Apparent Internal Friction Research Articles

The Measurement of Shear Characteristics of Paddy Soil in Poyang Lake Area

Understanding the shear characteristics of paddy fields is of great significance for the design of high-trafficability paddy wheels and to improve the trafficability of the tiller in paddy fields. Taking the paddy soil in Poyang Lake area of Jiangxi Province as the research object, a simple, self-designed bevameter was constructed to measure the apparent cohesion c and apparent internal friction angle φ of paddy soil with water content of 37% by weight using an annular shear plate. The effects of different shear speeds, shear grouser heights, and shear plate diameters on the measured c and φ were investigated. The measured values of c and φ were 1.89–2.35 kPa and 10.2–11.4°(deg), respectively. With the increase in shear speed, shear plate diameter, and grouser height, the value of c increased. Shear plate diameter and shear speed had small effect on c, whose change rate did not exceed 7.8%. However, shear grouser height had a greater influence on c, and the measured c increased by 24.5%. The influence of the three factors on φ followed the order: shear speed > shear plate diameter > shear grouser height, but the variation in φ did not exceed 1.2°(deg). The optimal operational conditions were: shear plate diameter of 250 mm with inner diameter of 150 mm, shear grouser height of 10 mm, with a shear speed of π/120 rad/s, and the apparent cohesion and apparent internal friction angle are 1887.8 pa and 11.06° (deg), respectively.

Basic Mechanical Properties of Wet Granular Materials: A DEM Study

Numerical simulations, by the discrete element method (DEM), of a model granular assembly, made of spherical balls, are used to investigate the influence of a small amount of an interstitial wetting liquid, forming capillary bridges between adjacent particles, on two basic aspects of granular material rheology: (1) the plastic response in isotropic compression, and (2) the critical state under monotonic shear strain, and its generalization to steady, inertial flow. Tensile strength F0=πΓa, in contacts between beads of diameter aa joined by a small meniscus of a liquid with surface tension Γ, introduces a new force scale and a new dimensionless control parameter, P∗=a2P/F0, for grains of diameter a under confining stress P. Under low P*, as cohesion dominates, capillary cohesion may stabilize very loose structures. Upon increasing pressure P in isotropic compression, such structures gradually collapse. The resulting irreversible compaction is well described by the classical linear relation between logP* and void ratio in some range, until a dense structure forms that retains its stability without cohesion as confinement dominates for large P*. In steady shear flow, with uniform velocity gradient γ˙=∂v1/∂x2γ˙=∂v1/∂x2 under normal stress P=σ22, the apparent internal friction coefficient, which is defined as μ∗=σ12/σ22, depends on P* and inertial number (reduced shear rate) I=γ˙√m/aP, and so does solid fraction Φ. The material exhibits, as P* decreases, a strongly enhanced resistance to shear (larger μ*). In the quasistatic limit, for I→0, it is roughly predicted by a simple effective pressure assumption by which the capillary forces are deemed equivalent to an isotropic pressure increase applied to the dry material as long as P*≥1, while the yield criterion approximately assumes the Mohr-Coulomb form. At lower P*, such models tend to break down as liquid bonding, causing connected clusters to survive over significant strain intervals, strongly influences the microstructure. Systematic shear banding is observed at very small P*

Dependence of Internal Friction on Native Topology

Apparent internal friction has been identified in the folding rates of several proteins and in the dynamics of unfolded proteins, via their dependence on solvent viscosity. Theoretical and computational studies have attributed this phenomenon, at least in part, to local barrier crossing events, in particular torsion angle isomerizations. However, there are still many systems for which no internal friction has been observed in experiment, and others for which the effect is only weak. Here, we elucidate the origin of this discrepancy by studying a model system whose native state can be either an α-helix or a β-hairpin. Remarkably, we find clear apparent internal friction for the helix, but no evidence of it for the hairpin. These results are consistent with the observation that proteins whose folding rates exhibit internal friction tend to be α-helical. We can explain the difference by examining the occurrence of torsional transitions along the folding coordinate of the hairpin and helix. Finally, we consider the folding of the Trp cage mini protein, whose structure includes both helical and hairpin elements. We obtain two barriers -- the major barrier for formation of the hairpin and a minor barrier for initial helix formation, allowing us to dissect the contribution of internal friction to different parts of the energy landscape. We find a clear signature of internal friction for the helical barrier and, within the uncertainty of our calculation, little internal friction for the hairpin barrier. Our results show how variation of solvent viscosity can be used to probe features of folding mechanisms.

Stick-slip behaviour of model granular materials in drained triaxial compression

Drained triaxial axisymmetric compression tests are performed on water-saturated short cylindrical samples of nearly monodisperse glass beads, initially assembled in a loose state by a moist tamping technique. Both deviator stress \(q\) and volumetric strain \(\epsilon _v\), measured as functions of axial strain \(\epsilon _a\), for different strain rates, are affected by stick-slip events of very large amplitude, while the classical behavior of loose, contractant granular assemblies, approaching the critical state for large \(\epsilon _a\), corresponds to the upper envelop of the stress-strain behaviour. Those events consist in \((i)\) a very fast (slip) part in which a drop of \(q\) coincides with a jump of \(\epsilon _v\) (contraction), while loss of control of \(\epsilon _a\) and generation of pore pressure signal a dynamic collapse of the material structure triggered by an instability; and then \((ii)\) a quasi-static (stick) part in which the sample regains its strength and, over a short strain interval, behaves similarly to a denser system that dilates before reaching its critical state. A unique stress-dilatancy relation applies to all stick-slip events. Apparent internal friction angles and effects of strain rate and confining pressure are discussed, and it is argued that stick-slip instabilities originate in physico-chemical aging phenomena coupled to contact mechanics.

A Model with Two Elastically Coupled Reaction Coordinates for the Internal Friction of Proteins

The rates of protein conformational changes are usually not only limited by external but also internal friction, however, the origin and significance of this latter phenomenon is poorly understood. It is often found experimentally that a linear fit to the reciprocal of the reaction rate as a function of the viscosity of the external medium has a non-zero value at zero viscosity, signifying the presence of internal friction. Furthermore, some of the experiments performed at different temperatures indicate that the internal friction follows an Arrhenius-like temperature dependence. To explain these phenomena we suggest a simple model for protein conformational changes in terms of two elastically coupled reaction coordinates, one of which being in contact with the external medium, and the other one experiencing the rough energy landscape of the protein. Our analytical calculations, supplemented with numerical simulations demonstrate that depending on the coupling strength (which is related to the flexibility of the protein) the short-wavelength components of the energy landscape roughness can be observed as an increased apparent internal friction with an apparent activation energy.

Protein Flexibility Partitions the Effects of Energy Landscape Roughness Between Activation Energy and Internal Friction

The rate of protein conformational changes are usually not only limited by external but also internal friction, however, the origin and significance of this latter phenomenon is poorly understood. By investigating the internal friction during the activation of two trypsin mutants at various temperatures and external viscosities we have discovered that the temperature dependence of the internal friction shows an Arrhenius-like behavior. The characteristic energy of the Arrhenius formula, however, can change dramatically upon the replacement of a single amino acid at a hinge position (thereby affecting the flexibility of the protein), or by crossing a critical temperature. At the same time, the activation energy of the conformational transition also changes with a similar magnitude, but in the opposite direction. These observations shed light on the intricate interplay between the apparent internal friction and activation energy. Moreover, we have found that the more flexible a protein is the greater proportion of its activation energy is partitioned into internal friction. All these results have allowed us to come to the general conclusion that the different hierarchical levels of the roughness of the energy landscape along a conformational transition can be observed as either activation energy or internal friction depending on the degree of flexibility of the protein.

Grain-scale mechanics of geologic materials and lunar simulants under normal loading

A realistic characterization of contact behavior is crucially important to the development of discrete element models of naturally occurring granular media. Although contact behavior can be inferred by adjusting the numerical simulations to agree with results from geotechnical laboratory tests, it is preferable to establish the contact laws directly with grain-scale experiments. Moreover, such an approach provides an objective way to establish the influence of characteristics such as mineralogy, microstructure, hardness, grain size, shape and surface roughness on contact behavior, and thus opens the door to a more fundamental understanding of granular media mechanics. With this motivation, we are conducting an integrated experimental/DEM modeling program with a focus on naturally occurring geologic materials. The goals of this work are to improve the physical basis of this powerful numerical modeling method, and to develop a broader understanding of the contact behavior of naturally occurring materials of interest to the geotechnical engineering community. This paper describes equipment and methods that we have developed to conduct normal contact experiments on pairs of unbonded grains of crushed and ball-milled gneiss, Ottawa sand, and lunar simulants. Contact curvatures ranged from 0.05 to 8.2 mm for the grains examined. The computer-controlled testing system applied normal forces ranging up to 10 N, and both monotonically increasing (ramp) and cyclic loading waveforms were employed. A laser proximity gauge with 100 μm resolution provided direct grain-to-grain deformation readings. The resulting force–displacement relationships showed that Hertzian behavior emerged above a normal force threshold ranging from several tenths of a Newton to several Newtons, depending on surface roughness, and approximately linear behavior was observed below the threshold for Hertzian behavior. Normal contact stiffness ranged from 0.2 to over 2 MN m−1 for forces up to 10 N, and depended on material type, local radius of curvature and surface roughness. Hysteresis was generally observed under cyclic loading and calculated values of the apparent internal friction ranged from 0.01 to 0.16, depending on material type, contact geometry and force level. The test system was capable of inducing damage in some contacts with a low radius of curvature, and it was observed that minor levels of damage typically increased stiffness and frictional loss of the contact.

Excess pore pressure generation potential within shear zone by means of ring shear tests

Excess pore pressure generation potential within shear zone by employment of the ring shear tests have been investigated on the saturated samples which have quite different grain crushing susceptibility. In naturally drained tests, the sample the grains of which are crushable showed the great reduction of apparent internal friction during shearing to generate rapid flow phenomena. Based on the results of permeability and grain size analyses, it is estimated that the crushed particles formed the less-permeable shear zone and excess pore pressure generation rate exceeded the dissipation rate to yield flow behaviour, and it occurred heavily in high shear speed or normal stress tests. And to express the susceptibility of the samples against flows, the new parameter “potential for rapid flow phenomena” was proposed as the ratio of internal friction angle (φm) to apparent friction angle (φa).In order to estimate the excess pore pressure in undrained condition from the drained tests, the concept of “equivalent normal stress” was introduced as the ratio of volumetric strain to the compressibility. Equivalent normal stress using compressibility which was obtained by changing normal stress during shearing was almost equal to excess pore pressure at the same shear displacement up to 1 m at which steady state was reached. And Excess pore pressure ratio in undrained tests and the logarithm of equivalent normal stress divided by normal stress with compressibility obtained during consolidation process showed the linear relationship.

Dynamics of stiff polymer chains

The dynamics of worm-like polymer chains is considered for models with constrained bond lengths and elastic or constrained bond angles. Previous work attempted either the representation of the constraints on a complete basis set, which is impractical for chains of more than a few bonds, or the analytical preaveraging of inverse constraint matrices, which is too crude an approximation for local motions. Here the constraint matrices are evaluated from equilibrium simulations. A comparison of the analytical results with dynamical simulations shows good agreement for both global and local motions, indicating that the relevant memory in chains without rotational barriers does not extend past vibrational relaxation times. The dynamical diffusion operator is diagonal on a Rouse basis set to an adequate approximation, indicating that the effects of constraints can be imitated by the inclusion of internal friction in the basic Langevin equation. The internal friction approximation is useful even for extremely stiff chains, and the dependence of the apparent internal friction on mode number, chain stiffness, and chain length is examined. With fluctuating hydrodynamic interaction included, the constraints generate a coupling between local motions and translational diffusion which causes a small decrease in the translational diffusion constant. The effects are similar to those found in a previous phenomenological study of the effects of internal friction on translational diffusion, and do not seem to vanish with increasing chain length.

Internal friction study on structural relaxation of metallic glasses

During structural relaxation of a glassy matrix, the apparent internal friction (Q-1) decreased with the increase of annealing time (t). The dependence of Q-1 on t can be shown as Q-1=At-β+B, where A, B and β are constants.

Internal friction of metallic glass Ni74P16B6Al4 near Tx

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Partially Activated Human Skeletal Muscle: An Experimental Investigation of Force, Velocity, and EMG

Experiments are described which establish quantitative relations between muscular force, contraction velocity, and the electrical activity of the muscle (as measured by the surface EMG) under conditions of steady motion. The six subjects who participated in these experiments were all athletes. Test results confirm that human skeletal muscle in vivo behaves differently when it is contracting under load than when it is extending under load. At maximum voluntary effort the force-velocity relation is similar to that found for excised, tetanized muscle (Hill’s equation). Antagonist activity was found to be low under all conditions of load and velocity. Simple equations are proposed to describe the observed force-velocity-activation relations. The parameters of these equations, which represent the apparent internal friction properties of the muscles, are evaluated and reported.

A Simplified Method for Calculation of Strain Dependence of Internal Friction in Transverse Vibrations

Damping phenomena in higher modes of free-free transverse vibration are analysed and tire effects of the distribution of the vibrational strain on the apparent internal friction are treated quantitatively. The functional relation of the observed internal friction with the maximum strain amplitude or the maximum displacement amplitude is different when different mode of vibration is used. A simplified method for finding the true strain amplitude dependence of the internal friction is presented where the average strain amplitude is used as an experimental variable. It is suggested that the amplitude-dependent part of the internal friction can be dependent on the frequency of the vibration.