Coulomb Friction Law Research Articles

Seismic Behavior of Reinforced Concrete Silos Considering Granular Material-Structure Interaction

Silos are structures that are used for storing different types of granular materials. Due to nonlinearity of reinforcedconcrete walls of silo and incrementally nonlinear behavior of granular material, overall seismic behavior of reinforced concrete silos is very complex, in this paper we have used ABAQUS finite element package for modeling of earthquake effect on a reinforced concrete silo, reinforced concrete silo walls are modeled by shell elements and their nonlinear behavior is considered by concrete damaged plasticity model, seismic behavior of granular material inside silo is highly nonlinear and requires a complex nonlinear description of the granular material, the behavior of granular material is incrementally nonlinear even at low strains. The hypoplasticity theory describes the stress rate as a function of stress, strain rate and void ratio. It can model the nonlinear and inelastic behavior of granular materials due to its rate-type formulation. Granular material inside silo is modeled by solid elements and its nonlinear behavior is considered with a hypoplastic constitutive model, for modeling of interaction between silo walls and granular material, surface to surface contact with coulomb friction law is considered between silo walls and granular material. After modeling, the behavior of reinforced concrete silo under earthquake excitation is compared with a model without considering granular material-structure interaction.

Modeling Large Sliding Frictional Contact Along Non-Smooth Discontinuities in X-FEM

Modeling large frictional contact is a numerical tool to simulate abrasion resistant material. We have therefore proposed a new method to impose contact constraints in eXtended Finite Element Method (XFEM) framework. For this technique we impose penalty constraint on Node To Segment(NTS) elements. Moreover, the effect of friction has been investigated based on the Coulomb friction law. In our algorithm, new Lagrangian shape functions are proposed to solve the problems of the conventional Heaviside enrichment function. Finally, two numerical simulations for non-smooth constraints are delivered to show the efficiency of our algorithm.

Finite Element Analysis of the Effects of Tool-Chip Friction on Cutting Temperature Field

The heat generation caused by tool-chip friction and chip deformation strongly influences the tool wear and tool life in metal cutting processes. The focus of this paper is on the effect of tool-chip on cutting temperature field. A series of ¬finite element simulations have been performed, in which a modifi¬ed Coulomb friction law is used to model the friction along tool–chip interface. A tool rake angle ranging from 10° to 45°, a inclination angle ranging from 0° to 20°, and a friction coefficient ranging from 0.1 to 0.6 have been considered in simulations. The results of these simulations show that the maximum cutting temperature increases with the increasing of tool-chip friction coefficient at different rake angle and inclination angle. The form of tool wear mainly appears as crater wear when the friction coefficient is less than 0.5, and the cutting edge tends to split when the friction coefficient is larger than 0.6.

The elastic contact influences on passive walking gaits

SUMMARYThis paper presents a new planar passive dynamic model with contact between the feet and the ground. The Hertz contact law and the approximate Coulomb friction law were introduced into this human-like model. In contrast to McGeer's passive dynamic models, contact stiffness, contact damping, and coefficients of friction were added to characterize the walking model. Through numerical simulation, stable period-one gait and period-two gait cycles were found, and the contact forces were derived from the results. After investigating the effects of the contact parameters on walking gaits, we found that changes in contact stiffness led to changes in the global characteristics of the walking gait, but not in contact damping. The coefficients of friction related to whether the model could walk or not. For the simulation of the routes to chaos, we found that a small contact stiffness value will lead to a delayed point of bifurcation, meaning that a less rigid surface is easier for a passive model to walk on. The effects of contact damping and friction coefficients on routes to chaos were quite small.

Friction of Wrinkles

Sufficiently thin elastic sheets wrinkle when they are in contact with a small adhesive counterbody. Despite significant progress on the dynamics of wrinkle formation and morphology, little is known about how wrinkles impede the relative sliding motion of the counterbody. Using molecular dynamics we demonstrate that instabilities are likely to occur during sliding when the wrinkle pattern has asymmetries not present in the counterbody. The instabilities then cause Coulomb's friction law. The behavior can be rationalized in terms of simple models for multistable elastic manifolds.

Verification of an anisotropic Coulomb adhesion‐friction law for contact surfaces with periodic structure

AbstractSliding friction forces and so‐called adhesion forces are the main mechanical characteristics to describe contact interaction. Both together are representing 2D surface constitutive laws in analogy to e.g. elasto‐plasticity for 3D continua. The classical model to generalize the Coulomb friction law into anisotropic domains is to introduce an anisotropic friction tensor. Michalowski and Mroz in [1] proposed the structure of the friction tensor considering the sliding of a rigid block on an inclined surface. Zmitrowicz in [2] developed the theoretical basis for the structure of the friction tensor on symmetry groups for the tensor. The current contribution is aimed at verification of this modeling process based on a homogenization procedure for a very fine discretization representing the exact structure of the surface. The validation issue with realistic experiments given in [4] is discussed as well. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Aging of the frictional properties induced by temperature variations

The dry frictional contact between two solid surfaces is well known to obey Coulomb friction laws. In particular, the static friction force resisting the relative lateral (tangential) motion of solid surfaces, initially at rest, is known to be proportional to the normal force and independent of the area of the macroscopic surfaces in contact. Experimentally, the static friction force has been observed to slightly depend on time. Such an aging phenomenon has been accounted for either by the creep of the material or by the condensation of water bridges at the microscopic contact points. By studying a toy model, we show that the small uncontrolled temperature changes of the system can also lead to a significant increase of the static friction force.

TWO-ZONE ANALYTICAL CONTACT MODEL APPLIED TO ORTHOGONAL CUTTING

In this study, the contact on the rake face is modeled analytically using a dual zone contact model at the tool-chip interface. The contact at the rake face comprises a sticking zone near the tool tip and a sliding zone where a Coulomb friction law is assumed. The model provides the values of global quantities (cutting force components, overall friction coefficient, and contact length) and of local variables (stress distribution along the rake face, lengths of the sticking and sliding zones) in terms of physical parameters (sliding friction coefficient, workpiece material parameters) and cutting conditions. The model can be used to characterize the sliding friction coefficient of the Coulomb law from few orthogonal cutting tests. Theoretical results are compared with experimental data in terms of contact lengths and cutting force predictions, and a good agreement is observed.

Estimate interface frictional coefficient of ceramic matrix composites from hysteresis loops

An approach to estimate fiber/matrix interface frictional coefficient of ceramic matrix composites under fatigue loading is developed by means of hysteresis loops. The Coulomb friction law is adopted to describe the interface shear stress in the debonded region. The matrix crack space and interface debonded length are obtained by matrix statistical cracking model and fracture mechanics interface debonding criterion. The hysteresis loops of four different cases are derived based on the damage mechanisms of fiber sliding relative to matrix in the debonded region during unloading and subsequent reloading. The hysteresis loss energy corresponding to different cycle is formulated in terms of interface frictional coefficient. By comparing the experimental hysteresis loss energy with computational values, the interface frictional coefficient of three different ceramic matrix composites under fatigue loading is derived.

On the stick-slip waves under unilateral contact and Coulomb friction

In this paper, the construction of analytic solutions of stick-slip waves propagating along the interface between an elastic half-space and a moving rigid one is investigated. The contact between the solids is governed by unilateral constraints and Coulomb friction law and the deformable body is loaded by remote uniform stresses \(\tau^{*}_{yy}<0\), \(\tau^{*}_{xy}>0\). The method of solution is based on the analytic continuation of Radok’s complex potentials within the framework of steady elastodynamical problems. The governing equations combined with the boundary conditions are reduced to a Riemann–Hilbert problem with discontinuous coefficient. This approach for the stick-slip study is novel and differs from those in literature, namely the series method and the Weertman’s dislocation formulation. We present the closed-form solution of the Riemann–Hilbert problem and show that the principal unknowns are of number two: the wave celerity and the ratio of the slip length by the stick one. The considered loading introduces an additional velocity V* related to the longitudinal elongation \(\varepsilon^{*}_{xx}\) due to the normal stress \(\tau^{*}_{yy}\). We show that if V* vanishes then there is no solution. When V* ≠ 0, it is possible to construct weakly singular solutions satisfying all stick-slip conditions except over a narrow zone at transition points: the shear stress is singular over a small zone and the normal contact stress exhibits a positive singularity over a very small zone in the slip region which implies a separation near the singular transition.

Frictional slip plane growth by localization detection and the extended finite element method (XFEM)

AbstractThis paper is concerned with developing a numerical tool for detecting instabilities in elasto‐plastic solids (with an emphasis on soils) and inserting a discontinuity at these instabilities allowing the boundary value problem to proceed beyond these instabilities. This consists of implementing an algorithm for detection of strong discontinuities within a finite element (FE) framework. These discontinuities are then inserted into the FE problem through the use of a displacement field enrichment technique called the extended finite element method (XFEM). The newly formed discontinuities are governed by a Mohr–Coulomb frictional law that is enforced by a penalty method. This implementation within an FE framework is then tested on a compressive soil block and a soil slope where the discontinuity is inserted and grown according to the localization detection. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Load Transfer and Recovery Length in Parallel Wires of Suspension Bridge Cables

A new simplified contact model aimed at capturing the load transfer and recovery length in parallel steel wires, commonly used in main cables of suspension bridges, is presented. The approach is based on placing elastic–perfectly plastic spring elements at the contact region between the objects. These springs have varying stiffness (Model I) or yielding (Model II) depending on their proximity to the clamping loads. Their stiffness or yielding is highest when they are closer to this force, and it decays when they are farther away from the clamp. This decayed behavior is assigned according to Boussinesq’s well-known solution to a point load (applied on a half space). Both models converge quickly compared with a full contact model and recover Coulomb friction law on a two-dimensional (2D) benchmark problem. Moreover, when the same properties are chosen for all springs (disregarding Boussinesq solutions), the models reduce to the classical shear-lag model, which for high clamping (point) loads gives inaccurat...

Numerical simulation of friction noise

Abstract A numerical study to analyze friction noise being radiated when two rough and dry surfaces are rubbed together, is presented in this paper. The explicit dynamic finite element software ABAQUS in 2D is used to simulate the roughness noise. Coulomb's friction law is used at the contact surface. This simulation provided the local contact conditions such as local contact forces and contact stresses, but also the number of impacts per second and their intensities. It is shown that roughness plays a crucial role to explain roughness noise. The shocks between antagonist asperities are responsible of the transfer between the kinetic energy of solids and the vibratory energy which produces the radiation of sound. It was also shown that roughness noise level is simultaneously an increasing function of the logarithm of the surface roughness and the sliding speed. Numerical results are in agreement with our experimental results and previous studies.

New second-order cone linear complementarity formulation and semi-smooth Newton algorithm for finite element analysis of 3D frictional contact problem

We propose a new second-order cone linear complementarity problem (SOCLCP) formulation for the numerical finite element analysis of three-dimensional (3D) frictional contact problems by the parametric variational principle. Specifically, we develop a regularization technique to resolve the multi-valued difficulty involved in the frictional contact law, and use a second-order cone complementarity condition to handle the regularized Coulomb friction law in contact analysis. The governing equations of the 3D frictional contact problem is represented by an SOCLCP via the parametric variational principle and the finite element method, which avoids the polyhedral approximation to the Coulomb friction cone so that the problem to be solved has much smaller size and the solution has better accuracy. In this paper, we reformulate the SOCLCP as a semi-smooth system of equations via a one-parametric class of second-order cone complementarity functions, and then apply the non-smooth Newton method for solving this system. Numerical results confirm the effectiveness and robustness of the SOCLCP approach developed.

Shock Response Analysis for a Journal-Bearing System by a Results Comparison

Shock response analysis of a journal-bearing system with the journal-bearing connection modeled as a spring link in radial direction and a dry contact joint respectively is presented. In the first model, the spring constants representing oil-film characteristic are determined by eight coefficients. In the second model, the friction forces are calculated using a modified Coulombs friction law. The contact detection points are the integration point and located at Gauss points. Only the contact normal pressure is treated as a Lagrange multiplier. The tangential contact stresses are calculated based on the penalty method. System’s time varying responses are obtained by FEM. A results comparison was performed between “spring link” model and “dry contact” model. The main conclusion is that stress distribution is nearly same in the system modeled by the two methods, but the amplitude in the former is smaller than that in the latter.

A numerical study of hydrologically driven glacier dynamics and subglacial flooding

A hydrologically coupled flowband model of ‘higher order’ ice dynamics is used to explore perturbations in response to supraglacial water drainage and subglacial flooding. The subglacial drainage system includes interacting ‘fast’ and ‘slow’ drainage elements. The fast drainage system is assumed to be composed of ice-walled conduits and the slow system of a macroporous water sheet. Under high subglacial water pressures, flexure of the overlying ice is modelled using elastic beam theory. A regularized Coulomb friction law describes basal boundary conditions that enable hydrologically driven acceleration. We demonstrate the modelled interactions between hydrology and ice dynamics by means of three observationally inspired examples: (i) simulations of meltwater drainage at an Alpine-type glacier produce seasonal and diurnal variability, and exhibit drainage evolution characteristic of the so-called ‘spring transition’; (ii) horizontal and vertical diurnal accelerations are modelled in response to summer meltwater input at a Greenland-type outlet glacier; and (iii) short-lived perturbations to basal water pressure and ice-flow speed are modelled in response to the prescribed drainage of a supraglacial lake. Our model supports the suggestion that a channelized drainage system can form beneath the margins of the Greenland ice sheet, and may contribute to reducing the dynamic impact of floods derived from supraglacial lakes.

Frictional contact algorithm study on the numerical simulation of large deformations in deep soft rock tunnels

There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlinearity caused by material, geometrical and contact boundary. In this paper, the numerical method to tackle the nonlinear contact and large deformation problem in A Software on Large Deformation Analysis for Soft Rock Engineering at Great Depth was presented. In the software, based on Lagrange multiplier method and Coulomb friction law, kinematic constraints on contact boundaries were introduced in functional function, and the finite element equations was established for two incremental large deformation analyses models, polar decomposition model and additive decomposition model. For every incremental loading step, by searching for the contact points in the potential contact interfaces (the excavation boundaries), the Lagrange multipliers, i.e., contact forces are calculated iteratively by Gauss-Seidel method, and justified through satisfy the inequalities of static constraint on contact boundaries. With the software, large deformation and frictional contact of a transport roadway were analyzed numerically by the two models. The numerical examples demonstrated the efficiency of the method used in the software.

Stress Relaxation Analysis of Polyurethane Foam Preloaded Structures

Based on the nonlinear finite element analysis method, FEA models which describe the viscoelastic friction contact state of the polyurethane foam preloaded structures are created. In the simulations, the general Maxwell viscoelastic constitutive relation is introduced and a seven-parameter general Maxwell viscoelastic model is used to fit the experimental stress relaxation curve of polyurethane foam. During the nonlinear contact analysis, coulomb friction law is adopted, and the effects of the coulomb friction coefficient on the reaction force in the axial direction are analyzed. The FE results show that the change tendencies of relation curves of the structures are similar to which of the polyurethane foams. In the end, the influences of stiffness ratio of polyurethane foam to the outer component on the structural relaxed force are discussed, and the FE results indicate that the stiffness ratios affect the stress (force) relaxation degree remarkably. That is to say a good structure design could optimize the mechanical performance of the complicated structures greatly.

COULOMB FRICTION AND OTHER SLIDING LAWS IN A HIGHER-ORDER GLACIER FLOW MODEL

We consider a widely used higher-order glacier flow model with a variety of parametrizations of wall slip, including Coulomb friction, regularized Coulomb friction laws and a power law. Mathematically, the Coulomb friction problem is found to be analogous to a classical friction problem in elasticity theory. We specifically analyze the case in which slip is possible everywhere at the boundary, in which case the weak formulation becomes a semi-coercive convex minimization problem which has a solution only if a solvability condition representing force and torque balance is satisfied. Going beyond previous work, we study the uniqueness of solutions in depth, finding that non-unique solutions are possible under very specialized circumstances. Further, in an extension of work by Campos, Oden and Kikuchi, we show that solutions to the regularized Coulomb friction and power law problems converge to the Coulomb friction problem in appropriate parametric limits, provided the latter is unique, and briefly discuss the implications of possible non-unique solutions for a priori error estimation in numerical approximations.

A new model for friction under shock conditions

This article is aimed at the developpement of a new model for friction under shock conditions. Thanks to a subgrid model and a specific Coulomb friction law, it takes into account the interface temperature and deformation but also the influence of asperities when the contact pressure is relatively low (≤ 3 GPa).