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.

ONSET CONDITION OF STRAIN LOCALIZATION IN MATRIX OF SATURATED POROUS MEDIA

Based on governing equations of saturated porous media and Liapunov＇ s stability here, onset conditions matrix of porous media used by solid stress and Terzaghi＇s effective stress constitutive description under seepage flow state, are presented, which have different forms with different representation of the solid phase, matrix or skeleton, constitutive model of porous media. The main difference relates with how to describe the interaction between solid phase and liquid phase in constitutive model. The derived onset condition of strain localization under Terzaghi＇ s effective stress description can be used to interpret different failure types, piping effect, landslides and mudflows, by means of the type and the magnitude ratio of relative movement between solid phase and liquid phase. Examples here illuminate the onset condition of how to work.

STUDY OF TEXTURE EFFECT ON STRAIN LOCALIZATION OF BCC STEEL SHEETS

Using elastic crystalline viscoplastic finite element (FE) annlysis, the formability of BCC steel sheets was assessed. An orientation probability assignment method in the FE modeling procedure, which can be categorized as an inhomogenized material modeling, was newly proposed. In the study, the crystal orientations of three materials, mild steel, dual phase steel and the high strength steel, were obtained by Xray diffraction and orientation distribution function (ODF) analyses. The measured ODF results have revealed clearly different textures in the sheets, featured by orientation fibers, skeleton lines and selected orientations in Euler angle space, which are closely related to the plastic anisotropy. Then, the crystal orientations were assigned to FE integration points by using this ODF data, individually. The FE analyses of the standard limiting dome height (LDH) test show how the fiber textures affect the extent of strain localization in the forming processes. It was confirmed by comparison with experimental results that this FE code could predict the extreme strain localization and assess the sheet formability.

Numerical simulation of strain localization and damage evolution in large plastic deformation using mixed finite element method

An investigation of computer simulation is presented to analyze the effectsof strain localization and damage evolution in large plastic deformation. The simulation is carriedout by using an elastic-plastic-damage coupling finite element program that is developed based onthe concept of mixed interpolation of displacement/pressure. This program has been incorporated intoa damage mechanics model as well as the corresponding damage criterion. To illustrate theperformance of the proposed approach, a typical strain localization problem has been simulated. Theresults show that the proposed approach is of good capability to capture strain localization andpredict the damage evolution.

Strain localization analyses of idealized sands in biaxial tests by distinct element method

This paper presents a numerical investigation on the strain localization of an idealized sand in biaxial compression tests using the distinct element method(DEM).In addition to the dilatancy and material frictional angle,the principal stress field,and distributions of void ratio,particle velocity,and the averaged pure rotation rate(APR)in the DEM specimen are examined to illustrate the link between microscopic and macroscopic variables in the case of strain localization.The study shows that strain localization of the granular material in the tests proceeds with localizations of void ratio,strain and APR,and distortions of stress field and force chains.In addition,both thickness and inclination of the shear band change with the increasing of axial swain,with the former valued around 10-14 times of mean grain diameter and the later overall described by the Mohr-Coulomb theory.

Tensile and cyclic deformation response of friction-stir-welded dissimilar aluminum alloy joints:Strain localization effect

Cyclic deformation behavior of friction-stir-welded dissimilar AA2024-T351 to AA7075-T65 aluminum alloy joints was evaluated via stepwise tests at different strain rates,along with transmission electron microscopy examinations to characterize the precipitates required to assess internal stresses.Electron backscatter diffraction was employed to observe the inhomogeneous microstructures of the FSWed joints.Strain localization appeared in the heat affected zone(HAZ)of AA2024 side.After cyclic deformation of 500 cycles at a total strain amplitude of 0.5%,the strength of the dissimilar joints resumed basically to that of AA2024 base material.And the AA2024 HAZ was obviously hardened,which should be attributed to the introduced dislocations during cyclic deformation process.Cyclic hardening capacity of the joints increased with decreasing strain rate.

Geotechnical stability analysis considering strain softening using micro-polar continuum finite element method

Geotechnical stability analyses based on classical continuum may lead to remarkable underestimations on geotechnical safety.To attain better estimations on geotechnical stability,the micro-polar continuum is employed so that its internal characteristic length(lc)can be utilized to model the shear band width.Based on two soil slope examples,the role of internal characteristic length in modeling the shear band width of geomaterial is investigated by the second-order cone programming optimized micro-polar continuum finite element method.It is recognized that the underestimation on factor of safety(FOS)calculated from the classical continuum tends to be more pronounced with the increase of lc.When the micro-polar continuum is applied,the shear band dominated by lc is almost kept unaffected as long as the adopted meshes are fine enough,but it does not generally present a slip surface like in the cases from the classical continuum,indicating that the micro-polar continuum is capable of capturing the non-local geotechnical failure characteristic.Due to the coupling effects of lc and strain softening,softening behavior of geomaterial tends to be postponed.Additionally,the bearing capacity of a geotechnical system may be significantly underestimated,if the effects of lc are not modeled or considered in numerical analyses.

Full-field mapping of internal strain distribution in red sandstone specimen under compression using digital volumetric speckle photography and X-ray computed tomography

It is always desirable to know the interior deformation pattern when a rock is subjected to mechanicalload. Few experimental techniques exist that can represent full-field three-dimensional （3D） straindistribution inside a rock specimen. And yet it is crucial that this information is available for fully understandingthe failure mechanism of rocks or other geomaterials. In this study, by using the newlydeveloped digital volumetric speckle photography （DVSP） technique in conjunction with X-ray computedtomography （CT） and taking advantage of natural 3D speckles formed inside the rock due to materialimpurities and voids, we can probe the interior of a rock to map its deformation pattern under load andshed light on its failure mechanism. We apply this technique to the analysis of a red sandstone specimenunder increasing uniaxial compressive load applied incrementally. The full-field 3D displacement fieldsare obtained in the specimen as a function of the load, from which both the volumetric and the deviatoricstrain fields are calculated. Strain localization zones which lead to the eventual failure of the rock areidentified. The results indicate that both shear and tension are contributing factors to the failuremechanism. 2015 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Deformation and failure characteristics of sandstone under uniaxial compression using distributed fiber optic strain sensing

This paper investigates the deformation and fracture propagation of sandstone specimen under uniaxial compression using the distributed fiber optic strain sensing(DFOSS)technology.It shows that the DFOSS-based circumferential strains are in agreement with the data monitored with the traditional strain gage.The DFOSS successfully scans the full-field view of axial and circumferential strains on the specimen surface.The spatiotemporal strain measurement based on DFOSS manifests crack closure and elastoplastic deformation,detects initialization of microcrack nucleation,and identifies strain localization within the specimen.The DFOSS well observes the effects of rock heterogeneity on rock deformation.The advantage of DFOSS-based strain acquisition includes the high spatiotemporal resolution of signals and the ability of full-surface strain scanning.The introduction to the DFOSS technology yields a better understanding of the rock damage process under uniaxial compression.

Effect of confining pressure on deformation and failure of rock at higher strain rate

Influence of confining pressure from 0 to 28 MPa, which acts on the two lateral edges of rock specimen in plane strain compression, on the shear failure processes and patterns as well as on the macroscopically mechanical responses were numerically modeled by use of FLAC. A material imperfection with lower strength in comparison with the intact rock, which is close to the lower-left corner of the specimen, was prescribed. In elastic stage, the adopted constitutive relation of rock was linear elastic; in strain-softening stage, a composite Mohr-Coulomb criterion with tension cut-off and a post-peak linear constitutive relation were adopted. The numerical results show that with an increase of confining pressure the peak strength of axial stress-axial strain curve and the corresponding axial strain linearly increase; the residual strength and the stress drop from the peak strength to the residual strength increase; the failure modes of rock transform form the multiple shear bands close to the loading end of the specimen （confining pressure=0-0.1 MPa）, to the conjugate shear bands （0.5-2.0 MPa）, and then to the single shear band （4-28 MPa）. Once the tip of the band reaches the loading end of the specimen, the direction of the band changes so that the reflection of the band occurs. At higher confining pressure, the new-formed shear band does not intersect the imperfection, bringing extreme difficulties in prediction of the failure of rock structure, such as rock burst. The present results enhance the understanding of the shear failure processes and patterns of rock specimen in higher confining pressure and higher loading strain rate.

Instability criterion for the system composed of elastic beam and strain-softening pillar based on gradient-dependent plasticity

A mechanical model is proposed for the system of elastic beam and strain-softening pillar where strain localization is initiated at peak shear stress. To obtain the plastic deformation of the pillar due to the shear slips of multiple shear bands, the pillar is divided into several narrow slices where compressive deformation is treated as uniformity. In the light of the compatibility condition of deformation, the total compressive displacement of the pillar is equal to the displacement of the beam in the middle span. An instability criterion is derived analytically based on the energy principle using a known size of localization band according to gradient dependent plasticity. The main advantage of the present model is that the effects of the constitutive parameters of rock and the geometrical size of structure are reflected in the criterion. The condition that the derivative of distributed load with respect to the deflection of the beam in the middle span is less than zero is not only equivalent to, but also even more concise in form than the instability criterion. To study the influences of constitutive parameters and geometrical size on stability, some examples are presented.

Fano Resonance Enabled Infrared Nano-Imaging of Local Strain in Bilayer Graphene

Detection of local strain at the nanometer scale with high sensitivity remains challenging.Here we report near-field infrared nano-imaging of local strains in bilayer graphene by probing strain-induced shifts of phonon frequency.As a non-polar crystal,intrinsic bilayer graphene possesses little infrared response at its transverse optical phonon frequency.The reported optical detection of local strain is enabled by applying a vertical electrical field that breaks the symmetry of the two graphene layers and introduces finite electrical dipole moment to graphene phonon.The activated phonon further interacts with continuum electronic transitions,and generates a strong Fano resonance.The resulted Fano resonance features a very sharp near-field infrared scattering peak,which leads to an extraordinary sensitivity of-0.002%for the strain detection.Our results demonstrate the first nano-scale near-field Fano resonance,provide a new way to probe local strains with high sensitivity in non-polar crystals,and open exciting possibilities for studying strain-induced rich phenomena.

Revealing the role of local shear strain partition of transformable particles in a TRIP-reinforced bulk metallic glass composite via digital image correlation

The coupling effects of the metastable austenitic phase and the amorphous matrix in a transformation-induced plasticity(TRIP)-reinforced bulk metallic glass(BMG)composite under compressive loading were investigated by employing the digital image correlation(DIC)technique.The evolution of local strain field in the crystalline phase and the amorphous matrix was directly monitored,and the contribution from the phase transformation of the metastable austenitic phase was revealed.Local shear strain was found to be effectively consumed by the displacive phase transformation of the metastable austenitic phase,which relaxed the local strain/stress concentration at the interface and thus greatly enhanced the plasticity of the TRIP-reinforced BMG composites.Our current study sheds light on in-depth understanding of the underlying deformation mechanism and the interplay between the amorphous matrix and the metastable crystalline phase during deformation,which is helpful for design of advanced BMG composites with further improved properties.

Generation of Quantum-dot Photon Emission in h-BN via Local Strain Engineering

We reported a low-cost and easy-to-make method to effectively generate quantum dot(QD)states in 2D hBN films for quantum emissions at room temperature by utilizing silica nanospheres,in comparison with the sophisticated nanofabrication method reported in previous studies.The QDs created in 2D hBN films using silica nanospheres exhibit pronounced photon emissions with a good photo-stability in air,a narrow distribution of the emission peaks within the range of 580-620 nm,and a directional emission pattern,behaving as a single electric dipole.Our work develops the method of controllable fabrication of quantum emitters in 2D materials by using nano materials and structures.

Analysis of granular assembly deformation using discrete element method

The discrete element method is used to simulate specimens under three different loading conditions（conventional triaxial compression,plane strain,and direct shear）with different initial conditions to explore the underlying mechanics of the specimen deformation from a microscale perspective.Deformations of specimens with different initial void ratios at different confining stresses under different loading conditions are studied.Results show that the discrete element models successfully capture the specimen deformation and the strain localization.Particle behaviors including particle rotation and displacement and the mesoscale void ratio distributions are used to explain the strain localization and specimen deformation.It is found that the loading condition is one of the most important factors controlling the specimen deformation mode.Microscale behavior of the granular soil is the driving mechanics of the macroscale deformation of the granular assembly.

Dynamic analysis of fault rockburst based on gradient-dependent plasticity and energy criterion

Fault rockburst is treated as a strain localization problem under dynamicloading condition considering strain gradient and strain rate. As a kind of dynamic fracturephenomena, rockburst has characteristics of strain localization, which is considered as aone-dimensional shear problem subjected to normal compressive stress and tangential shear stress.The constitutive relation of rock material is bilinear (elastic and strain softening) and sensitiveto shear strain rate. The solutions proposed based on gradient-dependent plasticity show thatintense plastic strain is concentrated in fault band and the thickness of the band depends on thecharacteristic length of rock material. The post-peak stiffness of the fault band was determinedaccording to the constitutive parameters of rock material and shear strain rate. Fault bandundergoing strain softening and elastic rock mass outside the band constitute a system and theinstability criterion of the system was proposed based on energy theory. The criterion depends onthe constitutive relation of rock material, the structural size and the strain rate. The staticresult regardless of the strain rate is the special case of the present analytical solution. Highstrain rate can lead to instability of the system.

Effect of 1Al addition on deformation behavior of Mg

Deformation behavior of 1 Al containing Mg alloy has been investigated in the present study.After annealing,the Mg-1 Al alloy shows a typical basal texture.When compared to the pure Mg having a similar texture and grain size,the Mg-1 Al alloy shows much higher strength and larger elongation.Slip trace analyses of the tensile strained specimens show that non-basal slips such as pyramidal I and II slips can be easily activated at an early stage of deformation in the Mg-1 Al alloy and the grains in the Mg-1 Al alloy are seen to accommodate a larger degree of deformation than those in the pure Mg at a given strain.With increasing tensile strain,however,there is a strain localization along the initially formed slip lines of non-basal slips,forming surface steps without activating multiple slip lines.

Macro-micro investigation of granular materials in torsional shear test

A three-dimensional numerical torsion shear test is presented on hollow cylinder specimen which is performed on a spherical assemblage with fixed principal stress axes using the discrete element code PFC3D.Stack wall technique boundary conditions are employed and optimized to reasonably capture the microstructure evolution.Parametric studies are conducted in terms of the ratio κ,normal and shear stiffness of particles,wall stiffness and friction coefficients.Afterwards,in comparison with physical test,numerical results for a fixed principal stress angle(α=45°) are presented.The results show that the numerical test could capture the macro-micro mechanical behavior of the spherical particle assembly.The evolution of the coordination number demonstrates that particles in shear banding undergo remarkable decrease.The effects of localization on specimens illustrate that global stress and strain recorded from a hollow cylinder apparatus could not represent the localized response.The shearing band initiation and evolution from porosity and shear rate are visualized by contour lines in different shear strains.

An approach to evaluate ground surface rupture caused by reverse fault movement

An approach for estimating ground surface rupture caused by strong earthquakes is presented in this paper, where the finite element （FE） method of continuous and discontinuous coalescent displacement fields is adopted. The onset condition of strain localization is introduced to detect the formation of the slippage line. In the analysis, the Drucker-Prager constitutive model is used for soils and the rate- and state-dependent friction law is used on the slippage line to simulate the evolution of the sliding. A simple application to evaluate the ground surface rupture induced by a reverse fault movement is provided, and the numerical simulation shows good agreement with failure characteristics observed in the field after strong earthquakes.

Volume Change of Heterogeneous Quasi-brittle Materials in Uniaxial Compression

The volumetric strain was categorized into elastic and plastic parts. The farmer camposed of axial and lateral strains is uniform and determined by Hooke＇s law ; however, the latter consisting of axial and lateral strains is a fuaction af thickness af shear band determined by grndieat-dependeat plasticity by cansidering the heterngeneity of quasi- brittle materials. The non- uniform lateral strain due to the fact that shear band was farmed in the middle of specimen was averaged within specimen to precisely assess the volumetric strain. Then, the analytical expression for volumetric strain was verified by comparison with two earlier experimental results for concrete and rack. Finally, a detailed parametric study was carried out to investigate effects of constitutive parameters （ shear band thickness, elastic and softening rnoduli ） and geometrical size of specimen（ height and width of specimen ） on the volume dilatancy.