A macro model for electroadhesive contact of a soft finger with a touchscreen

A contact problem of electroadhesion for a conductive elastic body pressed against a rigid plane surface of a dielectric coating covering a conductive substrate is formulated applying the Johnsen-Rahbek approximation for the attractive surface stresses and the Derjaguin-Muller-Toporov (DMT) hypothesis about the influence of the adhesive stresses on the deformable shape of the elastic body. An approximate solution is obtained using the Winkler--Fuss deformation model with the equivalent (contact load dependent) stiffness coefficient evaluated according to the Xydas--Kao soft finger model. The friction force under applied voltage is evaluated as the product of the coefficient of friction and the integral of the macro contact pressure over the apparent contact area. The upper and lower estimates for the friction force are discussed in the case of absence of any external normal load

Contact probing of stretched membranes and adhesive interactions: graphene and other two-dimensional materials

Contact probing is the preferable method for studying mechanical properties of thin two-dimensional (2D) materials. These studies are based on analysis of experimental force–displacement curves obtained by loading of a stretched membrane by a probe of an atomic force microscope or a nanoindenter. Both non-adhesive and adhesive contact interactions between such a probe and a 2D membrane are studied. As an example of the 2D materials, we consider a graphene crystal monolayer whose discrete structure is modelled as a 2D isotropic elastic membrane. Initially, for contact between a punch and the stretched circular membrane, we formulate and solve problems that are analogies to the Hertz-type and Boussinesq frictionless contact problems. A general statement for the slope of the force–displacement curve is formulated and proved. Then analogies to the JKR (Johnson, Kendall and Roberts) and the Boussinesq–Kendall contact problems in the presence of adhesive interactions are formulated. General nonlinear relations among the actual force, displacements and contact radius between a sticky membrane and an arbitrary axisymmetric indenter are derived. The dimensionless form of the equations for power-law shaped indenters has been analysed, and the explicit expressions are derived for the values of the pull-off force and corresponding critical contact radius

Size effect and multiscale fracture

We study fracture of notched samples made of quasi-brittle, polyphase materials like rock, concrete or ceramics. The fracture demonstrates the size effect during loading. This means that a full-size sample made of such a material exhibits different fracture behaviour than a laboratory-size sample. The effect is explained by the existence of an extended zone of distributed defects and cracks (process zone) that surrounds the tip of the propagating fracture. The growth mechanisms of the process zone is scale-dependent: in an unbounded sample or a full-size structure, the zone develops until its maximum width and then it remains of the same width, while in a bounded sample that is less than some critical size, the process zone cannot be fully developed. Various similarity and scaling approaches to mechanics of multiple fracture are discussed. The growing process zone is modelled as a pattern of fractures having fractal properties on the intermediate stage of the development of the pattern. A formula is derived for the critical tensile stress that depends on both the sample size and the size of the process zone

Fundamental relations for frictional and adhesive nonoindentation tests

Fundamental relations for depth-sensing nanoindentation are derived for indenters of various shapes and for various boundary conditions within the contact region. In particular, it is shown that some uncertainties in nanoindentation measurements, which are sometimes attributed to properties of the material, can be explained and quantitatively described by properly accounting for geometric deviation of the indenter tip from its nominal geometry

Indentation of thin elastic films glued to rigid substrate: Asymptotic solutions and effects of adhesion

Indentation of a thin elastic film attached through an interlayer to a rigid support is studied. Because the common interpretations of depth-sensing indentation tests are not applicable to such structured coatings, usually various approximating functions are employed to take into account influence of the interlayer. Contrary to the common approaches, a strict mathematical approach is applied here to study the problems under consideration assuming that the thickness of the two-layer structure is much less than characteristic dimension of the region of contact between the indenter and the coating. A simple derivation of asymptotic relations for displacements and stresses is presented. It is shown that often the leading term approximation to the non-adhesive contact problems is equivalent to contact problem for a Winkler-Fuss elastic foundation with an effective elastic constant. Because the contact between the indenter and the film at nanoscale may be greatly affected by adhesion, the adhesive problem for these bilayer coatings is studied in the framework of the JKR (Johnson, Kendall, and Roberts) theory of adhesion. Assuming the indenter shape near the tip has some deviation from its nominal shape and using the leading term approximation of the layered coatings, the explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius of adhesive contact region

Adhesive contact between silicon-based mems tooth surfaces modelled by the multiscale multi-block model

The contact interactions between microgear silicon-based MEMS teeth working in a clean and a vacuum environment are under consideration. A new approach has used to determine the friction force and the coefficient of friction over the whole meshing surfaces of the teeth. In this approach, the dry friction force is calculated through the energy dissipated during sliding contact between two meshed micro-tooth elastic rough surfaces. The energy dissipated may be caused by the different physical and chemical interactions between the counterparts surfaces. Due to the vacuum environment, these mechanisms reduced to the energy lost due to the dissociation of chemical and van der Waals bonds, and the energy lost through the elastic interlocking between the asperities located on the meshing micro-tooth surfaces. There is no plastic deformation of the microgear tooth surface asperities due to their size and the Polonsky-Keer effect. A multiscale hierarchical elastic structure (a multiscale block) is used to model the surface asperities. The tooth block roughness has modelled at two scales specified by the character of interactions: atomic level, where chemical interactions occur, and adhesive subscale, where van der Waals interactions are significant. The adhesion layer is defined similarly to Maugis approximation. The adhesion force of each nanoasperity has assumed to be equal to the pull-off force in the Boussinesq-Kendall model and corrected by the Borodich no-slip coefficient. Atomic Force Microscopy (AFM) techniques have been used to measure the tooth roughness. It is argued that there be a high probability for stiction between the clean silicon surfaces due to very high values of the friction force between the micro-conjunctions. On the other hand, the tooth surfaces having functionalized carbon-based layers are much less prone to stiction. However, due to wear of the functionalized coating the probability of stiction will start to increase. The results of the simulation for both the non-functionalized and functionalized micro-tooth surfaces (silicon-based MEMS surfaces) are presented