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The purpose of this paper is to develop a numerical approach to solve the transient rolling contact problem with the consideration of velocity dependent friction.

A three dimensional (3D) transient FE model is developed in elasticity by the explicit finite element method. Contact solutions with a velocity dependent friction law are compared in detail to those with the Coulomb’s friction law (i.e. a constant coefficient of friction).

The FE solutions confirm the negligible influence of the dependence on the normal contact. Hence, analysis is focussed on the tangential solutions under different friction exploitation levels. In the trailing part of the contact patch where micro-slip occurs, very high-frequency oscillations are excited in the tangential plane by the velocity dependent friction. This is similar to the non-uniform sliding or tangential oscillations observed in sliding contact. Consequently, the micro-slip distribution varies greatly with time. However, the surface shear stress distribution is quite stable at different instants, even though it significantly changes with the employed friction model.

This paper proposes an approach to solve the transient rolling contact problem with the consideration of velocity dependent friction. Such a problem was usually solved in the literature by the simplified contact algorithms, with which detailed contact solutions could not be obtained, or with the assumption of steady rolling.

The purpose of this paper is to expand the previously published fuzzy logic controller for contact method to normal frictionless contact for solving mechanical frictional contact problems. The secondary aim is to integrate a reduction model for each component in contact to decrease the size of the global finite element contact problem.

The proposed strategy relies on the design of two fuzzy logic controllers currently used in the automation domain. These controllers are considered to link normal and tangential gaps (for sticking conditions) with normal and tangential contact loads. A direct consequence of integrating a control-based approach into the numerical solving approach is the decomposition of the non-linear problem into a set of linear problems.

With this new strategy, no tangent or coupling matrix is defined for the contact problem that allows to consider a projection matrix to reduce the size of each component in contact and subsequently to decrease the associated computational time. As in condensation techniques, this matrix is composed of both modal bases of each component in contact and static modes that capture behaviors at the contact interface. Moreover, the proposed numerical application highlights the efficiency of the proposal in terms of computation time and precision of contact data.

The developments are currently implemented in Matlab only for 2D static numerical applications. Therefore, as obtained results are very promising in terms of precision and computational time, the objective is to complete the proposed method in future research to manage frictional contact for 3D finite element models in a dynamic context.

In conclusion, this paper highlights the interest of studying mechanical frictional contact problems by considering fuzzy logic control approaches.

In this paper, the effect of the FE discretization density on the results of both convex and nonconvex‐nonsmooth frictional contact and adhesive contact interface problems is investigated. The tool for this study is a variational formulation leading to an iterative method for the numerical solution of the arising nonconvex‐nonsmooth optimization problems. Various cases of monotone and nonmonotone interface laws are considered and interesting results are obtained.

The purpose of this paper is to develop a discrete element (DE) and multiscale modeling methodology to represent granular media at their particle scale as they interface solid deformable bodies, such as soil‐tool, tire, penetrometer, pile, etc., interfaces.

A three‐dimensional ellipsoidal discrete element method (DEM) is developed to more physically represent particle shape in granular media while retaining the efficiency of smooth contact interface conditions for computation. DE coupling to finite element (FE) facets is presented to demonstrate initially the development of overlapping bridging scale methods for concurrent multiscale modeling of granular media.

A closed‐form solution of ellipsoidal particle contact resolution and stiffness is presented and demonstrated for two particle, and many particle contact simulations, during gravity deposition, and quasi‐static oedometer, triaxial compression, and pile penetration. The DE‐FE facet coupling demonstrates the potential to alleviate artificial boundary effects in the shear deformation region between DEM granular media and deformable solid bodies.

The research is being extended to couple more robustly the ellipsoidal DEM code and a higher order continuum FE code via overlapping bridging scale methods, in order to remove dependence of penetration/shear resistance on the boundary placement for DE simulation.

When concurrent multiscale computational modeling of interface conditions between deformable solid bodies and granular materials reaches maturity, modelers will be able to simulate the mechanical behavior accounting for physical particle sizes and flow in the interface region, and thus design their tool, tire, penetrometer, or pile accordingly.

A closed‐form solution for ellipsoidal particle contact is demonstrated in this paper, and the ability to couple DE to FE facets.

This paper aims to describe the application of the virtual element method (VEM) to contact problems between elastic bodies.

Polygonal elements with arbitrary shape allow a stable node-to-node contact enforcement. By adaptively adjusting the polygonal mesh, this methodology is extended to problems undergoing large frictional sliding.

The virtual element is well suited for large deformation contact problems. The issue of element stability for this specific application is discussed, and the capability of the method is demonstrated by means of numerical examples.

This work is completely new as this is the first time, as per the authors’ knowledge, the VEM is applied to large deformation contact.

The purpose of this paper is to extend the penalty concept to treat partial slip, free surface, contact and related boundary conditions in viscous flow simulation.

The penalty partial‐slip formulation is analysed and related to the classical Navier slip condition. The same penalty scheme also allows partial penetration through a boundary, hence the implementation of porous wall boundaries. The finite element method is used for investigating and interpreting penalty approaches to boundary conditions.

The generalised penalty approach is verified by means of a novel variant of the circular‐Couette flow problem, having partial slip on one of the cylindrical boundaries, for which an analytic solution is derived. Further verificationis provided by consideration of viscous flow over a sphere with partial slip on the surface, and comparison of numerical and classical solutions. Numerical studies illustrate the versatility of the approach.

The penalty approach is applied to some different boundaries: partial slip and partial penetration with no/full slip/penetration as limiting cases; free surface; space‐ and time‐varying boundary conditions which allow progressive contact over time. Application is made to curved and inclined boundaries. Sensitivity of flow to penalty parameters is an avenue for continued research, as is application of the penalty approach for non‐Newtonian flows.

This is the first work to show the relation between penalty formulation of boundary conditions and physical boundary conditions. It provides a method that overcomes past difficulties in implementing partial slip on boundaries of general shape, and which handles progressive contact. It also provides useful benchmark problems for future studies.

The objective of this paper is to determine fretting parameters of hoisting rope according to the hoisting parameters in coalmine and to explore the effect of contact load on fretting-fatigue behavior of steel wires.

Based on the mechanical model of hoisting rope in coalmine, the dynamic tension simulation of hoisting rope was performed. Static equations of hoisting rope under tension and torsion and theories of contact mechanics were applied to obtain fretting parameters. Fretting-fatigue tests of steel wires at different contact loads were conducted using a fretting-fatigue test rig. The fretting regime, normalized tangential force and fretting-fatigue life were studied. The morphologies of fretting contact scars and fracture surfaces were observed by scanning electron microscopy and optical microscopy to examine wear and failure mechanisms.

Dynamic tension changes from 0 to 30,900 N. In outer strand layer, contact loads between steel wires in certain wire layers are 60.5 and 38.3 N compared with 378 and 102.7 N between wire layers; relative displacements between wires are 62.5 and 113.2 μm, respectively. Mixed fretting regimes develop in all cases. Increasing contact load decreases the stabilized relative slip and normalized tangential force, reduces the fretting fatigue life, induces accelerated adhesive wear and fatigue wear and results in rougher fracture surface topographies. In all cases, fretting zone induces crack initiation; crack propagation and rupture zones present brittle cleavage and longitudinal splitting, respectively.

This paper presents the systemic study on determination of fretting parameters of hoisting rope according to the hoisting parameters in coalmine and the fretting-fatigue behavior of its internal steel wires. The results of fretting-fatigue tests show that the increase of contact load decreases the stabilized relative slip in mixed fretting regime and normalized tangential force, reduces the fretting fatigue life, induces accelerated adhesive wear and fatigue wear and results in rougher fracture surface topographies.

The authors warrant that the paper is original submission and is not being submitted to any other journal. And the research does not involve confidentiality, copyright infringement, leaks and other issues, all the responsibilities that the authors will take.

Following earlier work on the combined finite/discrete element simulation of shot peening process in 2D case, 3D representation of the problem is established with respect to DE modelling and contact interaction laws. An important relevant computational issue regarding the critical time step is carefully studied, and a new time stepping scheme that can ensure both short and long term stability of the contact models is developed. Numerical tests are performed to evaluate the proposed normal and frictional contact interaction laws with various model parameters. The influences of single and multiple shot impact, as well as element sizes are also numerically investigated. The established contact interaction laws can also be applied to other multi‐body dynamic simulations.

To present a discrete particle model for granular materials.

Starting with kinematical analysis of relative movements of two typical circular grains with different radii in contact, both the relative rolling and the relative sliding motion measurements at contact, including translational and angular velocities (displacements) are defined. Both the rolling and sliding friction tangential forces, and the rolling friction resistance moment, which are constitutively related to corresponding relative motion measurements defined, are formulated and integrated into the framework of dynamic model of the discrete element method.

Numerical results demonstrate that the importance of rolling friction resistance, including both rolling friction tangential force and rolling friction resistance moment, in correct simulations of physical behavior in particulate systems; and the capability of the proposed model in simulating the different types of failure modes, such as the landslide (shear bands), the compression cracking and the mud avalanching, in granular materials.

Each grain in the particulate system under consideration is assumed to be rigid and circular. Do not account for the effects of plastic deformation at the contact points.

To model the failure phenomena of granular materials in geo‐mechanics and geo‐technical engineering problems; and to be a component model in a combined discrete‐continuum macroscopic approach or a two‐scale discrete‐continuum micro‐ macro‐scopic approach to granular media.

This paper develops a new discrete particle model to describe granular media in several branches of engineering such as soil mechanics, power technologies or sintering processes.

This paper presents a general procedure for solving 3D contact problems with implicit finite element codes. Emphasis is put on generality and robustness. Bodies in contact can be 3D solids or shells. Material and geometric nonlinearities can be dealt with (elasto‐plasticity, elasto‐visco‐plasticity, nonlinear elasticity, large displacements, strains and rotations). Different kinds of interaction are supported (tied, slip, friction). Advantage is taken of the solution history in order to improve the efficiency of the search algorithm. Numerical examples illustrate the general character of the proposed algorithm.