Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Modelling adhesion and friction in contact problems

The main objective of this thesis is to obtain a better understanding of adhesive contacts and their frictional behaviour. Both natural and man-made surfaces are rough over a wide range of length scales. Tribological studies of rough surfaces need to account for the interactions between these asperities. In this work a sim- ple atomistically–inspired macro-scale model is developed to study smooth and rough contacts between elastically deformable bodies where adhesion and fric- tion are simultaneously active at the interface. A full description of the model is presented in Chapter 2. There, the Green’s function molecular dynamics (GFMD) technique is extended to explicitly de- scribe the two solids in contact and their mixed-mode interface interactions. The interactions between surfaces are described through a coupled cohesive-zone model implemented in the GFMD technique. The extended GFMD technique includes an incremental iterative scheme, which is necessary to capture the con- tact area evolution when tangential tractions develop at the interface between the solids under loading.MSE-

Modelling coupled normal and tangential tractions in adhesive contacts

This paper presents a nanoscale-inspired continuum model to capture the coupling of adhesion and friction in contact-mechanics problems. The method relies on Green's function molecular dynamics to calculate the elastic body fields and on a phenomenological mixed-mode coupled cohesive-zone model to describe the interplay between normal and tangential tractions, i.e. adhesion and friction. While the presented formulation is applicable to linearly elastic solids with generic surface roughness, the focus of our analysis is on the indentation of an array of circular rigid punches into a flat, deformable solid. Our results show that the coupling between adhesion and friction leads to an increase in the contact size and a decrease in the pull-off load

Modeling adhesive contacts under mixed-mode loading

Experiments show that when an adhesive contact is subjected to a tangential load the contact area reduces, symmetrically or asymmetrically, depending on whether the contact is under tension or compression. What happens after the onset of sliding is more difficult to be assessed because conducting experiments is rather complicated, especially under tensile loading. Here, we provide through numerical simulations, a complete picture of how the contact area and tractions of an adhesive circular smooth punch evolve under mixed-mode loading, before and after sliding. First, the Green's function molecular dynamics method is extended to include the description of the interfacial interactions between contacting bodies by means of traction–separation constitutive laws that enforce coupling between tension (or compression) and shear. Next, simulations are performed to model sliding of a circular smooth punch against a flat rigid substrate, under tension and compression. In line with the experimental observations, the reduction in the contact area during shear loading is found to be symmetric under tension and asymmetric under compression. In addition, under tensile loading, full detachment is observed at the onset of sliding with a non-zero value of the tangential force. After the onset of sliding and the occurrence of slip instability, the contact area abruptly increases (reattachment), under both tension and compression. For interfaces with high friction, the reattachment occurs only partially. However, a full reattachment is attainable when friction is low.(OLD) MSE-

On the proportionality between area and load in line contacts

The relative contact area of rough surface contacts is known to increase linearly with reduced pressure, with proportionality factor κ. In its common definition, the reduced pressure contains the root-mean-square gradient (RMSG) of the surface. Although easy to measure, the RMSG of the entire surface does not coincide, at small loads, with the RMSG over the actual contact area g¯ r, which gives a better description of the contact between rough surfaces. It was recently shown that, for Hertzian contacts, linearity between area and load is indeed obtained only if the RMSG is determined over the actual contact area. Similar to surface contacts, in line contacts, numerical data are often studied using theories that predict linearity by design. In this work, we revisit line contact problems and examine whether or not the assumption of linearity for line contacts holds true. We demonstrate, using Green’s function molecular dynamics simulations, that κ for line contacts is not a constant: It depends on both the reduced pressure and the Hurst exponent. However, linearity holds when the RMSG is measured over the actual contact area. In that case, we could compare κ for line and surface contacts and found that their ratio is approximately 0.9. Finally, by analytically deriving the proportionality factor using g¯ r in the original model of Greenwood and Williamson, a value is obtained that is surprisingly in good agreement with our numerical results for rough surface contacts.(OLD) MSE-

On the load-area relation in rough adhesive contacts

It is well established that, at small loads, a linear relation exists between contact area and reduced pressure for elastic bodies with non-adhesive rough surfaces. In the case of adhesive contacts, however, there is not yet a general consensus on whether or not linearity still holds. In this work evidence is provided, through numerical simulations, that the relation is non-linear. The simulations here presented can accurately describe contact between self-affine adhesive rough surfaces, since they rely on Green's function molecular dynamics to describe elastic deformation and on coupled phenomenological traction-separation laws for the interfacial interactions. The analysis is performed for two-dimensional compressible and incompressible bodies under plane strain conditions. Interfaces with various roughness parameters and work of adhesion are considered.(OLD) MSE-7(OLD) MSE-