Numerical Analysis of a Contact Problem with Wear

This paper represents a sequel to the previous one, where numerical solution of a quasistatic contact problem is considered for an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact surface of the body caused by the friction. Some preliminary error analysis for a fully discrete approximation of the contact problem was provided in the previous paper. In this paper, we consider a more general fully discrete numerical scheme for the contact problem, derive optimal order error bounds and present computer simulation results showing that the numerical convergence orders match the theoretical predictions.Comment: 13 pages, 6 figure

Wetting of Flat Gradient Surfaces

Gradient, chemically modified, flat surfaces enable directed transport of droplets. Calculation of apparent contact angles inherent for gradient surfaces is challenging even for atomically flat ones. Wetting of gradient, flat solid surfaces is treated within the variational approach, under which the contact line is free to move along the substrate. Transversality conditions of the variational problem give rise to the generalized Young equation valid for gradient solid surfaces. The apparent (equilibrium) contact angle of a droplet, placed on a gradient surface depends on the radius of the contact line and the values of derivatives of interfacial tensions. The linear approximation of the problem is considered. It is demonstrated that the contact angle hysteresis is inevitable on gradient surfaces. Electrowetting of gradient surfaces is discussed.Comment: 14 pages, 4 figure

Modelling linered engine blocks

Factors that affect heat transfer in the linered aluminium engine block are examined to determine their importance. Conduction is found to be the dominant mode of heat transfer, and the interface is characterised as imperfect contact if there are no surface manufacturing defects larger than 139 microns. A model is proposed to estimate the effective conductivity for imperfect contact. This thermal conductance depends on the area of contact, macroscopic roughness, the contact pressure and the interstitial medium. The transfer of heat and the distribution of stress in line red engine blocks are coupled, and the problem is strongly non-linear. A finite element solution procedure for solving the heat transfer problem in the linered engine block is outlined

Controlling sliding droplets with optimal contact angle distributions and a phase field model

We consider the optimal control of a droplet on a solid by means of the static contact angle between the contact line and the solid. The droplet is described by a thermodynamically consistent phase field model from [Abels et al., Math. Mod. Meth. Appl. Sc., 22(3), 2012] together with boundary data for the moving contact line from [Qian et al., J. Fluid Mech., 564, 2006]. We state an energy stable time discrete scheme for the forward problem based on known results, and pose an optimal control problem with tracking type objective.TU Berlin, Open-Access-Mittel - 201

Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem

In this work we analyze a non-clamped dynamic viscoelastic contact problem involving thermal effect. The friction law is described by a nonmonotone relation between the tangential stress and the tangential velocity. This leads to a system of hyperbolic inclusion for displacement and parabolic equation for temperature. We provide a fully discrete approximation of studied problem and find optimal error estimates without any smallness assumption on the data. The theoretical result is illustrated numerically.Comment: 19 pages, unfinishe

Wheel–rail contact: experimental study of the creep forces–creepage relationships

The wheel–rail contact problem plays an important role in the simulation methods used to solve railway dynamics problems. As a consequence, many different mathematical models have been developed to calculate wheel–rail contact forces. However, most of them tackle this problem purely from a theoretical point of view and need to be experimentally validated. Such validation could also reveal the influence of certain parameters not taken into account in the mathematical developments. This paper presents the steps followed in building a scaled test-bench to experimentally characterise the wheel–rail contact problem. The results of the longitudinal contact force as a function of the longitudinal creepage are obtained and the divergences with respect to Kalker's simplified theory are analysed. The influence of lateral creepage, angular velocity and certain contaminants such as cutting fluid or high positive friction modifier is also discussed