Shear-induced Dilation Research Articles

Shear-flow coupling characteristics of a three-dimensional discrete fracture network-fault model considering stress-induced aperture variations

This study presents a three-dimensional discrete fracture network-fault (3D DFN-fault) model that contains a 3D DFN and a deformable 3D fault. The fault slip-induced shear displacement and normal displacement are taken into account. Under a constant normal stiffness (CNS) boundary condition, the normal displacement gives rise to an increase in the normal stress and a decrease in the aperture of the fractures connected to the fault, which are then incorporated into the model. Finally, a numerical code is developed to simulate fluid flow through the 3D DFN-fault model during shearing and the effects of the aperture heterogeneity, shear displacement and fracture structure on the hydraulic properties of fractured rock masses are estimated. The results show that an obvious channeling flow in the fracture networks is observed as remarkable localizations of the flow paths within limited areas of fracture planes. The aperture heterogeneity of fractures tends to hinder the overall flow through the DFN-fault model during shearing. The equivalent permeability decreases at the beginning of shear because of the stress-induced closure of fractures. With increasing the shear displacement, the equivalent permeability of the model in direction perpendicular to the fault slip direction either increases or decreases, depending on the competition of two effects: (i) the permeability is enhanced by the shear-induced dilation of the fault and the newly generated flow paths by connecting the dead-ends of fractures that are intersected to the fault; (ii) the permeability decreases due to the closure of fractures, which is influenced by the increase in the dilation-dependent normal stress. However, as the shear displacement continuously increases, the equivalent permeability in the direction parallel to the fault slip direction steadily increases.

Tailoring Evolution of Configuration Entropy Change During Plastic Flow of Metallic Glasses

Based on the energy balance principle for a serrated shear event, the configuration entropy change of plastic flow within a shear band in metallic glasses is precisely quantified. With this method, we successfully tailored the evolution of entropy change with the plastic displacement/strain. It was found that the evolution of entropy changes for various metallic glasses follows a unified linear relation. The experimental result is consistent with the thermodynamic deduction from the free volume theory, corroborating the nature of shear-induced dilation for the plastic flow of metallic glasses.

DEM-aided direct shear testing of granular sands incorporating realistic particle shape

Discrete element method (DEM) of granular sands incorporating the effect of the realistic particle shape has been an important issue for many years. In this context, this study proposed a novel framework for the generation of realistic-shaped particles of natural sands in 3D DEM simulations. The generation framework mainly included micro-CT (μCT) scanning of sand particles, image processing of μCT images, spherical harmonic reconstruction of the particle surface, and clump generation by the overlapping multisphere clump method (OMCM) in DEM simulations. To validate the accuracy of OMCM, the volume and inertia moment of the clump were carefully investigated, and a set of optimized generation parameters was then determined to ensure the accuracy of the clump and the limit number of the filling spheres. Based on the generation framework, a clump sample with realistic particle shapes and a corresponding sphere sample were generated to conduct a series of direct shear testing. The simulation results demonstrated that the realistic particle shape highly increases the particle interlocking rather than the anisotropic intensity of strong contact force chains, and in turn enhances the shear resistance and the shear-induced dilation of the sands. It was also found that the inter-particle contacts of the clump sample have higher friction mobilization than that of the sphere sample, which identified the micromechanism of the shape effect on the particle interlocking.

A Forchheimer Equation-Based Flow Model for Fluid Flow Through Rock Fracture During Shear

Shear deformation-induced hydraulic conductivity change in fracture has been studied for decades. However, the existing models to link shear deformation and hydraulic behaviors are less accurate due to complex flow in rock fractures. This study presents an improved flow model for calculating nonlinear flow behaviors in rock fractures during shear. In this model, the linear and nonlinear coefficients in the Forchheimer equation were determined using mechanical aperture and fracture roughness coefficients. The mechanical aperture was equal to the initial aperture plus the change of the aperture due to shear-induced dilation. The dilation curve was divided into three stages and analytical expressions for modeling the dilation curve were established by incorporating the joint roughness coefficient (JRC) and the mobilized roughness coefficient (JRCmob). In addition, shear-flow tests were conducted on marble and granite fractures with normal stress between 0.5 and 3.0 MPa. The experimental data were used to verify the proposed model. The results show that the proposed model predicts flow in rock fractures well.

Oxidation feature and diffusion mechanism of Zr-based metallic glasses near the glass transition point

The oxidation behaviors of as-cast, pre-deformed, and crystallized Zr47.9Ti0.3Ni3.1Cu39.3Al9.4 metallic glasses (MGs) were studied near the glass transition point. The oxidation kinetics of the crystallized MGs followed a parabolic-rate law, and the as-cast and pre-deformed MGs exerted a typical two-stage behavior above the glass transition temperature (Tg). Most interesting, pre-deformed treatment can significantly improve the oxidation rate of MGs, as the initial oxidation appeared earlier than for the as-cast MGs, and was accompanied by much thicker oxide scale. The EDS and XPS results showed that the metal Al acted as the preferred scavenger that absorbed intrinsic oxygen in the near-surface region of as-cast MGs. However, a homogeneous mixed layer without Al was observed in the pre-deformed MGs. We speculated the accelerated diffusion of other elements in the MGs was due to the local increase in the free volume and significant shear-induced dilation of the local structure. The results from this study demonstrate that MGs exhibit controllable atomic diffusion during the oxidation process, which can facilitate use in super-cooled liquid region applications.

A New Rock Joint Generation Method and Its Verification in PFC2D

The first part of this paper presents the major drawbacks of the traditional methods for generating joints in Particle Flow Code 2D (PFC2D). Violent oscillations in the postpeak shear stress and shear‐induced dilation in the normal direction occur in specimens generated by directly removing bonds in joints and using the discrete fracture network (DFN) method. The specimens generated by the additional wall method can be used to simulate realistic shear mechanical properties in the direct shear test, but it is difficult to achieve a uniform initial stress distribution within the specimen due to the constraint of particle motion. The second part of this paper explores an improved method to generate realistic joints based on the particle grouping technique and the smooth joint model, and the validity of this method is verified by a set of numerical direct shear tests. The numerical results show that the proposed joint generation method can effectively eliminate the oscillation of the postpeak shear stress and shear‐induced dilation in the normal direction. In addition, the mechanical behaviours of the rough jointed rock mass correspond well with the theoretical results obtained from Patton’s and Barton’s models. The proposed model can also simulate the asperity degradation of rough jointed rock masses.

Response of a loess landslide to rainfall: observations from a field artificial rainfall experiment in Bailong River Basin, China

Rainfall-induced landslides are a significant hazard in many areas of loess-covered terrain in Northwest China. To investigate the response of a loess landslide to rainfall, a series of artificial rainfall experiments were conducted on a natural loess slope, located in the Bailong River Basin, in southern Gansu Province. The slope was instrumented to measure surface runoff, pore water pressure, soil water content, earth pressure, displacement, and rainfall. The hydrological response was also characterized by time-lapse electrical resistivity tomography. The results show that most of the rainfall infiltrated into the loess landslide, and that the pore water pressure and water content responded rapidly to simulated rainfall events. This indicates that rainfall infiltration on the loess landslide was significantly affected by preferential flow through fissures and macropores. Different patterns of pore water pressure and water content variations were determined by the antecedent soil moisture conditions, and by the balance between water recharge and drainage in the corresponding sections. We observed three stages of changing pore water pressure and displacement within the loess landslide during the artificial rainfall events: Increases in pore water pressure initiated movement on the slope, acceleration in movement resulting in a rapid decrease in pore water pressure, and attainment of a steady state. We infer that a negative pore water pressure feedback process may have occurred in response to shear-induced dilation of material as the slope movement accelerated. The process of shear dilatant strengthening may explain the phenomenon of semi-continuous movement of the loess landslide. Shear dilatant strengthening, caused by intermittent or continuous rainfall over long periods, can occur without triggering rapid slope failure.

Effect of rainfall on a colluvial landslide in a debris flow valley

A colluvial landslide in a debris flow valley is a typical phenomena and is easily influenced by rainfall. The direct destructiveness of this kind of landslide is small, however, if failure occurs the resulting blocking of the channel may lead to a series of magnified secondary hazards. For this reason it is important to investigate the potential response of this type of landslide to rainfall. In the present paper, the Goulingping landslide, one of the colluvial landslides in the Goulingping valley in the middle of the Bailong River catchment in Gansu Province, China, was chosen for the study. Electrical Resistivity Tomography (ERT), Terrestrial Laser Scanning (TLS), together with traditional monitoring methods, were used to monitor changes in water content and the deformation of the landslide caused by rainfall. ERT was used to detect changes in soil water content induced by rainfall. The most significant findings were as follows:(1) the water content in the centralupper part (0~41 m) of the landslide was greater than in the central-front part (41~84 m) and (2) there was a relatively high resistivity zone at depth within the sliding zone. The deformation characteristics at the surface of the landslide were monitored by TLS and the results revealed that rainstorms caused three types of deformation and failure: (1) gully erosion at the slope surface; (2) shallow sliding failure; (3) and slope foot erosion. Subsequent monitoring of continuous changes in pore-water pressure, soil pressure and displacement (using traditional methods) indicated that long duration light rainfall (average 2.22 mm/d) caused the entire landslide to enter a state of creeping deformation at the beginning of the rainy season. Shear-induced dilation occurred for the fast sliding (30.09 mm/d) during the critical failure sub-phase (EF). Pore-water pressure in the sliding zone was affected by rainfall. In addition, the sliding L1 parts of the landslide exerted a discontinuous pressure on the L2 part. Through the monitoring and analysis, we conclude that this kind of landslide may have large deformation at the beginning and the late of the rainy season.

The “ tension transformation zone” model of amorphous alloys

An amorphous alloy is a glassy solid that is formed through the supercooling of a melt. As the melt cools via the glass transition, its atoms freeze into a long-range disordered structure. Amorphous alloys represent a relatively young class of materials, having been first reported in 1960 when Duwez and co-workers produced Au-Si alloys by developing the rapid-quenching technology. The advent of amorphous alloys, especially the bulk samples with their characteristic size in excess of 1 mm, has aroused much interests in the basic science of glass transition, glass structure, and their intriguing properties. For crystalline metals, their structure can be well described by the period lattices and lattice defects including dislocations, twins, stacking faults, grain doundaries, etc. However, these traditional structural defects are not defined in amorphous alloys. Therefore, this type of atomic-disordered alloys manifest a series of excellent mechanical properties, including extraordinary strength, high hardness, large elastic limit and relatively high fracture toughness, making them attractive candidates for many potential applications as structural materials. At temperatures far below the glass transition temperature, the failure of amorphous alloys is generally induced by 10 nm thick shear banding with the single-dominated or multiple mode. It is well known that the shear banding is an instability mode of plastic flow from homogeneous to localized feature. Although the precise mechanism for amorphous plasticity is not well discovered, it is widely accepted that the shear-banding-mediated plasticity originates from a cascade of inelastic shear rearrangements of local atomic groups, called shear transformation zones (STZs). The STZs are thermally activated events with the transient nature, driven by shear stress and giving rise spatially to Eshelby fields. However, many recent works have shown that the failure of amorphous alloys is not always dominated by the shear banding; instead, a brittle failure will take place with a tension mode. The latter is usually accompanied with a new type of fracture surface morphology: fine dimples and/or nanoscale periodic corrugations. In order to understand such a dissipation process of fracture energy, we proposed the “tension transformation zone (TTZ)” model of amorphous alloys in 2008. The TTZ describes the brittle nucleation-controlled cavitation of local atomic groups that can be activated by shear-induced dilatation or direct hydrostatic tension. Here, we review how the TTZ model was developed, including its inherent nature, activation conditions, atomistic simulations and relevant experiments. The difference and relationship between the proposed TTZ and the classical cavitation are extensively discussed. Therefore, the energy dissipation in fracture of amorphous alloys is determined by two competing elementary processes, via. STZs and TTZs ahead of the crack tip. Based on this STZ vs. TTZ picture, the ductile-to-brittle transition of amorphous alloys can be understood as the change in the nature of transformation zones from shear-dominated STZs to dilatation-dominated TTZs. This review ends with the key aspects that deserve further study regarding the TTZ model. These aspects, at least, include (1) the experimental capture of TTZs, (2) the dynamics properties, (3) the spatio-temporal evolution, and (4) the theoretical construction from TTZs to brittle failure in amorphous alloys.

Secondary flows in slow granular flows

Recent findings by Krishnaraj and Nott [1] show that a granular material sheared in a cylindrical Couette cell at low shear rates forms a single secondary vortex. The vortex spans the entire width of the Couette cell and has a sense opposite to the centrifugally driven Taylor-Couette vortex in a Newtonian fluid – it is in fact shown to be driven by shear-induced dilation. Krishnaraj and Nott [1] show that the vortex also explains a Theological anomaly observed earlier [2], wherein all components of the stress on the outer cylinder increase nearly exponentially with depth from the free surface. In this study, we test the robustness of this vortex by varying the parameters of the grain contact model. We show that the presence of a free surface is not essential for the formation of the secondary vortex. The vortex forms even when a rigid plate of finite weight confines the granular column at the top. We find that as the shear rate is increased, an additional centrifugally-driven vortex appears. This new vortex keeps growing until, at Savage number close to one, the dilation-driven vortex disappears. We also present the variation of the wall stresses at the inner cylinder with depth. Finally, we argue that the secondary flow can also help to understand the rheological behaviour observed in geometries such as the split-bottom Couette device [3].

Dilatancy in semi-solid steels at high solid fraction

The study of mushy-zone deformation in steels is important for limiting defect formation in continuous casting. Here, we use in situ synchrotron radiography to quantify the shear deformation mechanisms of an equiaxed carbon steel at a solid fraction >0.9 and to understand how these mechanisms lead to casting defects. We show that the grain assembly undergoes shear-induced dilation (Reynolds' dilatancy) which opens liquid-filled fissures and cracks at high solid fraction. We further show a complex interaction between grain rearrangement, grain deformation and local coarsening, where rearrangement reduces the grain-grain contact area and coordination number which alters the stress network and also drives coarsening as grains move apart.

New aspects for friction coefficients of finite granular avalanche down a flat narrow reservoir

This work examines the bulk internal friction coefficient, \(\mu \), and effective wall friction coefficient, \(\mu _w\), for finite number of nearly identical dry glass spheres in avalanche down a narrow inclined reservoir of smooth frictional bed using a validated discrete element scheme. Instantaneous deviatoric strain rate tensor \(\dot{\gamma }^d_{ij}\) and stress tensor \(\tau _{ij}\) are computed locally to evaluate a three-dimensional constitutive model developed based on the rheology of steady homogeneous surface flows. On one side, the algebraic \(\mu -I\) relation conforms to conventional relation for glass beads, \(\mu =0.34+0.31/(1+0.15/I)\) (Jop et al. in J. Fluid Mech. 541:167–192, 2005, Midi in Eur. Phys. J. E 14:341–365, 2004, Jop in Comptes Rendus Phys. 16:62–72, 2015), when the inertial number \(I>I_{c}=2\times 10^{-2}\). The assumption of collinear \(\tau _{ij}\) and \(\dot{\gamma }^d_{ij}\), however, does not hold and such misalignment agrees to the findings in non-uniform inhomogeneous flows (Cortet et al. in Europhys. Lett. 88(1):14001, 2009). Below \(I_c\), we observe a decaying \(\mu -I\) as found in slowly deforming rheology tests and a simplified model is developed in view of shear-induced dilatation upon yielding. Non-constant effective wall friction coefficient is measured to grow in time and with I towards the sphere-wall sliding friction coefficient in the contact model while preserving the depth-weakening feature as in confined steady surface flows (Richard et al. in Phys. Rev. Lett. 101:248002, 2008, Brodu et al. in Phys. Rev. E 87:022202, 2013). The fact that rotation at one sphere center can divert surface relative velocity across the contact area to render lower sliding friction is considered to develop a model describing how \(\mu _w\) drops with the ratio between rotation-induced velocity and sliding velocity, \(\varOmega \). The simulation data compares fairly well to the predicted monotonic decay of \(\mu _w\) with \(\varOmega \).

Intermittent slipping of landslide regulated by dilatancy evolution and velocity-weakening friction law: an efficient numerical scheme

When a block of dense sandy soil moves downhill, the shear-induced soil dilatancy along the basal shear boundary produces a negative value of excess pore pressure that increases the basal frictional resistance. Dilatancy angle, , the degree to which the basal soil dilates due to the shear, normally evolves during slope failure. A study by other researchers shows that if is constant, the block of dense soil will remain stable (or unstable) sliding when the velocity-weakening rate of the basal friction coefficient of the block is small (or large) enough. Moreover, during unstable sliding processes, the block of dense soil exhibits "periodic" patterns of intermittent slipping. Here, we used a more efficient and accurate numerical scheme to revisit that study. We expanded their model by assuming evolves during slope failure. Consequently, we acquired completely different results. For instance, even though the velocity-weakening rate of the friction coefficient is fixed at the same smaller (or larger) value that those researchers use, the stable (or unstable) steady states of landslide they predict will inversely change to unstable (or stable) when decreases (or increases) with the increase of slide displacement to a value small (or large) enough. Particularly, in unstable processes, the soil block exhibits "aperiodic" styles of intermittent slipping, instead of "periodic". We found out that the stick states appearing later last longer (or shorter) in the case of decreasing (or increasing) . Moreover, because the basic states of landslides with impacts of dilatancy evolution are not steady nor periodic, traditional stability-analysis methods cannot be "directly" used to analyze the stability of such landslides. Here, we broke through this technical problem to a degree. We showed that combining a concept called "quasi-steady-state approximation" with a traditional stability-analysis technique can qualitatively predict the instability onset of the landslides. Through this study, we demonstrated that the combination of Chebyshev collocation (CC) and 4th-order Runge-Kutta methods is more accurate and efficient than the numerical scheme those researchers use.

Constitutive modeling the plastic deformation of bone-like materials

Bone-like materials such as cortical bone, dentin and nacre possess complex hierarchical structure, which gives rise to superior mechanical performance. Despite numerous efforts devoted to characterizing the mechanical behavior of such materials, there does not exist a general continuum theory describing the plastic deformation of these materials. The present study provides a theoretical framework for the plasticity of bone-like materials. Based on the theoretical framework, a constitutive model is developed. The plastic flow of bone-like materials is modeled by incorporating a shear-dominated mechanism and a dilatation mechanism. We model the shear-dominated mechanism by accounting for the cohesive-frictional nature of bone-like materials, and for the dilatation mechanism, the shear-induced plastic dilatation and the dilatation due to hydrostatic tension are taken into account. Furthermore, the constitutive model incorporates the strain-rate effect on plastic deformation. By fitting the experimental data of uniaxial compression of antler bone, parametric studies are performed and the effect of model parameters on mechanical properties of bone-like materials is discussed. In addition, numerical simulations of cortical bone and dentin under compressive and tensile loadings are carried out; it is found that the model quantitatively captures pressure-sensitive plastic deformation behavior of bone-like materials and a good agreement between numerical simulation and experiment is achieved, substantiating that the continuum model developed in this study can be used to describe the plastic properties of bone-like materials effectively. The plastic deformation of the two-layer structure of dentin subjected to tensile loading is also simulated, and the role of protein-rich intertubular dentin is identified.

Stability of wall bounded, shear flows of dense granular materials: the role of the Couette gap, the wall velocity and the initial concentration

In this paper, the stability of a plane, unidirectional Couette flow of a dense granular material is investigated via the means of a normal mode stability analysis. Our studies are based on a continuum mechanical model for the flows of interest coupled with the constitutive expressions for the normal and the shear stresses of the granular material induced by the ${\it\mu}(I)$-rheology. According to our analysis, both the Couette gap and the wall velocity play a destabilizing role in the flows of interest as opposed to the initial concentration that acts as stabilizer. For sufficiently high Couette gaps and wall velocities, unstable modes are recovered. The predicted instability manifests itself through shear-induced dilatancy that, in turn, engenders particle migration and the formation of bulbs, similar to the ones that have been acquired through molecular dynamics simulations.

A dilation-driven vortex flow in sheared granular materials explains a rheometric anomaly.

Granular flows occur widely in nature and industry, yet a continuum description that captures their important features is yet not at hand. Recent experiments on granular materials sheared in a cylindrical Couette device revealed a puzzling anomaly, wherein all components of the stress rise nearly exponentially with depth. Here we show, using particle dynamics simulations and imaging experiments, that the stress anomaly arises from a remarkable vortex flow. For the entire range of fill heights explored, we observe a single toroidal vortex that spans the entire Couette cell and whose sense is opposite to the uppermost Taylor vortex in a fluid. We show that the vortex is driven by a combination of shear-induced dilation, a phenomenon that has no analogue in fluids, and gravity flow. Dilatancy is an important feature of granular mechanics, but not adequately incorporated in existing models.

A finite volume method for two-phase debris flow simulation that accounts for the pore-fluid pressure evolution

The temporal and spatial evolution of pore-fluid pressure exerts strong control on debris flow motion because it can counteract normal stresses at grain contacts, reduce friction, and enhance bulk flow mobility. In Iverson’s two-phase debris flow model, the depth-averaged pore pressure equation, which takes into account the effect of shear-induced dilatancy, was combined with a previous model to describe the simultaneous evolution of flow velocity and depth, solid mass, and pore-fluid pressure. In this work, a high-resolution scheme based on the finite volume method was used to solve the system of equations. Several numerical tests were performed to verify the ability of the presented model and the accuracy of the proposed numerical method. Numerical results were compared with experimental data obtained in a laboratory, and the effectiveness of the proposed numerical method for solving practical problems has been proven. Numerical results indicated that increases of the pore-fluid pressure could enhance the motion of debris flow and expand the spread area. Furthermore, results showed that the debris shear-induced dilatancy could affect the evolution of pore-fluid pressure, thus further influencing the motion of debris flow.

Plasticity and strain localization around a horizontal wellbore drilled through a porous rock formation

Predicting plastic deformation and localization band around a wellbore drilled through a porous rock is a challenging task that could have important implications for the prediction of instability and sand production. This study focuses on analyzing stress field, plastic zones, and localized deformations around a horizontal borehole drilled at a great depth through a highly porous rock formation. Several laboratory studies demonstrate that, depending on the loading path, highly porous rocks are susceptible to different failure mechanisms, but most of these mechanisms are mainly due to shear-induced dilation and shear-enhanced compaction. Plasticity models, in conjunction with bifurcation analysis, represent an extremely useful framework for describing such detailed constitutive responses. This paper presents a new elastoplastic constitutive model characterized by two yield surfaces intersecting smoothly, that is able to capture the different failure modes. The model is validated against experimental data for several different porous rocks, and it is then used to determine the stress and strain distributions around a horizontal wellbore using nonlinear finite element analysis. Particular interest is devoted to predicting the condition for the formation of a localized band of intense deformation, elucidating the factors that either prevent or enhance the band initiation. Results of simulations show the key role played by the elastoplastic constitutive model and the effects of the mud pressure, the in-situ stress condition and geometric imperfections in the development and propagation of plastic zone, as well as in the initiation of localization zone.

On the Initial Stages of the Densification and Lithification of Sediments

This paper presents a model that can simulate early rock-forming processes, including the influence of the initial packing of the grains on the subsequent rearrangement that occurs as a consequence of pressure-induced grain damage. The paper is concerned with the behaviour of assemblies of loose grains and the mechanics of early lithification. Consider the concept of shear-induced negative dilatancy, where any shear deformation has a tendency to produce densification even at very low pressures. As shear deformation progresses, positive dilatancy starts to contribute and at the critical state the two effects balance. This concept is encapsulated within the mathematics of the model. The model building scheme is first outlined and demonstrated using a hard particle model. Then, the concept of ‘self cancelling shear deformations’ that contribute to the shear–volume coupling but not to the macroscopic shear deformation is explained. The structure of the hard particle model is modified to include low levels of damage at the grain contacts. A parameter that describes bonding between the grains and possible damage to those bonds is incorporated into a term that, depending on its magnitude, also accounts for frictional resistance between unbonded grains. This parameter has the potential to develop with time, increasing compressive stress, or in response to evolving chemical concentrations. Together these modifications allow densification in the short term, and the formation of sedimentary rocks in the long term, by pressure alone, to be simulated. Finally, simulations using the model are compared with experimental results on soils.

Origin of stress overshoot in amorphous solids

Based on the shear-transformation-zone (STZ) theory, we propose a constitutive model for describing homogeneous elastoplastic deformation of amorphous solids where the interaction of shear transformations and free volume dynamics is incorporated. This theoretical model can reproduce the stress overshoot behavior that shows the dependence of strain rate, temperature, STZ population and dilatancy of systems. It reveals that the stress overshoots its steady state value due to the delayed activation of shear transformations that results from the insufficient free volume in the system. However, the subsequent strain softening (stress drop) is attributed to the shear-induced dilatation that is a result of the positive interplay between shear transformations and free volume creation, the latter playing the dominant role. Our analysis also demonstrates that the STZs, as basic carriers of amorphous plasticity, govern the yielding of the system, whereas the free volume dynamics significantly affects the post-yielding behaviors.