Frictionless Walls Research Articles

Investigation on the responses of geotechnical materials to unloading and seepage based on the CFD-DEM coupling method

The unloading issue is prevalent in underground engineering and significantly affects construction safety and the operation of surrounding facilities, while research regarding it is still relatively scarce. A novel CFD-DEM coupling method with dynamic fluid meshes is proposed to reproduce the unloading effect and reveal its micro-scale mechanisms. It adopts uniformly distributed point sets to generate/update fluid meshes and solves with a proposed numerical mapping method. The one-dimensional linear unloading modeling method is further established. The numerically obtained excess pore pressure and rebound deformation under the one-way drained condition are compared with the analytical solutions. The coupling method demonstrates considerable reliability in forecasting the pore pressure response and its advantage for predicting rebound deformation is revealed. The evolutions of the fluid velocity field, particle displacement field, and pore pressure distribution profile are described. The influences of fluid compressibility, unloading rate, unloading volume and initial pore pressure on the unloading characteristics are carefully investigated. The results indicate that the pore pressure is obviously influenced by the selected factors. However, the impact of unloading volume on the final rebound deformation is most significant. Finally, influences of frictionless walls, two-way drained conditions, buoyancy and fluid viscosity on the unloading response are further discussed.

Study of Strain-rate Effect in Two-dimensional Biaxial Test on Granular Material using Discrete Element Method

Numerical study to investigate the effect of various strain rates on global friction angle in the sand has been performed. Granular material behavior is influenced by several factors, among others: pack configuration, grain macro and micro roughness, confinement pressure, loading rate, etc. Sand is a granular material composed of discrete particles that the most refined microscopic techniques are needed to study its mechanical properties. In Indonesia, research related to the Discrete Element Method is still very limited. The two-dimensional discrete element method is capable to calculate the motion and interparticle contacts of large number of small particles, and each particle is modeled as a rigid circular element. The study started with the validation of the DEM model using YADE. Particles with a local friction angle of 35° are arranged in a closed rectangular box (frictionless wall). The number of particles used in this model validation simulation is 1000 sphere-type particles with monodisperse particle gradations. The simulation was done by a drained biaxial test with confinement stress of 100 kPa, thereafter varying strain rate are applied. Based on the deviatoric stress–axial strain curve from YADE, the result can be depicted on the Mohr circle to obtain the value of the global friction angle. It is found that the different value of strain rate affects its global friction angle. Increasing the value of the strain rate can increase the material global friction angle, which increases the strain rate from 1% to 5%, 10%, 25%, and 50% will increase its global friction angle by 5%, 5%, 14%, and 18%, respectively.

Analytical Scaling Solutions for the Evolution of Cosmic Domain Walls in a Parameter-Free Velocity-Dependent One-Scale Model

We derive an analytical approximation for the linear scaling evolution of the characteristic length L and the root-mean-squared velocity σv of standard frictionless domain wall networks in Friedmann–Lemaître–Robertson–Walker universes with a power law evolution of the scale factor a with the cosmic time t (a∝tλ). This approximation, obtained using a recently proposed parameter-free velocity-dependent one-scale model for domain walls, reproduces well the model predictions for λ close to unity, becoming exact in the λ→1− limit. We use this approximation, in combination with the exact results found for λ=0, to obtain a fit to the model predictions valid for λ∈[0,1] with a maximum error of the order of 1%. This fit is also in good agreement with the results of field theory numerical simulations, especially for λ∈[0.9,1]. Finally, we explicitly show that the phenomenological energy-loss parameter of the original velocity-dependent one-scale model for domain walls vanishes in the λ→1− limit and discuss the implications of this result.

On the post-buckling behavior of laterally constrained multilayers

Material layering occurs in natural, biological, geological and synthetic load-bearing structures. The bucking and post-buckling behavior of such structures is a subject of great interest. While many studies were devoted to the case of a thin film attached to a thick substrate, little is available on the behavior of multilayers. We explore this subject using a model system consisting of 2-D, linearly elastic hard/soft multilayer under uniform edge displacement. The lateral edges of the multilayer are constrained by rigid, frictionless walls. The number of stiff layers n and layer-to-interlayer thickness and elastic moduli ratios, h and E, are systematically varied. The deformation and stresses in the multilayer are obtained with the aid a FEA. Buckling initiates in the interior layers and spreads to the outer ones. The layers adjacent to the constraining walls tend to flatten as the load is increased. For relatively large h or small E, this causes large membrane stresses that may lead to a buckling mode transition. As many as ≈ 50 stiff layers are needed in order for the multilayer to approach a laminate configuration (n ≫ 1). The multilayer as a whole displays nonlinear elastic stress–strain response. By a proper choice of the system variables n, h and E, a variety of strain hardening effects as well as large energy absorption can be achieved. The results of this study provide useful insights into the effects of b.c., material choice and load level on the response of multilayers in general.

Self-diffusivity of dense confined fluids

Molecular transport through tight porous media is crucial to shale gas exploration, but deeper insights of the elemental physics are still required, particularly under high pressures and nanoscale confinements, where Navier–Stokes and Boltzmann solutions are no longer valid. In this work, we carry out a fundamental and systematic study of self-diffusion using event-driven molecular dynamics simulations, varying fluid rarefaction, confinement, and surface friction. We differentiate between fluid–fluid and fluid-wall collisions to identify the interplay of the underpinning diffusive mechanisms, namely, molecular and Knudsen diffusion. We find that the Bosanquet formula, which has been used for describing rarefied gases, is also able to provide a good semi-analytical description of self-diffusivities in confined dense fluids, as long as the pore height is not smaller than five molecular diameters. Importantly, this allows us to predict the self-diffusion coefficient, regardless of the fluid rarefaction, confinement state, and surface roughness, in a wide range of Knudsen numbers that were not possible before. Often as a source of debate, we prove here that despite strong fluid inhomogeneities arising in these conditions, the Einstein self-diffusivity can still be used within Fick's law, provided boundary effects are considered when using Fick's setup. Finally, we notice that a previously identified linear scaling of self-diffusivities with confinement is only valid in the limit of low densities and frictionless walls, which is not representative of shale reservoirs. This work will serve as a foundation for investigating the anomalous gas transport behavior observed in the recent work of dense, confined fluids.

Modeling the Contact Mechanics of Hydrogels

A computationally lean model for the coarse-grained description of contact mechanics of hydrogels is proposed and characterized. It consists of a simple bead-spring model for the interaction within a chain, potentials describing the interaction between monomers and mold or confining walls, and a coarse-grained potential reflecting the solvent-mediated effective repulsion between non-bonded monomers. Moreover, crosslinking only takes place after the polymers have equilibrated in their mold. As such, the model is able to reflect the density, solvent quality, and the mold hydrophobicity that existed during the crosslinking of the polymers. Finally, such produced hydrogels are exposed to sinusoidal indenters. The simulations reveal a wavevector-dependent effective modulus E * ( q ) with the following properties: (i) stiffening under mechanical pressure, and a sensitivity of E * ( q ) on (ii) the degree of crosslinking at large wavelengths, (iii) the solvent quality, and (iv) the hydrophobicity of the mold in which the polymers were crosslinked. Finally, the simulations provide evidence that the elastic heterogeneity inherent to hydrogels can suffice to pin a compressed hydrogel to a microscopically frictionless wall that is undulated at a mesoscopic length scale. Although the model and simulations of this feasibility study are only two-dimensional, its generalization to three dimensions can be achieved in a straightforward fashion.

Comparison of two numerical approaches (DEM and MPM) applied to unsteady flow

In order to provide a comprehensive comparison between two current numerical methods employed in the modelling of rock avalanches, the discrete element method (DEM) and the material point method (MPM) were used to simulate the mass propagation along a $$45^{\circ }$$ plane transitioning to a horizontal plane. For the DEM simulations, an in-house 3D code whose particles can be modelled as tetrahedral elements was used. Additionally, the flow was canalised using frictionless walls. For the MPM simulations, a 2D code was also developed and employed to run plane strain simulations. Comparisons were made in terms of runout distance, spreading and energy dissipated. Influence of parameters such as initial sample geometry, basal friction coefficient and shape of blocks composing the sample was studied. We found that there are proper correlations between the two methods when the basal friction coefficient has a low value, or when the rolling of the blocks is hindered by using elongated shapes for the blocks. These correlations become less satisfactory as the basal friction coefficient is increased, due to the oversimplified constitutive law employed in MPM.

Influence of wall friction on granular column**Project supported by the National Natural Science Foundation of China (Grant Nos. 11705256, 11772095, and 11572091) and the National Key Research and Development Program of China (Grant No. 2016YFB0700103).

Granular packings under gravity in frictional and frictionless silos were simulated and the influence of the wall friction on the normal force distribution was investigated. Although there is an obvious Janssen effect in frictional silos, only a slight influence on the geometry of packing was found. The law of normal force distribution is different for frictional and frictionless walls, which is related to the pressure profile. A modified formula with consideration of the pressure profile was well fitted to the simulation results.

Constrained buckling of variable length elastica: Solution by geometrical segmentation

The paper proposes a method to analyze the post-buckling response of a planar elastica subjected to unilateral constraints. The method rests on assuming a deformed shape of the elastica that is consistent with an assumed buckling mode and given unilateral constraints, and on uniquely segmenting the elastica so that each segment is a particular realization of the same canonical problem. An asymptotic solution of the canonical problem, which is characterized by clamped–pinned boundary conditions, is derived using a perturbation technique. The complete solution of the constrained elastica is constructed by assembling the solution for each segment. It entails solving a nonlinear system of algebraic equations that embodies the continuity conditions between the segments and the contact constraints.The method is then applied to analyze the post-buckling response of a planar weightless elastica compressed inside two rigid frictionless horizontal walls. The length of the elastica could be either constant, or variable, but the focus of the analysis is on the response of a variable length elastica, which is gradually inserted inside the conduit. In the insertion problem, a configurational force is generated at the insertion point, which is not present in the classical problem of a constant length elastica (Bigoni et al., 2015).The proposed approach is shown to lead to a simple and accurate numerical technique to simulate the constrained buckling of an elastica. The optimal sequence of equilibrium configurations of the elastica associated with a monotonic force- or displacement-control loading is deduced in accordance with the principle of minimum energy.

Extremely Black Vertically Aligned Carbon Nanotube Arrays for Solar Steam Generation.

The unique structure of a vertically aligned carbon nanotube (VACNT) array makes it behave most similarly to a blackbody. It is reported that the optical absorptivity of an extremely black VACNT array is about 0.98-0.99 over a large spectral range of 200 nm-200 μm, inspiring us to explore the performance of VACNT arrays in solar energy harvesting. In this work, we report the highly efficient steam generation simply by laminating a layer of VACNT array on the surface of water to harvest solar energy. It is found that under solar illumination the temperature of upper water can significantly increase with obvious water steam generated, indicating the efficient solar energy harvesting and local temperature rise by the thin layer of VACNTs. We found that the evaporation rate of water assisted by VACNT arrays is 10 times that of bare water, which is the highest ratio for solar-thermal-steam generation ever reported. Remarkably, the solar thermal conversion efficiency reached 90%. The excellent performance could be ascribed to the strong optical absorption and local temperature rise induced by the VACNT layer, as well as the ultrafast water transport through the VACNT layer due to the frictionless wall of CNTs. Based on the above, we further demonstrated the application of VACNT arrays in solar-driven desalination.

Large deflections of an elastic rod in contact with a flat wall

This paper presents an analytical solution of two types of contact between an elastic rod and a flat frictionless rigid wall. The first problem deals with large deflections of a rod with one end clamped and the other end pushing towards the clamped end by the wall. The second problem deals with the deflections of a rod that is pushed between fixed wedges. The solutions of both problems are given in terms of Jacobi elliptic functions. The solutions are illustrated using several examples, including deformed rod shapes and load-deflection paths.

A generic wear prediction procedure based on the discrete element method for ball mill liners in the cement industry

A generic procedure to predict the wear evolution of lining surfaces, namely the spatial distribution of wear and the progressive modification of the geometry due to wear, is introduced in the context of shell liners in ball mills. The wear data is accumulated on the surface of the liner by 3D discrete element method (DEM) simulations of the ball charge in an axial slice of the mill, which is either closed by a periodic boundary condition or by frictionless end walls. The calibration of this wear data with the measured wear profiles of the shell liner in a 5.8m diameter industrial cement tube mill shows that the tangential damping energy defined by the linear spring-slider-damper DEM contact law is the best fitting wear model of 6 different models. The gradual update of the liner shape delivers adequate results for liners without an axial height variation, while the accuracy of fully variable geometrical modifications is limited by the computation time. Nevertheless, detailed phenomena, like the creation of grooves in the liner, were for the first time numerically modeled.

The Characteristic of Thermoelastic Waves in Transversely Isotropic Finite Cylinders

A theoretical as well as a numerical investigation of the propagation of thermoelastic waves and vibration of transversely isotropic cylinders of finite length is discussed. Lord-Shulman theory is adopted here to model the thermoelastic deformation of cylinders. A semi analytical finite element (SAFE) method is employed to study dispersion of thermoelastic waves and natural frequencies of vibration of finite cylinders with traction free curved surfaces having both ends insulated and constrained by frictionless rigid walls. Numerical results obtained by the SAFE method for the frequencies of vibration of a sapphire rod are found to be in excellent agreement with published results. Natural frequencies of vibration for first three axisymmetric and asymmetric modes are presented graphically for a silicon nitride thermoelastic cylinder. Also, numerical results showing dispersion of both propagating and evanescent circumferential waves in infinite and finite cylinders are presented also.

A comparison between DEM and MPM for the modeling of unsteady flow

In order to provide a comprehensive comparison between two current numerical methods employed in the modeling of rock avalanches, the Discrete Element Method (DEM) [3] and the Material Point Method (MPM) [1] were used to simulate the mass propagation along a 45° plane transitioning to an horizontal plane. When using the DEM, a 3D code using tetrahedral elements was used and the flow was channelized by means of frictionless walls. For the MPM simulations, a 2D code was developed and plane strain simulations were run. Comparisons were made in terms of run-out distance and energy dissipated. Influence of parameters such as initial sample geometry, basal friction coefficient and shape of blocks composing the sample was studied.

Analysis of passive earth thrust in an unsaturated sandy soil using discontinuity layout optimization

This paper addresses a numerical study into passive earth pressure in an unsaturated sandy soil. The computational limit analysis method, discontinuity layout optimization (DLO), is extended to take into consideration the effect of saturation and suction on strength. The extended analysis was utilised to model a retaining wall case study using a sandy soil as a simulated backfill material and the results were compared with Rankine equations which were modified to take into account the capillary rise effect. The numerical results demonstrated that an increase of the total passive thrust up to 47%, for a frictionless wall, at ϕ ′ = 30° due to the effect of partial saturation in the sandy soil.

Limbless locomotion on solid surfaces: a case study in soft bio-inspired robotics

We examine the problem of snake-like locomotion by studying a model system consisting of a planar inextensible elastic rod that is able to control its spontaneous curvature. Using Cosserat theory we derive the equations of motion for two special cases: one in which the system is confined inside a channel with frictionless walls, and one in which the system is placed on an anisotropic frictional environment with an infinite contrast between longitudinal and transversal friction, so that the rod can slide longitudinally along its axis, but cannot slip laterally (i.e., in the transversal direction). The results obtained by solving these equations of motion are reminiscent of classical experimental results in the biological literature, and provide a scheme to rationalise the observed behaviour.

Verification of Rankine Earth Pressure Theory Using Finite Element Analysis with Elastic-Plastic Material

To simulate the Rankine earth pressure theory in the finite element analysis, a frictionless rigid wall and backfill system supported by rollers can be used. Beginning from the initial at-rest pressure conditions, the wall is moved towards or away from the backfill in a series of increments, until the passive or active earth pressure condition is reached. To obtain numerical solutions, twenty-five finite isoparametric elements are used to simulate the backfill and six linear bar elements to represent the rigid retaining wall. In order to simulate the incremental displacements, bar elements with a very high stiffness are used. The effect of wall displacement can be accomplished by applying a load equal to the value of the bar stiffness times the displacement to the nodal points that connect bars and soil elements. The elastic-plastic Drucker-Prager soil model is used in this study. Two earth pressure study cases have been analyzed. The first case deals with a cohesionless soil, while the second one a cohesive soil. The obtained load-displacement curves and stress-displacement curves are presented. It is found that the earth pressures behind the retaining wall at different heights based on the numerical solutions are identical with the calculations obtained from the Rankine earth pressure theory.

Revisiting the Ladder on a Wall Problem

The problem of a ladder leaning on a wall has been a staple of introductory physics for years. It is discussed in numerous physics textbooks and in journals.1–4 Now, it even has an Internet presence. Postings from students seek help for “ladder on a wall” problems. A quick review of those postings would show that they all deal with frictionless walls. This is also how the situation is presented in most textbooks. One may get the impression that the friction between a ladder and a wall is always negligible, or that dealing with it is so difficult that it should be left out of the realm of introductory physics. The truth of the matter is that the magnitude of the friction coefficient between a ladder and a wall is not much different from that with the floor, and that friction with the wall is an important part of the conditions for having a static ladder. This paper derives a simple relationship between the friction coefficients of the ladder with the floor (μ1) and with the wall (μ2), when the ladder is in static equilibrium. Figure 1 shows the forces that act on a ladder that leans on a wall.

Reliability of passive earth pressure

Passive earth pressure calculations in geotechnical analysis are usually performed with the aid of the Rankine or Coulomb theories of earth pressure based on uniform soil properties. These traditional earth pressure theories assume that the soil is uniform. The fact that soils are spatially variable leads to two potential problems in design: do sampled soil properties adequately reflect the effective properties of the entire soil mass and does spatial variability in soil properties lead to passive earth pressures that are significantly different from those predicted using traditional theories? This paper combines non-linear finite element analysis with random field simulation to investigate these two questions. The specific case investigated is a two-dimensional frictionless passive wall with a cohesionless drained soil mass. The wall is designed against sliding using Rankine's earth pressure theory. The unit weight is assumed to be constant throughout the soil mass and the design friction angle is obtained by sampling the simulated random soil field. For a single sample, the friction angle is used as an effective soil property in the Rankine model. For two samples, an average of the sampled friction angles is used. Failure is defined as occurring when the Rankine predicted passive resistance acting on the wall, modified by a factor of safety, is greater than that computed by the random finite element method. Using Monte Carlo simulation, the probability of failure of the traditional design approach is assessed as a function of the factor of safety using and the spatial variability of the soil.

Small Indentations of Rubber Blocks: Effect of Size and Shape of Block and of Lateral Compression

Abstract Many gaskets and seals consist of a long rubber strip or thin-walled ring, placed on a flat rigid surface and indented by a flat-ended rigid indenter. We have examined their resistance to small indentations by FEA. They are treated as infinitely-long elastic blocks of rectangular cross-section, resting on a rigid frictionless base. The indentation stiffness is calculated for various ratios of indenter tip width to block width and to block thickness, using two restraint conditions on the outer surfaces: frictionless walls (zero outwards displacement), as for a gasket placed in a recess; or stress-free, as for a gasket with no lateral restraint. For an infinitely-wide and infinitely-thick block, the theoretical resistance to indentation is zero. For comparison, the indentation stiffness is calculated for cylindrical rubber blocks of varied radius and thickness, indented by a flat-ended cylindrical indenter. In this case the result for an infinitely-large block is finite. A second study treats indentation of a rubber block, pre-compressed in the surface plane. Biot showed that the indentation stiffness of a half-space becomes zero at a critical compression, about 33% for equi-biaxial compression and 44 % for plane strain compression, for both a neo-Hookean and a Mooney-Rivlin elastic solid. FEA calculations were made of the indentation stiffness of neo-Hookean blocks of various sizes, pre-compressed to various degrees. The results are compared with Biot's result. In an Appendix, the critical degree of compression is calculated for a more realistic strain energy function than either the neo-Hookean or the Mooney-Rivlin approximation.