate,the average grain size of compression-shear(CS)and compression-torsion(CT)samples are decreased,and the grain size of dynamic recrystallization(DRX)grains is also decreased.This is because that the precipitation number ofβphases is increased,and the hindering effect on grain growth can be significantly enhanced.The DRX fractions of CS and CT samples are decreased with increased strain rate.The low DRX fraction at high strain rate is related to the insufficient time for grains to nucleate.The DRX process can be promoted by the PSN mechanism of second phases,and the grain growth can be restricted by the pinning effect.At the same time,the texture strength is enhanced as the strain rate increased.Besides,the kinking degree of lamellar long-period stacking ordered(LPSO)phases is increased.Under complex shear stress conditions,non-basal slip,especially pyramidal slip,is easily activated and the texture is deflected greatly.Compared with the CS samples,CT samples have smaller average grain size,higher DRX fraction,and lower texture strength for a certain strain rate.This is because that the equivalent stress of the CT sample is larger,the stress triaxiality is smaller,so more serious dislocations are piled up near grain boundaries and second phases.At the same time,since CT sample was sheared with torsion,the dislocation movement path can be called“rotational dislocation accumulation”,and the longer distribution path of the CT sample is generated,so more sub-grains and low-angle grain boundaries(LAGBs)are formed.Compared with the CS sample,more huge-angle grain boundaries(HAGBs)and DRX grains are formed from grain boundary to grain interior,so better grain refinement effect is achieved.

MECHANICAL BEHAVIOR OF AMORPHOUS POLYMERS IN SHEAR

Based on the non-equilibrium thermodynamic theory, a new thermo-viscoelastic constitutive model for an incompressible material is proposed. This model can be considered as a kind of generalization of the non-Gaussian network theory in rubber elasticity to include the viscous and the thermal effects. A set of second rank tensorial internal variables was introduced, and in order to adequately describe the evolution of these internal variables, a new expression of the Helmholtz free energy was suggested. The mechanical behavior of the thermo-viscoelastic material under simple shear deformation was studied, and the “viscous dissipation induced” anisotropy due to the change of orientation distribution of molecular chains was examined. Influences of strain rate and thermal softening produced by the viscous dissipation on the shear stress were also discussed. Finally, the model predictions were compared with the experimental results performed by G'Sell et al., thus the validity of the proposed model is verified.

Design and verification of portable direct shear tester with application to remolded colluvium geomaterials

The mechanical properties of colluvium strongly govern the stability of colluvial slopes, and they arc essential for the related analysis and design. Nevertheless, their measurement is not easy on account of heterogeneity in property and difficulty of sampling. This study attempted to evaluate the shear strength of remolded colluvium by means of a simple direct shear test in the field. A portable direct shear tester was designed to overcome the inconvenience and expensiveness of the conventional large-scale in-situ direct shear test. It can be easily assembled and applied for the silnplc field direct shear test. For calibration, the results of the portable direct shear tester were compared with the results of the laboratory direct shear tester for four different types of soil samples, i.e. standard sand, slate debris, arenaceous shale debris and mixture of gravel and sand. Correlation formulas were established based on the calibration, enabling the portable direct shear tester to measure and estimate the shear strength of remoldcd colluvium in field. This study primarily focuses on the colluvium in Central Taiwan, including the lateritic Dadu Terrace and the arcnaceous shale of Taiping-Wufcng mounts. The portable direct shear tester was applied to sites selected in these areas, and the results were furthcr analyzed and discussed.

A new semi-empirical spectrum model for complex steady shear viscosity of complex fluids

A semi-empirical spectrum model is proposed to describe the experimental data of the steady shear properties of a Shengli waxy crude oil near its gel point, where sophisticated structural effects become apparent due to the existence of waxy crystals in the crude oil. The model, consisting of a time spectrum, can well fit the steady shear viscosities of the waxy crude oil over the whole experimental shear rate region from 10-4 to 102 s- 1. Two other experiments on complex fluids reported recently in the literature are also well described by this model demonstrating the applicability and accuracy of the model.

The Early Mesozoic NE-SW Extensional Model and Exhumation Processes at the Southeastern Margin of the Central Asian Orogenic Belt:Insights from the Strain and Kinematic Vorticity Analysis of the Sonid Zuoqi Ductile Detachment Zone

The Sonid Zuoqi ductile detachment zone is located at the southeastern margin of the Central Asian orogenic belt(CAOB),striking EW and dipping to the S.The major rock type of the Sonid Zuoqi ductile detachment zone is mylonite derived from granite.The sequence of mylonite features is:(1)S and C foliations of mylonite,and(2)extensional crenulation cleavage(ecc)or C′and the kinematic vorticity(Wk)value changed from 0.70 to 0.95 and from 0.37 to 0.69,respectively;the strain type of the mylonites within the Sonid Zuoqi ductile detachment zone is compressional to planar strain.The strong deformation mylonite and Halatu plutons yielded a zircon U-Pb age of 244 Ma and a zircon(U-Th)/He age of 214 Ma,respectively.Based on the strain and kinematic vorticity analysis,together with the zircon U-Pb and zircon(U-Th)/He ages and the regional tectonic background,the study area experienced three stage evolution:tangential simpleshear(244 Ma),simple-shear-dominated general shear represented by upper crustal extension(224 Ma)and pure-shear-dominated general shear represented by the Halatu pluton doming(214 Ma),which constrained the early Mesozoic NE-SW crustal extension at the southeastern margin of the CAOB.This NE-SW extension probably originated from the postorogenic extensional collapse of the CAOB,subsequent exhumation being controlled by the far afield effects of the closure of the Mongol-Okhotsk belt.

An elasto-plastic constitutive model incorporating strain softening and dilatancy for interface thin-layer element and its verification

The mechanical behaviors of the interface between coarse-grained soil and concrete were investigated by simple shear tests under condition of mixed soil slurry (bentonite mixed with cement grout).For comparison,the interfaces both without slurry and with bentonite slurry were analyzed.The experimental results show that different slurries exert much influence on the strength and deformation of soil/structure interface.Under mixed soil slurry,strain softening and shear dilatation are observed,while shear dilatation appears under the small normal stress of the interface without slurry,and shear contraction is significant under the condition of the bentonite slurry.The thickness of the interface was determined by analyzing the disturbed height of the sample with both simple shear test and particle flow code (PFC).An elasto-plastic constitutive model incorporating strain softening and dilatancy for thin layer element of interface was formulated in the framework of generalized potential theory.The relation curves of shear stress and shear strain,as well as the relation curves of normal strain and shear strain,were fitted by a piecewise function composed by hyperbolic functions and resembling normal functions.The entire model parameters can be identified by tests.The new model is verified by comparing the measured data of indoor cut-off wall model tests with the predictions from finite element method (FEM).The FEM results indicate that the stress of wall calculated by using Goodman element is too large,and the maximum deviation between the test data and prediction is about 45%.While the prediction from the proposed model is close to the measured data,and the error is generally less than 10%.

STUDY ON THE GENERALIZED PRANDTL-REUSS CONSTITUTIVEEQUATION AND THE COROTATIONALRATES OF STRESS TENSOR

In this paper, the generalized Prandtl-Reuss (P-R) constitutive equations of elastic-plastic material in the presence of finite deformations through a new approach are studied. It analyzes the generalized P-R equation based on the material corotational rate and clarifies the puzzling problem of the simple shear stress oscillation mentioned in some literature. The paper proposes a modified relative rotational rate with which to constitute the objective rates of stress in the generalized P-R equation and concludes that the decomposition of total deformation rate into elastic and plastic parts is not necessary in developing the generalized P-R equations. Finally, the stresses of simple shear deformation are worked out.

Probability analysis of contact forces in quasi-solid-liquid phase transition of granular shear flow

The quasi-solid-liquid phase transition exists widely in different fields,and attracts more attention due to its instinctive mechanism.The structure of force chains is an important factor to describe the phase transition properties.In this study,the discrete element model(DEM) is adopted to simulate a simple granular shear flow with period boundary condition on micro scale.The quasi-solid-liquid phase transition is obtained under various volume fractions and shear rates.Based on the DEM results,the probability distribution functions of the inter-particle contact force are obtained in different shear flow phases.The normal,tangential and total contact forces have the same distributions.The distribution can be fitted as the exponential function for the liquid-like phase,and as the Weibull function for the solid-like phase.To describe the progressive evolution of the force distribution in phase transition,we use the Weibull function and Corwin-Ngan function,respectively.Both of them can determine the probability distributions in different phases and the Weibull function shows more reasonable results.Finally,the force distributions are discussed to explain the characteristics of the force chain in the phase transition of granular shear flow.The distribution of the contact force is an indicator to determine the flow phase of granular materials.With the discussions on the statistical properties of the force chain,the phase transition of granular matter can be well understood.

Behavior of compacted clay-concrete interface

Tests of interface between compacted clay and concrete were conducted systematically using interface simple shear test apparatus.The samples,having same dry density with different water content ratio,were prepared.Two types of concrete with different surface roughness,i.e.,relatively smooth and relatively rough surface roughness,were also prepared.The main objectives of this paper are to show the effect of water content,normal stress and rough surface on the shear stress-shear displacement relationship of clay-concrete interface.The following were concluded in this study:1)the interface shear sliding dominates the interface shear displacement behavior for both cases of relatively rough and smooth concrete surface except when the clay water content is greater than 16%for the case of rough concrete surface where the shear failure occurs in the body of the clay sample;2)the results of interface shear strength obtained by direct shear test were different from that of simple shear test for the case of rough concrete surface;3)two types of interface failure mechanism may change each other with different water content ratio;4)the interface shear strength increases with increasing water content ratio especially for the case of clay-rough concrete surface interface.