Energy Loss in the Impact of Elastic Spheres on a Rigid Half-Space in Presence of Adhesion

Adhesion can cause energy losses in asperities or particles coming into dynamic contact resulting in frictional dissipation, even if the deformation occurring is purely elastic. Such losses are of special significance in impact of nanoparticles and friction between surfaces under low contact pressure to hardness ratio. The objective of this work is to study the effect of adhesion during the normal impact of elastic spheres on a rigid half-space, with an emphasis on understanding the mechanism of energy loss. We use finite element method for modeling the impact phenomenon, with the adhesion due to van der Waals force and the short-range repulsion included as body forces distributed over the volume of the sphere. This approach, in contrast with commonly used surface force approximation, helps to model the interactions in a more precise way. We find that the energy loss in impact of elastic spheres is negligible unless there are adhesion-induced instabilities. Significant energy loss through elastic stress waves occurs due to jump-to-contact and jump-out-of-contact instabilities and can even result in capture of the elastic sphere on the half-space.

Fast decay of the velocity autocorrelation function in dense shear flow of inelastic hard spheres

We find in complementary experiments and event-driven simulations of sheared inelastic hard spheres that the velocity autocorrelation function psi(t) decays much faster than t(-3/2) obtained for a fluid of elastic spheres at equilibrium. Particle displacements are measured in experiments inside a gravity-driven flow sheared by a rough wall. The average packing fraction obtained in the experiments is 0.59, and the packing fraction in the simulations is varied between 0.5 and 0.59. The motion is observed to be diffusive over long times except in experiments where there is layering of particles parallel to boundaries, and diffusion is inhibited between layers. Regardless, a rapid decay of psi(t) is observed, indicating that this is a feature of the sheared dissipative fluid, and is independent of the details of the relative particle arrangements. An important implication of our study is that the non-analytic contribution to the shear stress may not be present in a sheared inelastic fluid, leading to a wider range of applicability of kinetic theory approaches to dense granular matter.

Non-slipping Adhesive Contact between Mismatched Elastic Cylinders

要: We have recently proposed a generalized JKR model for non-slipping adhesive contact between two elastic spheres subjected to a pair of pulling forces and a mismatch strain (Chen, S., Gao, H., 2006c. Non-slipping adhesive contact between mismatched elastic spheres: a model of adhesion mediated deformation sensor. J. Mech. Phys. Solids 54, 1548-1567). Here we extend this model to adhesion between two mismatched elastic cylinders. The attention is focused on how the mismatch strain affects the contact area and the pull-off force. It is found that there exists a critical mismatch strain at which the contact spontaneously dissociates. The analysis suggests possible mechanisms by which mechanical deformation can affect binding between cells and molecules in biology.

Mapping forces in 3D elastic assembly of grains

Our understanding of the elasticity and rheology of disordered materials, such as granular piles, foams, emulsions or dense suspensions relies on improving experimental tools to characterize their behaviour at the particle scale. While 2D observations are now routinely carried out in laboratories, 3D measurements remain a challenge. In this paper, we use a simple model system, a packing of soft elastic spheres, to illustrate the capability of X-ray microtomography to characterise the internal structure and local behaviour of granular systems. Image analysis techniques can resolve grain positions, shapes and contact areas; this is used to investigate the material's microstructure and its evolution upon strain. In addition to morphological measurements, we develop a technique to quantify contact forces and estimate the internal stress tensor. As will be illustrated in this paper, this opens the door to a broad array of static and dynamical measurements in 3D disordered systems

Mapping forces in a 3D elastic assembly of grains

Our understanding of the elasticity and rheology of disordered materials, such as granular piles, foams, emulsions or dense suspensions relies on improving experimental tools to characterise their behaviour at the particle scale. While 2D observations are now routinely carried out in laboratories, 3D measurements remain a challenge. In this paper, we use a simple model system, a packing of soft elastic spheres, to illustrate the capability of X-ray microtomography to characterise the internal structure and local behaviour of granular systems. Image analysis techniques can resolve grain positions, shapes and contact areas; this is used to investigate the materials microstructure and its evolution upon strain. In addition to morphological measurements, we develop a technique to quantify contact forces and estimate the internal stress tensor. As will be illustrated in this paper, this opens the door to a broad array of static and dynamical measurements in 3D disordered systems. © 2011 Elsevier Ltd. All rights reserved.

Transitions Between Different Contact Models

The transitions between the different contact models which include the Hertz, Bradley, Johnson-Kendall-Roberts (JKR), Derjaguin-Muller-Toporov (DMT) and Maugis-Dugdale (MD) models are revealed by analyzing their contact pressure profiles and surface interactions. Inside the contact area, surface interaction/adhesion induces tensile contact pressure around the contact edge. Outside the contact area, whether or not to consider the surface interaction has a significant influence on the contact system equilibrium. The difference in contact pressure due to the surface interaction inside the contact area and the equilibrium influenced by the surface interaction outside the contact area are physically responsible for the different results of the different models. A systematic study on the transitions between different models is shown by analyzing the contact pressure profiles and the surface interactions both inside and outside the contact area. The definitions of contact radius and the flatness of contact surfaces are also discussed. (C) Koninklijke Brill NV, Leiden, 2008.

Tuning The Geometrical Parameters Of Biomimetic Fibrillar Structures To Enhance Adhesion

Fibrillar structures are common features on the feet of many animals, such as geckos, spiders and flies. Theoretical analyses often use periodical array to simulate the assembly, and each fibril is assumed to be of equal load sharing (ELS). On the other hand, studies on a single fibril show that the adhesive interface is flaw insensitive when the size of the fibril is not larger than a critical one. In this paper, the Dugdale Barenblatt model has been used to study the conditions of ELS and how to enhance adhesion by tuning the geometrical parameters in fibrillar structures. Different configurations in an array of fibres are considered, such as line array, square and hexagonal patterns. It is found that in order to satisfy flaw-insensitivity and ELS conditions, the number of fibrils and the pull-off force of the fibrillar interface depend significantly on the fibre separation, the interface interacting energy, the effective range of cohesive interaction and the radius of fibrils. Proper tuning of the geometrical parameters will enhance the pull-off force of the fibrillar structures. This study may suggest possible methods to design strong adhesion devices for engineering applications.

Non-Slipping Jkr Model For Transversely Isotropic Materials

A generalized plane strain JKR model is established for non-slipping adhesive contact between an elastic transversely isotropic cylinder and a dissimilar elastic transversely isotropic half plane, in which a pulling force acts on the cylinder with the pulling direction at an angle inclined to the contact interface. Full-coupled solutions are obtained through the Griffith energy balance between elastic and surface energies. The analysis shows that, for a special case, i.e., the direction of pulling normal to the contact interface, the full-coupled solution can be approximated by a non-oscillatory one, in which the critical pull-off force, pull-off contact half-width and adhesion strength can be expressed explicitly. For the other cases, i.e., the direction of pulling inclined to the contact interface, tangential tractions have significant effects on the pull-off process, it should be described by an exact full-coupled solution. The elastic anisotropy leads to an orientation-dependent pull-off force and adhesion strength. This study could not only supply an exact solution to the generalized JKR model of transversely isotropic materials, but also suggest a reversible adhesion sensor designed by transversely isotropic materials, such as PZT or fiber-reinforced materials with parallel fibers. (c) 2007 Elsevier Ltd. All rights reserved.

Acoustic radiation force of a Bessel beam on a porous sphere.

The possibility of using acoustic Bessel beams to produce an axial pulling force on porous particles is examined in an exact manner. The mathematical model utilizes the appropriate partial-wave expansion method in spherical coordinates, while Biot's model is used to describe the wave motion within the poroelastic medium. Of particular interest here is to examine the feasibility of using Bessel beams for (a) acoustic manipulation of fine porous particles and (b) suppression of particle resonances. To verify the viability of the technique, the radiation force and scattering form-function are calculated for aluminum and silica foams at various porosities. Inspection of the results has shown that acoustic manipulation of low porosity (<0.3) spheres is similar to that of solid elastic spheres, but this behavior significantly changes at higher porosities. Results have also shown a strong correlation between the backscattered form-function and the regions of negative radiation force. It has also been observed that the high-order resonances of the particle can be effectively suppressed by choosing the beam conical angle such that the acoustic contribution from that particular mode vanishes. This investigation may be helpful in the development of acoustic tweezers for manipulation of micro-porous drug delivery carrier and contrast agents.

Secondary flow induced by the rotation of two concentric spheres about their common diameter in micropolar fluids

In this paper, we have studied the secondary flow induced in a micropolar fluid by the rotation of two concentric spheres about a fixed diameter. The secondary flow exhibits behaviour commonly observed in visco-elastic fluids. In particular we have obtained the expressions for microrotation vector. Numerical results have been obtained for a number of values of relative rotations of the two spheres for a chosen set of values of fluid parameters. The results are presented graphically and compared with the previous investigations.

Bio-inspired mechanics of reversible adhesion: Orientation-dependent adhesion strength for non-slipping adhesive contact with transversely isotropic elastic materials

Geckos and many insects have evolved elastically anisotropic adhesive tissues with hierarchical structures that allow these animals not only to adhere robustly to rough surfaces but also to detach easily upon movement. In order to improve Our understanding of the role of elastic anisotropy in reversible adhesion, here we extend the classical JKR model of adhesive contact mechanics to anisotropic materials. In particular, we consider the plane strain problem of a rigid cylinder in non-slipping adhesive contact with a transversely isotropic elastic half space with the axis of symmetry oriented at an angle inclined to the surface. The cylinder is then subjected to an arbitrarily oriented pulling force. The critical force and contact width at pull-off are calculated as a function of the pulling angle. The analysis shows that elastic anisotropy leads to an orientation-dependent adhesion strength which can vary strongly with the direction of pulling. This study may suggest possible mechanisms by which reversible adhesion devices can be designed for engineering applications. (C) 2006 Elsevier Ltd. All rights reserved.

Vibration of pressurised, elastic, spherical shells

Balloons are one example of pressurised, elastic, spherical shells. Whilst analytical solutions exist for the vibration of pressurised spheres, these models only incorporate constant tension in the membrane. For elastic shells, changes in curvature will result in restoring forces that are proportional to the elasticity in the membrane; hence the assumption of constant tension is not valid. This paper describes an analytical solution for the natural frequencies of an elastic spherical shell subject to internal pressure. When the membrane tension is set to zero, the results are shown to converge to the analytical solution for a spherical shell, and when the skin elasticity is neglected, the results converge to the constant-tension solution. This analytical solution is used to predict the natural frequencies of a small balloon, based on a value for the elastic modulus that is determined using biaxial tensile testing. These predictions are compared to experimental measurements of balloon vibrations using impact hammer testing, and good agreement is seen.

The effect of elastic modulus and equilibrium vapor adsorption on capillary forces

Die Kapillarkraft entsteht durch die Bildung eines Meniskus zwischen zwei Festkörpen. In dieser Doktorarbeit wurden die Auswirkungen von elastischer Verformung und Flϋssigkeitadsorption auf die Kapillarkraft sowohl theoretisch als auch experimentell untersucht. Unter Verwendung eines Rasterkraftmikroskops wurde die Kapillarkraft zwischen eines Siliziumoxid Kolloids von 2 µm Radius und eine weiche Oberfläche wie n.a. Polydimethylsiloxan oder Polyisopren, unter normalen Umgebungsbedingungen sowie in variierende Ethanoldampfdrϋcken gemessen. Diese Ergebnisse wurden mit den Kapillarkräften verglichen, die auf einem harten Substrat (Silizium-Wafer) unter denselben Bedingungen gemessen wurden. Wir beobachteten eine monotone Abnahme der Kapillarkraft mit zunehmendem Ethanoldampfdruck (P) fϋr P/Psat > 0,2, wobei Psat der Sättigungsdampfdruck ist.rnUm die experimentellen Ergebnisse zu erklären, wurde ein zuvor entwickeltes analytisches Modell (Soft Matter 2010, 6, 3930) erweitert, um die Ethanoladsorption zu berϋcksichtigen. Dieses neue analytische Modell zeigte zwei verschiedene Abhängigkeiten der Kapillarkraft von P/Psat auf harten und weichen Oberflächen. Fϋr die harte Oberfläche des Siliziumwafers wird die Abhängigkeit der Kapillarkraft vom Dampfdruck vom Verhältnis der Dicke der adsorbierten Ethanolschicht zum Meniskusradius bestimmt. Auf weichen Polymeroberflächen hingegen hängt die Kapillarkraft von der Oberflächenverformung und des Laplace-Drucks innerhalb des Meniskus ab. Eine Abnahme der Kapillarkraft mit zunehmendem Ethanoldampfdruck hat demnach eine Abnahme des Laplace-Drucks mit zunehmendem Meniskusradius zur folge. rnDie analytischen Berechnungen, fϋr die eine Hertzsche Kontakt-deformation angenommen wurde, wurden mit Finit Element Methode Simulationen verglichen, welche die reale Deformation des elastischen Substrats in der Nähe des Meniskuses explizit berϋcksichtigen. Diese zusätzliche nach oben gerichtete oberflächenverformung im Bereich des Meniskus fϋhrt zu einer weiteren Erhöhung der Kapillarkraft, insbesondere fϋr weiche Oberflächen mit Elastizitätsmodulen < 100 MPa.rn