Homogeneous Shear Research Articles

Generalized quasilinear approximations in homogeneous shear turbulence

Generalized quasilinear approximations in homogeneous shear turbulence

Effect of storage temperatures treatment of coconut flesh (Cocos nucifera L.) based on the quality of coconut milk

Coconut plant (Cocos nucifera) is one of the potential industrial plants and has an important role both in terms of nutrition and in terms of economy in Indonesia. The number of coconut plants in Indonesia is used by the community, one of which is as a raw material for making coconut milk. Coconut milk is obtained from the extract of old coconut flesh that has been grated, either with the addition or without water, this white coconut milk liquid is an emulsion of oil and water. Coconut milk contains 230 kilocalories and consists of 67.5% water, 23.8% total fat, 5.54% carbohydrates, 2.29% protein and 0.70% ash. During production, coconut milk needs to undergo pretreatment homogeneous high-speed shear. Generally, this type of pretreatment can improve the emulsion stability in coconut milk. This needs to be done because the coconut milk emulsion system is very easily unstable after thawing. Temperature pretreatmentin coconut flesh is the main factor that influences the quality of the coconut milk produced. This study was conducted to analyze changes in the quality of coconut milk after it was done pretreatment storage of coconut flesh before being grated and squeezed into coconut milk and knowing the temperature pretreatment the most appropriate method to obtain the best quality coconut milk by using the Multiple Attribute Zeleny. The research was carried out in stages including the preparation of tools and materials, making coconut milk starting with cleaning the coconut, then giving pretreatment coconut flesh with 3 storage treatments using cold temperatures (6°C ± 2°C) and freezing temperatures (-16°C ± 2°C) stored for 24 hours and room temperature (27°C ± 2°C) without storage time. Then the coconut flesh is grated and the coconut milk is squeezed and continued with testing the quality parameters of coconut milk. The best treatment in the manufacture of coconut milk is to use pretreatment at freezing temperatures (-16°C ± 2°C) which is stored for 24 hours with the quality of coconut milk in the form of 22% yield, 30.59% water content, pH 6.27, and Viscosity 86.70 cP.

Functionally Graded Beams as Surrogate Structural Models: Shear Beam with Exponentially Graded Rigidity

An exact analytical solution, in terms of Bessel functions, was derived for the dynamic response of a shear beam with uniform cross section and mass density, and shear modulus that varies exponentially in the axial direction. The solution was generalized to a chain of such beam elements. The model may be appropriate for frame structures, which deform predominantly in shear, with gradually increasing rigidity toward the base. The results of a parametric study are presented for the frequencies of vibration and their ratios, mode shapes, transfer functions, and impulse response functions. The gradation affected the ratios between the frequencies of the higher modes of vibration and that of the fundamental mode, which were smaller than the corresponding ratios for a homogeneous shear beam and were progressively smaller for larger gradation constants. The mode shapes and the ratios of the amplitudes of the pulses in impulse response functions had amplitude amplification toward the top, which was larger for larger gradation constants, and suggests trapping of energy in the upper part of the structure. This effect may be responsible for observed damages and failure of structures in parts far from the base. The gradation also affected the symmetry and shape of the pulses in impulse response functions. The results of the parametric study may be useful for interpretation of the seismic response of full-scale structures. The model is intended for use as a simple surrogate model in structural system identification and health monitoring of frame structures.

Tension–compression biaxial test with ±45° symmetric angle-ply laminates for determining the pure shear response in principal material directions of a lamina

The tension–compression biaxial test with cruciform specimens using ±45° symmetric angle-ply laminates is proved to be suitable for determining the in-plane pure shear response of a lamina in principal material directions. The full stress–strain evolution presents a linear stage followed by an inelastic region with high shear deformations. At the linear stage a pure and homogeneous shear strain state is measured by Digital Image Correlation (DIC). Afterwards, the DIC registers the initiation of a shear band in the measurement region at 45° from the loaded directions that leads to the final failure plane. It is verified that the arms of the specimen, which are uniaxially loaded, do not develop pseudo-ductile effects during testing that could affect the central response. For comparison purposes, the ability to obtain an accurate shear elastic response from uniaxial loading with ±45° angle-ply laminates is investigated. Based on the elastic strain energy involved in the linear stage of the testing process, it is concluded that both uniaxial tensile and compressive tests could overestimate the shear stiffness. Moreover, if the material has higher tensile than compressive elastic properties, the uniaxial tensile tests should provide a slightly better approximation of the shear elastic modulus than uniaxial compressive tests.

Shock-induced energy localization and reaction growth considering chemical-inclusions effects for crystalline explosives

Chemical inclusions significantly alter shock responses of crystalline explosives in macroscale gap experiments but their microscale dynamics origin remains unclear. Herein shock-induced energy localization, overall physical responses, and reactions in α-1,3,5-trinitro-1,3,5-triazinane (α-RDX) crystal entrained various chemical inclusions were investigated by the multi-scale shock technique implemented in the reactive molecular dynamics method. Results indicated that energy localization and shock reaction were affected by the intrinsic factors within chemical inclusions, i.e., phase states, chemical compositions, and concentrations. The atomic origin of chemical-inclusions effects on energy localization is dependent on the dynamics mechanism of interfacial molecules with free space volume, which includes homogeneous intermolecular compression, interfacial impact and shear, and void collapse and jet. As introducing various chemical inclusions, the initiation of those dynamics mechanisms triggers diverse decay rates of bulk RDX molecules and hereby impacts on growth speeds of final reactions. Adding chemical inclusions can reduce the effectiveness of the void during the shock impacting. Under the shockwave velocity of 9 km/s, the parent RDX decay rate in RDX entrained amorphous carbon decreases the most and is about one fourth of that in RDX with a vacuum void, and solid HMX and TATB inclusions are more reactive than amorphous carbon but less reactive than dry air or acetone inclusions. The less-dense shocking system denotes the greater increases in local temperature and stress, the faster energy liberation, and the earlier final reaction into equilibrium, revealing more pronounced responses to the present intense shockwave. The quantitative models associated with the relative system density (RDsys) were proposed for indicating energy-localization mechanisms and evaluating initiation safety in the shocked crystalline explosive. RDsys is defined by the density ratio of defective RDX to perfect crystal after dynamics relaxation and reveals the global density characteristic in shocked systems filled with chemical inclusions. When RDsys is below 0.9, local hydrodynamic jet initiated by void collapse dominates upon energy localization instead of interfacial impact. This study sheds light on novel insights for understanding the shock chemistry and physical-based atomic origin in crystalline explosives considering chemical-inclusions effects.

A compressible turbulence model for the dissipation rate

In this work, the ability of a Reynolds stress model to compute turbulent homogeneous shear flow with significant compressibility effects is discussed. Several studies of compressible turbulent flows carried out in the past years have shown that the pressure strain correlation is mainly responsible for the strong changes in the magnitude of the Reynolds stress anisotropies. Two recent compressible models of this term are considered in conjunction with the standard model of the dissipation rate of the turbulent kinetic energy to predict compressible homogeneous flow highly sheared are tested. It is found that deficiencies appear in the calculations even if the pressure strain model is improved by compressibility corrections. Consistent with earlier studies, this deficiency is attributed to the use of the incompressible model for turbulent dissipation. However, a compressibility correction of this equation model uncovers the main focus of the present study. This correction makes the standard coefficients of this equation depend on the turbulent gradient Mach and Mach numbers. The proposed model is tested for low and strong compressibility cases from the DNS results of Sarkar. A comparison of the proposed model predictions with the DNS results shows good qualitative agreement. Therefore, compressibility correction for the incompressible model of the turbulent dissipation rate is found to be an important issue for the compressible homogeneous turbulent shear flow.

Stochastic model for the alignment and tumbling of rigid fibers in two-dimensional turbulent shear flow

Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess, rod-shaped particles embedded in a two-dimensional turbulent flow with homogeneous shear. A Lagrangian stochastic model for the rods angular dynamics is introduced and compared to the results of direct numerical simulations. The model consists in superposing a short-correlated random component to the steady large-scale mean shear, and can thereby be integrated analytically. To reproduce the single-time orientation statistics obtained numerically, it is found that one has to properly account for the combined effect of the mean shear, for anisotropic velocity gradient fluctuations, and for the presence of persistent rotating structures in the flow that bias Lagrangian statistics. The model is then used to address two-time statistics. The notion of tumbling rate is extended to diffusive dynamics by introducing the stationary probability flux of the rods unfolded angle. The model is found to reproduce the long-term effects of an average shear on the mean and the variance of the fibres angular increment. Still, it does not reproduce an intricate behaviour observed in numerics for intermediate times: the unfolded angle is there very similar to a L\'evy walk with distributions of increments displaying intermediate power-law tails.

A tailored passive driver for liver MRE in pediatric patients.

Magnetic resonance elastography (MRE) is increasingly used in the pediatric population for diagnosis and staging of liver fibrosis. However, the MR-compatible driver and sequences are usually those used for adult patients. Our feasibility study aimed to adapt the standardized adult MRE passive driver and vibrational parameters to a pediatric population. We designed an elliptic passive driver shaped on a torus equipped with an elastic membrane and adapted to children's morphologies. As a first step, eight children (aged 8-18 years) were enrolled in a prospective pilot study aiming to determine the threshold vibrational amplitude for MRE using a custom passive driver, based on phase aliasing assessment and the occurrence of signal void artifacts on magnitude MR images. In the second step, the practicality and the consistency of the custom driver were assessed in a further 11 pediatric patients (aged 7-18 years). In the third step, we compared our custom driver vs. the commercial driver on six adult volunteers, in terms of the reliable region of interest area within the acquired MRE slices, the shear wave maps' quality, and measured stiffness values obtained. Based on pediatric patient data, the threshold vibrational amplitude expressed as percentage of maximum output was found to be 0.4 and 1.1 times the body weight (kg) at 40 and 60 Hz frequencies, respectively. In comparison to the commercial passive driver, the custom driver improved threefold the contact with the body surface, also enabling a more comfortable examination as self-assessed by the volunteers. Our custom driver was more comfortable for the volunteers and was able to generate more homogenous shear waves, yielding larger usable hepatic area, and more reliable stiffness values.

Mini- and macro-scale direct perfusion bioreactors with optimized flow for engineering 3D tissues.

Bioreactors enabling direct perfusion of cell suspensions or culture media through the pores of 3D scaffolds have long been used in tissue engineering to improve cell seeding efficiency as well as uniformity of cell distribution and tissue development. A macro-scale U-shaped bioreactor for cell culture under perfusion (U-CUP) has been previously developed. In that system, the geometry of the perfusion chamber results in rather uniform flow through most of the scaffold volume, but not in the peripheral regions. Here, the design of the perfusion chamber has been optimized to provide a more homogenous perfusion flow through the scaffold. Then, the design of this macro-scale flow-optimized perfusion bioreactor (macro-Flopper) has been miniaturized to create a mini-scale device (mini-Flopper) compatible with medium-throughput assays. Computational fluid dynamic (CFD) modeling of the new chamber design, including a porous scaffold structure, revealed that Flopper bioreactors provide highly homogenous flow speed, pressure, and shear stress. Finally, a proof-of-principle of the functionality of the Flopper systems by engineering endothelialized stromal tissues using human adipose tissue-derived stromal vascular fraction (SVF) cells has been offered. Preliminary evidence showing that flow optimization improves cell maintenance in the engineered tissues will have to be confirmed in future studies. In summary, two bioreactor models with optimized perfusion flow and complementary sizes have been proposed that might be exploited to engineer homogenous tissues and, in the case of the mini-Flopper, for drug testing assays with a limited amount of biological material.

Effect of heat source on kinetic energy transfer in compressible homogeneous shear turbulence

The effects of heat sources on kinetic energy transfer in compressible homogeneous shear turbulence are studied using numerical simulations at turbulent Mach numbers 0.1 and 0.4 for two levels of heat source. It is found that the strong heat source can significantly enhance both positive and negative components of subgrid-scale (SGS) kinetic energy flux and pressure–dilatation. After adding a strong heat source, compression motions enhance the positive SGS flux, and expansion motions enhance the negative SGS flux at a low turbulent Mach number. According to the Helmholtz decomposition, we found that the solenoidal and dilatational components of pressure–dilatation and SGS kinetic energy flux are increased greatly by a strong heat source at a low turbulent Mach number. The solenoidal mode plays a dominant role in the kinetic energy transfer process, but the contribution of the dilatational mode is not negligible. The dilatational component of the production term is increased by a strong heat source at a low turbulent Mach number, providing the main source of kinetic energy to the dilatational mode. The strong heat source also enhances the kinetic energy exchange between solenoidal mode and dilatational mode through nonlinear advection at a low turbulent Mach number. Moreover, the strong heat source enhances pressure anisotropy, redistribution of the kinetic energy of two transverse components, and energy transfer from internal energy to the kinetic energy through pressure–dilatation term. At a high turbulent Mach number, the strong heat source has little impact on the solenoidal and dilatational components of kinetic energy transfer terms.

Effect of cutting speed on shear band formation and chip morphology of Ti–6Al–4V alloy using nanoindentation and EBSD mapping

The hardness and orientations of the primary α grains (αp) and the transformed β (βt) grains in segmented chips obtained by turning an as-received solution treated-and-aged bar of Ti–6Al–4V (wt.%) at cutting speeds of 1, 1.5 and 2 m/s (61, 91, and 122 m/min) were analyzed using nanoindentation mapping and electron backscattered diffraction (EBSD) maps. The hardness of each αp grain in the as-received Ti–6Al–4V bar highly depends on the crystal orientation, varying from 4.5 GPa to 6.7 GPa, and the hardness values of βt were about 20% lower. In the machined chips, αp grains showed hardness values similar to the as-received material while βt became slightly harder. The homogeneous shear strain within the segments (between shear bands) was estimated to be around 0.4–0.7 at all three cutting speeds. The width of the shear bands in the 1 and 1.5 m/s chips were ∼1.3 μm and ∼2 μm in the 2 m/s chips, which are 10–40% of thicknesses predicted by Molinari's isotropic continuum model, respectively. A smaller homogeneous shear strain was correlated with larger shear cracks at each cutting speed. Grain orientations favored by prism ⟨a⟩ slip in αp when cutting at 1 m/s made the localized shear band less “adiabatic” since both the shear stress and strain were lower when these orientations were dominant. In contrast, in orientations that favored pyramidal <c+a> slip, the αp grains experienced much higher shear stress and more localized shear strain when cutting at 2 m/s, leading to higher temperatures that were much more likely to induce the α to β phase transformation. A transformation to soft β phase during shearing accelerates plastic instabilities. These observations and comparisons with finite element simulations indicate that temperatures reached the α+β phase field locally, and higher cutting speeds led to more β phase that is detrimental to the tool life.

Atomistic investigation of modulating structural heterogeneities to achieve strength-ductility synergy in metallic glasses

Structural heterogeneities, i.e., spatial fluctuations of free volume, are of vital importance to the plasticity of irradiation-rejuvenated metallic glasses (MGs), but the mechanisms on how they affect the irreversible deformation and strength remain poorly understood. To address this issue, with the help of atomistic simulations, we systematically investigate the effect of structural heterogeneities on the mechanical behavior of tailored heterogenous MGs with uniformly distributed rejuvenated phases from several critical aspects such as pattern distribution, volume fraction and size effect. The results revealed that the periodically arranged soft rejuvenated phases with low diagonal orientation, high volume fraction and fine phase size alleviate the propensity of strain localization during the tensile deformation, hence promote the homogenous-like plastic flow mediated by the mass of homogenous shear transformation zones (STZ) operations. More importantly, the strength-ductility synergy of MGs was achieved at the given volume fraction of the rejuvenated phases via properly designing the arrangements of the heterogenous phases. The present study sheds light on the atomistic understanding of the relationship between the structural heterogeneity of rejuvenated amorphous structures and mechanical properties in MGs, which can provide useful insights for designing or processing MGs with a strength-ductility synergy.

Turbulence in Two-Phase Flows with Macro-, Micro- and Nanoparticles: A Review

Turbulent flows are nonstationary in nature. Since the turbulent fluctuations of most flow parameters satisfy a symmetric Gaussian distribution, the turbulent characteristics have the property of symmetry in the statistical meaning. A widespread simplest model of turbulent flows is the model of “symmetric” turbulence, namely, homogeneous isotropic turbulence (HIT). The presence of particles with non-uniform distribution of their concentration in the turbulent flow, even under HIT conditions, can lead to redistribution of different components of fluctuation velocities of the carrier gas, i.e., to the appearance of asymmetry. The subject of the review is turbulent flows of gas with solid particles. Particular attention is paid to the problem of the back influence of particles on carrier gas characteristics (first of all, on the turbulent kinetic energy). A review of the results of experimental and computational-theoretical studies of the effect of the presence of the dispersed phase in the form of particles on the parameters of the turbulent flow of the carrier gas phase has been carried out. The main physical mechanisms and dimensionless criteria determining the direction and magnitude of the impact of particles of different inertia on the carrier gas phase turbulence energy are described and analyzed. The peculiarities of the influence of particles on the turbulence energy of the gas for different classes of flows: homogeneous isotropic turbulence, homogeneous shear flow, and wall turbulence in a pipe (channel) have been considered. For the near-wall flow in the pipe, it is shown that the turbulizing effect of extremely low-inertia particles of sub-micrometer size (nanoparticles) is replaced by the laminarizing effect of low-inertia particles of micrometer size (microparticles), and then again it is replaced by turbulizing due to additional generation of turbulence in the wakes of large particles of millimeter size (macroparticles). The review is intended to some extent to fill in the currently existing gap associated with the absence of dimensionless criteria (or complexes of physical parameters) responsible for the direction (attenuation or enhancement) of turbulence modification, and the value of this change. Possible directions for further researches are given in the conclusion of the review.

A Semi-Analytical Method for Channel and Pipe Flows for the Linear Phan-Thien-Tanner Fluid Model with a Solvent Contribution

This work presents a semi-analytical method for laminar steady-state channel and pipe flows of viscoelastic fluids using the Linear Phan-Thien-Tanner (LPTT) constitutive equation, with solvent viscosity contribution. For the semi-analytical method validation, it compares its results and two analytical solutions: the Oldroyd-B model and the simplified LPTT model (without solvent viscosity contribution). The results adopted different values of the dimensionless parameters, showing their influence on the viscoelastic fluid flow. The results include the distribution of the streamwise velocity component and the extra-stress tensor components in the wall-normal direction. In order to investigate the proposed semi-analytical method, different solutions were obtained, both for channel and pipe flows, considering different values of Reynolds number, solvent viscosity contribution in the homogeneous mixture, elongational parameter, shear parameter, and Weissenberg number. The results show that the proposed semi-analytical method can find a laminar solution using the non-Newtonian LPTT model with solvent viscosity contribution and verify the effect of the parameters in the resulting flow field.

Wind turbine wake simulation with explicit algebraic Reynolds stress modeling

Abstract. Reynolds-averaged Navier–Stokes (RANS) simulations of wind turbine wakes are usually conducted with two-equation turbulence models based on the Boussinesq hypothesis; these are simple and robust but lack the capability of predicting various turbulence phenomena. Using the explicit algebraic Reynolds stress model (EARSM) of Wallin and Johansson (2000) can alleviate some of these deficiencies while still being numerically robust and only slightly more computationally expensive than the traditional two-equation models. The model implementation is verified with the homogeneous shear flow, half-channel flow, and square duct flow cases, and subsequently full three-dimensional wake simulations are run and analyzed. The results are compared with reference large-eddy simulation (LES) data, which show that the EARSM especially improves the prediction of turbulence anisotropy and turbulence intensity but that it also predicts less Gaussian wake profile shapes.

Self-diffusion in inhomogeneous granular shearing flows.

In this Letter, we discuss how flow inhomogeneity affects the self-diffusion behavior in granular flows. Whereas self-diffusion scalings have been well characterized in the past for homogeneous shearing, the effect of shear localization and nonlocality of the flow has not been studied. We, therefore, present measurements of self-diffusion coefficients in discrete numerical simulations of steady, inhomogeneous, and collisional shearing flows of nearly identical, frictional, and inelastic spheres. We focus on a wide range of dense solid volume fractions, that correspond to geophysical and industrial shearing flows that are dominated by collisional interactions. We compare the measured values first with a scaling based on shear rate and, then, on a scaling based on the granular temperature. We find that the latter does much better than the former in collapsing the data. The results lay the foundations of diffusion models for inhomogeneous shearing flows, which should be useful in treating problems of mixing and segregation.

On the origin of shear-band network patterns in ductile shear zones

Ductile yielding of rocks and similar solids localize shear zones, which often show complex internal structures due to the networking of their secondary shear bands. Combining observations from naturally deformed rocks and numerical modelling, this study addresses the following crucial question: What dictates the internal shear bands to network during the evolution of an initially homogeneous ductile shear zone? Natural shear zones, observed in the Chotonagpur Granite Gneiss Complex of the Precambrian craton of Eastern India, show characteristic patterns of their internal shear band structures, classified broadly into three categories: type I (network of antithetic low-angle Riedel (R) and synthetic P-bands), type II (network of shear-parallel C and P/R bands) and type III (distributed shear domains containing isolated undeformed masses). Considering strain-softening rheology, our two-dimensional viscoplastic models reproduce these three types, allowing us to predict the condition of shear band growth with a specific network pattern as a function of the following parameters: normalized shear zone thickness, bulk shear rate and bulk viscosity. This study suggests that complex anastomosing shear-band structures can evolve under simple shear kinematics in the absence of any pure shear component.

Single-lap joint creep behaviour of two soft adhesives

ABSTRACT Two hot melt pressure sensitive adhesives have been submitted to bonded joint creep tests. An amorphous and a semicrystalline adhesives have been considered for their different microstructures leading to different mechanical behaviors. The adhesives are referred as soft since their glass transition temperatures stand well below the temperatures of applications, resulting in low stiffnesses. The creep of structural joints has been characterized with single-lap joint tests. Two types of adherends were considered either glass or stainless steel. The adherend roughness and the adhesive wettability have been characterized before testing. The significant stiffness contrast between the stiff adherends and the soft adhesives promoted homogeneous simple shear creeps. The amorphous adhesive showed creep behaviors that depend on the type of substrates, showing that the joint viscoelasticity could not be predicted knowing the bulk adhesive viscoelasticity only, unlike for stiff adhesives as recently reported in the literature. Finally, the single-lap joint creep behaviors of both adhesives on the same glass adherends were compared and discussed at the light of their different microstructures inducing different mechanical behaviors.

Influence of accelerated corrosion on bi-material steel-CFRP double-lap joints bonded with thick adhesive

Bi-material steel-composite joints attract interest for marine applications. The marine environment imposes corrosion which is a prolonged process. This work presents a two-electrode electrochemical setup for accelerating free corrosion of the steel surfaces of bi-material joints. It is used to study the impact of accelerated corrosion on the mechanical performance of bi-material double lap specimens subjected to quasi-static tensile testing. Several test series have been conducted to evaluate the influence of overlap length and bond line thickness on shear strength and failure mode. Sixty specimens with a thick layer of methyl methacrylate adhesive have been fabricated and cured at room temperature for at least 24 h. Subsequently, 30 specimens were aged by subjecting them to electrochemical corrosion for 24 h. All specimens were tested for failure in quasi-static tensile loading while monitoring the strain fields in the joint area using digital image correlation. The measurements reveal a homogeneous shear strain field at the onset of loading, with a rapidly increasing shear strain concentration near the edges of the bond line preceding final failure. Both a decrease in the adhesive thickness and an increase in the overlap length increase the shear strength. Higher shear strength was observed for the electrochemically aged specimens than that of non-aged specimens. This is attributed to the faster residual curing of the adhesive during ageing because an increasing percentage of copper ions (released from the anode) accelerates the curing of the MMA adhesive. The electrochemically aged specimens showed mixed failure modes, i.e. cohesive failure and adhesive failure at the interface between steel and adhesive, and skin failure within the composite laminates.

Spatial correlation of irreversible displacement in oscillatory-sheared metallic glasses

We report computer simulations on the oscillatory of CuZr metallic glasses at zero temperature with different shear amplitudes. In small system a homogenous shear deformation is found, while in large system an inhomogeneous shear deformation is found with a shear band formed. Concomitantly, spatial correlation of irreversible displacement exhibits an isotropic and exponential decay in the case of homogeneous deformation, whereas a mixed power-law and exponential decay in the case of anisotropic and inhomogeneous deformation. By projecting the azimuthal-dependent correlation function onto the spherical harmonics, we found a strong polar symmetry that accounts for the emerged shear band, and a weaker quadrupolar symmetry that accounts for the elastic filed generated by Eshelby inclusions. By this, we conclude that the anisotropy and decaying formula of the plastic correlation are dominated by the homogeneity or inhomogeneity for the deformation in the metallic glasses.