Frictional Boundaries Research Articles

Modeling of disc springs based on energy method considering asymmetric frictional boundary

Disc springs have excellent ability to absorb and dissipate energy, and are widely used as basic vibration isolation units in the design of vibration isolators for naval power systems. Focusing on the effect of friction on disc springs, a mechanical model of disc springs considering asymmetric frictional boundary is developed. The additional load to overcome the Coulomb friction damping is derived analytically by the energy method. Finite element analysis of disc springs is carried out and the results for large and small frictional conditions are compared with the theoretical results. Quasi-static experiments on disc springs are carried out and the proposed method is further validated. The results show that the analytical model based on energy method can describe the load–displacement characteristics of disc springs and their combinations under symmetric and asymmetric frictional boundaries accurately. Based on the analytical solution, the influence of the structural parameters of the disc springs on the damping effect is investigated. The stiffness and damping of disc springs are linearly related to the friction coefficient. In addition, the magnitude of the effect of asymmetry of the boundary friction on the mechanical properties of the disc springs varies with the structural parameters.

Regularized SPH model for soil–structure interaction with generalized frictional boundary

AbstractThis paper proposes a regularized smoothed particle hydrodynamics (SPH) scheme to solve the problems of tensile instability and stress noise in large‐deformation soil–structure interaction. Particle shifting and stress regularization are combined to maintain uniform stresses and particle distributions. A generalized frictional boundary condition is presented to model soil–structure interfaces with abitrary friction coefficients. A modified particle shifting technique is developed to regularize particles near the frictional boundaries. Furthermore, GPU acceleration algorithm is adopted to improve the efficiency. The proposed scheme is compared with the conventional SPH methods using numerical examples, including the collapse of three‐dimensional granular column, the collapse of the cohesive soil, and pipe penetrates into soft clay. The comparison indicates that the proposed regularized SPH model can give highly accurate results for large‐deformation soil–structure interaction problems with arbitrary friction coefficient.

BFEMP: Interpenetration-free MPM–FEM coupling with barrier contact

This paper introduces BFEMP, a new approach for monolithically coupling the Material Point Method (MPM) with the Finite Element Method (FEM) through barrier energy-based particle–mesh frictional contact using a variational time-stepping formulation. The fully implicit time integration of the coupled system is recast into a barrier-augmented unconstrained nonlinear optimization problem. A modified line-search Newton’s method is adopted to strictly prevent material points from penetrating the FEM domain, ensuring convergence and feasibility regardless of the time step size or the mesh resolutions. The proposed coupling scheme also reduces to a new approach for imposing separable frictional kinematic boundaries for MPM when all nodal displacements in the FEM domain are prescribed with Dirichlet boundary conditions. Compared to standard implicit time integration, the extra algorithmic components associated with the contact treatment only depend on simple point-segment (or point-triangle in 3D) geometric queries which robustly handle arbitrary FEM mesh boundaries represented with codimension-1 simplices. Experiments and analyses are performed to demonstrate the robustness and accuracy of the proposed method.

Investigations on nonlinear aerothermoelastic behaviors of multilayered composite panels subject to frictional boundaries and random acoustic loads in supersonic flow

This paper is focused on the nonlinear aerothermoelastic analysis of composite laminated panels having non-smooth frictional boundaries and simultaneously subject to combined supersonic aerodynamic, thermal and random acoustic loads. The Reddy's third-order shear deformation plate theory with zig-zag effects is employed to formulate the structural model of the panels. The von Karman strain relationships are considered in order to take into account the geometrical nonlinearities of the panels. The aerodynamic loads and the random acoustic loads acting on the panel are characterized by the quasi-steady first-order piston theory and the Gaussian band-limited white noise, respectively. A four-node finite element is developed to establish the aerothermoelastic models of the panels, and the non-smooth frictional boundaries of the panels are represented by a number of macro-slip friction models. The effects of the aerodynamic forces, acoustic loads, thermal forces and the spatial location of the frictional boundaries on the nonlinear aerothermoelastic responses (including the stable limit-cycle oscillations, chaotic and random vibration responses) of composite laminated panels are examined. The effects of non-uniform distribution of the temperature on the aerothermoelastic behaviors of composite laminated panels are discussed.

Simulation of emergent compaction banding fronts caused by frictional boundaries

This study examines the role of boundary friction in promoting heterogeneous compaction in soft rock specimens loaded at high confining pressure outside the domain of compaction localisation. An elastoplastic constitutive model characterised by tunable hardening/softening behaviour is used to conduct the analyses. Finite-element simulations suggest that material instability is a non-necessary condition for the emergence of compaction fronts. Such fronts propagated as a result of a severe deviation in the local responses induced by frictional constraints. These findings suggest that boundary effects can bias the assessment of the extent of the compaction localisation domain. Experimental countermeasures and informed model calibration procedures are therefore necessary to minimise such bias and enable more accurate predictions of soft rock compaction.

Effects of Low‐Velocity Fault Damage Zones on Long‐Term Earthquake Behaviors on Mature Strike‐Slip Faults

AbstractMature strike‐slip faults are usually surrounded by a narrow zone of damaged rocks characterized by low seismic wave velocities. Observations of earthquakes along such faults indicate that seismicity is highly concentrated within this fault damage zone. However, the long‐term influence of the fault damage zone on complete earthquake cycles, that is, years to centuries, is not well understood. We simulate aseismic slip and dynamic earthquake rupture on a vertical strike‐slip fault surrounded by a fault damage zone for a thousand‐year timescale using fault zone material properties and geometries motivated by observations along major strike‐slip faults. The fault damage zone is approximated asan elastic layer with lower shear wave velocity than the surrounding rock. We find that dynamic wave reflections, whose characteristics are strongly dependent on the width and the rigidity contrast of the fault damage zone, have a prominent effect on the stressing history of the fault. The presence of elastic damage can partially explain the variability in the earthquake sizes and hypocenter locations along a single fault, which vary with fault damage zone depth, width and rigidity contrast from the host rock. The depth extent of the fault damage zone has a pronounced effect on the earthquake hypocenter locations, and shallower fault damage zones favor shallower hypocenters with a bimodal distribution of seismicity along depth. Our findings also suggest significant effects on the hypocenter distribution when the fault damage zone penetrates to the nucleation sites of earthquakes, likely being influenced by both lithological (material) and rheological (frictional) boundaries.

The AIFM, Depositary and the Prime Broker in the Prime Brokerage relationship

Depending upon whether a prime broker is solely acting as a counterparty or as a counterparty and a depositary/sub-custodian, the prime broker may either enter into a prime brokerage agreement with the alternative investment fund manager (the “AIFM”) for acting as a counterparty and an agreement with the depositary for acting as a sub-custodian. Often this results in a tripartite agreement between the AIFM, prime broker and the depositary. The checks and balances under the AIFM Law/AIFMR require the AIFM, prime broker and depositary to fulfil certain duties in the prime brokerage relationship. The duties of AIFMs regarding its organization and disclose/reporting need to be proportionally applied, whereas the depositary’s (or depositary division of the prime broker’s) duties depend on whether and to what extent the prime broker holds financial instruments that can be held in custody. This article discusses the role and the duties of the AIFM, the depositary and the prime broker duties in the prime brokerage relationship under the AIFM Law/AIFMR. In particular, the frictional boundaries between the prime broker’s counterparty and depositary functions will be highlighted. This contribution concludes by discussing prime broker models that are used in practice to resolve these frictional boundaries.

Physical theory for near-bed turbulent particle suspension capacity

Abstract. The inability to capture the physics of solid-particle suspension in turbulent fluids in simple formulas is holding back the application of multiphase fluid dynamics techniques to many practical problems in nature and society involving particle suspension. We present a force balance approach to particle suspension in the region near no-slip frictional boundaries of turbulent flows. The force balance parameter Γ contains gravity and buoyancy acting on the sediment and vertical turbulent fluid forces; it includes universal turbulent flow scales and material properties of the fluid and particles only. Comparison to measurements shows that Γ = 1 gives the upper limit of observed suspended particle concentrations in a broad range of flume experiments and field settings. The condition of Γ > 1 coincides with the complete suppression of coherent turbulent structures near the boundary in direct numerical simulations of sediment-laden turbulent flow. Γ thus captures the maximum amount of sediment that can be contained in suspension at the base of turbulent flow, and it can be regarded as a suspension capacity parameter. It can be applied as a simple concentration boundary condition in modelling studies of the dispersion of particulates in environmental and man-made flows.

Eddy transport as a key component of the Antarctic overturning circulation

The exchange of water masses across the Antarctic continental shelf break regulates the export of dense shelf waters to depth as well as the transport of warm, mid-depth waters towards ice shelves and glacial grounding lines. The penetration of the warmer mid-depth waters past the shelf break has been implicated in the pronounced loss of ice shelf mass over much of west Antarctica. In high-resolution, regional circulation models, the Antarctic shelf break hosts an energetic mesoscale eddy field, but observations that capture this mesoscale variability have been limited. Here we show, using hydrographic data collected from ocean gliders, that eddy-induced transport is a primary contributor to mass and property fluxes across the slope. Measurements along ten cross-shelf hydrographic sections show a complex velocity structure and a stratification consistent with an onshore eddy mass flux. We show that the eddy transport and the surface wind-driven transport make comparable contributions to the total overturning circulation. Eddy-induced transport is concentrated in the warm, intermediate layers away from frictional boundaries. We conclude that understanding mesoscale dynamics will be critical for constraining circumpolar heat fluxes and future rates of retreat of Antarctic ice shelves.

A New Hybrid Computational Framework and Validations for Handling Steady-State Problems with Contact Boundaries

A hybrid computational framework consisting of Eulerian boundary zone concept augmented to Lagrangian finite element formulations with moving meshes is proposed for effectively handling the steady-state problems. This is in conjunction with a novel L-stable time discretized framework that is necessary in conjunction with the hybrid formulations to enable computationally attractive features for practical problems. The L-stable algorithm is developed and implemented and is of second order accuracy and modified for nonlinear dynamic systems with frictional contact boundaries. No nonlinear iterations are necessary for the non-linear dynamic system of equations, and one only needs to update the artificial damping matrix once at every time step for non-linear dynamic problems. The proposed method is suitable for steady state problems with complex contact boundary conditions.

Global analysis on slope stability and its engineering application

In hydraulic engineering, sometimes it is necessary to consider the stability of sliding bodies with lateral frictional boundaries. Neither the existing three dimensional limit equilibrium methods nor the commercial software products are able to treat such situations. The three dimensional factor of safety is accordingly underestimated; while the shearing strength based on the three dimensional back analysis is overestimated. In this study, the lateral boundaries are regarded as the part of the slip surface. Based on the expression of the normal pressure on the slip surface and the patch interpolation, a rigorous solution for the three dimensional limit equilibrium analysis is realized. Meanwhile, the proposed procedure is applied to the stability analysis of the slope with a cable platform on the right bank in Da Gang Shan hydraulic project under construction.

Computer simulation of landslides by the contact element method

In the paper, an improved contact element method was adopted to analyze the sliding process of slopes. The normal and shear strengths of materials on potential sliding surfaces of slopes were considered. The convergence of nonlinear problems on frictional contact boundaries was reached through a repeated contact calculation. A step-by-step procedure was used to simulate the process of landslides. The energy change of the slope system at each step was calculated, considering the strain energy, kinetic energy and the work of friction force, etc. In the simulation of rock slopes, it was found that there were three main states: a ‘perfectly bounded’ state, a ‘local sliding’ state and a ‘whole sliding’ state. The effects of weathering and water infiltrating into the sliding surfaces were considered, and the displacements of landslides were obtained. For a real case history, application of the code to results of an actual landslide is given. The simulation method described here may be employed to predict other kinds of landslides because it is not restricted to particular slopes, material properties of slopes or shapes of potential sliding surfaces.

Velocity profiles, stresses, and Bagnold scaling of sheared granular system in zero gravity

We report the results of three-dimensional event-driven simulations of sheared granular system in a Couette geometry. The simulations use realistic boundary conditions that may be expected in physical experiments. For a range of boundary properties we report velocity and density profiles, as well as forces on the boundaries. In particular, we find that the results for the velocity profiles throughout the shearing cell depend strongly on the interaction of the system particles with the physical boundaries. Even frictional boundaries can allow for significant slippage of the particles, therefore reducing the shear in the system. Next, we present stress distributions both for controlled volume and for controlled stress configurations. We discuss the dependence of solid volume fraction on shear rate under the constant-pressure condition, and Bagnold scaling in volume-controlled simulations. In addition, we study the influence of oscillatory driving of one of the domain boundaries on the system properties.

Comparison of Double-Shearing and Coaxial Models for Pressure-Dependent Plastic Flow at Frictional Boundaries

The qualitative difference in solution behavior in the vicinity of maximum friction surfaces is demonstrated for two distinct models of pressure-dependent plasticity (the double-shearing and coaxial models) using closed-form solutions for planar flow through an infinite wedge-shaped channel and plane-strain compression of an infinite block between parallel plates. Singular velocity fields (some components of the strain rate tensor approach infinity at the friction surface) occur in the solutions based on the double-shearing model. This is similar to behavior in the vicinity of maximum friction surfaces in classical plasticity of pressure-independent materials. A singular velocity field is also obtained in the solution based on the coaxial model for the problem of channel flow; but, in contrast to the double-shearing model and classical plasticity, sticking must occur at this friction surface. For the problem of compression of a material obeying the coaxial model, no solution based on conventional assumptions exists with the maximum friction law. This is quite different from both the corresponding solution based on the double-shearing model and the channel flow solution based on the coaxial model.

Theoretical study of the dynamic effect on the warping of rolled strip and loss of flatness

Dynamic phenomena in rolling mills, generally known as chatter, not only overload the mechanical components of the rolling mill structure but also give rise to variations in gauge or to a shape defect in the rolled strip. In this paper a mathematical model of the system developed by combining a model of non-steady state plastic deformation with a mass-spring model of the vibration of the rolling mill is presented. This model enables the exploration of the influence of the dynamic effects in the rolling mill on the loss of flatness of the rolling product. Analyses have been conducted with particular emphasis on differing roll velocities and different frictional boundaries between the rolls and the deforming metal on the upper and lower surfaces.

Stress and deformation analysis of plane‐strain rolling process

A finite‐element elastic‐plastic deformation analysis is required in order to predict a complete stress and deformation in a material for metal forming. There have been a few attempts for rolling analysis using the elastic‐plastic code, because the boundary conditions between roll and deforming material become complicated.In this study, an elastic‐plastic plane‐strain rolling analysis with friction has been attempted by the updated Lagrange code. Both slipping and sticking were taken into account for boundary conditions between roll and material. The stress and deformation analysis is performed using a nonsymmetric stiffness matrix solution (for curved and frictional boundaries).The elastic‐plastic analysis, coupled with the proposed frictional boundary model, evidently provides a reliable stress and deformation solution in the metal rolling process.