Effect of Body Lateral Extension Upon the Elastic Contact

2009 ◽  
Author(s):  
Marilena Glovnea ◽  
Emanuel Diaconescu
Keyword(s):  
Half Space ◽  
Outer Radius ◽  
Force Balance ◽  
Contact Theory ◽  
Contact Radius ◽  
Elastic Contact ◽  
Space Theory ◽  
Lateral Extension ◽  
Load Direction ◽  
Force Balance Equation

Half-space contact theory cannot be applied when either contacting bodies are thin or they possess small transversal dimensions. The former situation is often dealt with, but the latter seems to be neglected. This paper investigates the effect of outer radius of cylindrical bodies upon the contact stress field. The method consists in adding supplementary displacements and stresses to the half-space solution in order to fulfill the boundary conditions and the force balance equation on load direction. It is found that the half-space theory is applicable if transversal radius exceeds contact radius.

scholarly journals Intersurface Adhesion in the Presence of Capillary Condensation

2018 ◽  
Vol 85 (6) ◽  
Author(s):  
Jianfeng Sun ◽  
Sinan Müftü ◽  
April Z. Gu ◽  
Kai-Tak Wan
Keyword(s):  
Capillary Condensation ◽  
Finite Size ◽  
Force Balance ◽  
Contact Theory ◽  
Contact Radius ◽  
Water Molecules ◽  
Hertz Contact ◽  
Rigid Substrate ◽  
Approach Distance ◽  
Classical Models

An elastic sphere adheres to a rigid substrate in the presence of moisture. The adhesion–detachment trajectory is derived based on the Hertz contact theory that governs the contact mechanics and Laplace–Kelvin equation that governs the water meniscus at the interface. The intersurface attraction is solely provided by the Laplace pressure within the meniscus. Interrelation between the applied load, contact radius, and approach distance is derived based on a force balance. The resulting “pulloff” force to detach the sphere exceeds the critical load in the Derjaguin–Muller–Toporov (DMT) limit which only holds at saturated moisture. The new model accounts for the finite size of water molecules that is missing in virtually all classical models.

Static Determinacy in the Theory of Finite Width Foil Bearings

1974 ◽  
Vol 41 (1) ◽  
pp. 51-54 ◽  
Author(s):  
W. E. Langlois
Keyword(s):  
Force Balance ◽  
Finite Width ◽  
Foil Bearings ◽  
Lubrication Equation ◽  
Foil Bearing ◽  
Edge Conditions ◽  
Single Force ◽  
Static Determinacy ◽  
Force Balance Equation ◽  
Determinate Problem

The assumption of “perfect flexibility” is shown to be self-consistent in an important class of finite-width foil bearing problems. When the membrane equations are written in the “stretched coordinates” of foil bearing theory, the usual edge conditions on the tape result in a statically determinate problem. The tape dynamics couples to the Reynolds lubrication equation through a single force-balance equation which does not entail the elastic strain.

Numerical Investigation of the Combined Effects of Biomolecular Adsorption and Microdroplet Evaporation on the Performance of the Electrocapillary-Based Digital Microfluidic Systems

2011 ◽  
Author(s):  
Ali Ahmadi ◽  
Mina Hoorfar
Keyword(s):  
Mass Loss ◽  
Protein Concentration ◽  
Adsorption Rate ◽  
Force Balance ◽  
Combined Effects ◽  
Microfluidic Systems ◽  
Gibbs Equation ◽  
Rate Effects ◽  
Digital Microfluidic ◽  
Force Balance Equation

In this article, microdroplet motion in the electrocapillary-based digital microfluidic systems is modeled accurately, and the combined effects of the biomolecular adsorption and micro-droplet evaporation on the performance of the device are investigated. An electrohydrodynamic approach is used to model the driving and resisting forces, and Fick’s law and Gibbs equation are used to calculate the microdroplet evaporation and adsorption rate. Effects of the adsorption and evaporation rates are then implemented into the microdroplet dynamics by adding new terms into the force balance equation. It is shown that mass loss due to the evaporation tends to increase the protein concentration, and on the other hand, the increased concentration due to the mass loss increases the biomolecular adsorption rate which has a reverse effect on the concentration. The modeling results indicate that evaporation and adsorption play crucial roles in the microdroplet dynamics.

The Elastic Contact of Rough Spheres

1967 ◽  
Vol 34 (1) ◽  
pp. 153-159 ◽  
Author(s):  
J. A. Greenwood ◽  
J. H. Tripp
Keyword(s):  
Pressure Distribution ◽  
Physical Contact ◽  
Contact Theory ◽  
Elastic Contact ◽  
Smooth Surfaces ◽  
Effective Pressure ◽  
Electric Contact

The Hertzian theory of elastic contact between spheres is extended by considering one of the spheres to be rough, so that contact occurs, as in practice, at a number of discrete microcontacts. It is found that the Hertzian results are valid at sufficiently high loads, but at lower loads the effective pressure distribution is much lower and extends much further than for smooth surfaces. The relevance to the physical-contact theory of friction and electric contact is considered.

scholarly journals The Elastic Contact of Rough Spheres Investigated Using a Deterministic Multi-Asperity Model

2019 ◽  
Vol 10 (01) ◽  
pp. 1841002 ◽  
Author(s):  
Vladislav A. Yastrebov
Keyword(s):  
Contact Area ◽  
Rough Surfaces ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Contact Radius ◽  
Geometrical Shape ◽  
Elastic Contact ◽  
Deterministic Analysis ◽  
Asperity Model ◽  
Deformation Modes

In this paper, we use a deterministic multi-asperity model to investigate the elastic contact of rough spheres. Synthetic rough surfaces with controllable spectra were used to identify individual asperities, their locations and curvatures. The deterministic analysis enables to capture both particular deformation modes of individual rough surfaces and also statistical deformation regimes, which involve averaging over a big number of roughness realizations. Two regimes of contact area growth were identified: the Hertzian regime at light loads at the scale of a single asperity, and the linear regime at higher loads involving multiple contacting asperities. The transition between the regimes occurs at the load which depends on the second and the fourth spectral moments. It is shown that at light indentation the radius of circumference delimiting the contact area is always considerably larger than Hertzian contact radius. Therefore, it suggests that there is no scale separation in contact problems at light loads. In particular, the geometrical shape cannot be considered separately from the surface roughness at least for approaching greater than one standard roughness deviation.

Seismic velocities and Poisson’s ratio of shallow unconsolidated sands

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 559-564 ◽  
Author(s):  
Ran Bachrach ◽  
Jack Dvorkin ◽  
Amos M. Nur
Keyword(s):  
Wave Velocity ◽  
Poisson’S Ratio ◽  
Tangential Component ◽  
Poisson's Ratio ◽  
Contact Theory ◽  
Beach Sand ◽  
Contact Radius ◽  
Seismic Velocities ◽  
S Wave ◽  
Unconsolidated Sands

We determined P- and S-wave velocity depth profiles in shallow, unconsolidated beach sand by analyzing three‐component surface seismic data. P- and S-wave velocity profiles were calculated from traveltime measurements of vertical and tangential component seismograms, respectively. The results reveal two discrepancies between theory and data. Whereas both velocities were found to be proportional to the pressure raised to the power of 1/6, as predicted by the Hertz‐Mindlin contact theory, the actual values of the velocities are less than half of those calculated from this theory. We attribute this discrepancy to the angularity of the sand grains. Assuming that the average radii of curvature at the grain contacts are smaller than the average radii of the grains, we modify the Hertz‐Mindlin theory accordingly. We found that the ratio of the contact radius to the grain radius is about 0.086. The second disparity is between the observed Poisson’s ratio of 0.15 and the theoretical value (0.008 for random pack of quartz spheres). This discrepancy can be reconciled by assuming slip at the grain contacts. Because slip decreases the shearing between grains, Poisson’s ratio increases.

Effects of strain hardening and residual stress in impression on the instrumented indentation technique

2006 ◽  
Vol 21 (7) ◽  
pp. 1680-1686
Author(s):  
L.Z. Liu ◽  
Y.W. Bao ◽  
Y.C. Zhou
Keyword(s):  
Residual Stress ◽  
Strain Hardening ◽  
Energy Analysis ◽  
Maximum Load ◽  
Contact Theory ◽  
Elastic Contact ◽  
Instrumented Indentation ◽  
Indentation Technique ◽  
Indentation Tests ◽  
Elastic Loading

Finite element analyses were carried out to simulate the loading, unloading, and reloading processes of indentation tests. It was found that the validity of applying the elastic contact theory to the indentation unloading process is strongly related to the strain hardening and residual stress in impression. It is the combination of strain hardening and residual stress that causes the unloading or reloading curves to show elastic loading in the range from zero to the maximum load whereas the reloading curve on the impression without strain hardening and residual stress shows elastic–plastic loading in the same range. These computations indicate that applying the elastic contact theory to the unloading or reloading processes, the fundamental prerequisite of the instrumented indentation technique, is valid because of the existence of strain hardening and residual stress. The mechanism of this hardening effect is discussed through energy analysis.

On the Applicability of Sneddon's Solution for Interpreting the Indentation of Nonlinear Elastic Biopolymers

2014 ◽  
Vol 81 (9) ◽  
Author(s):  
Man-Gong Zhang ◽  
Jinju Chen ◽  
Xi-Qiao Feng ◽  
Yanping Cao
Keyword(s):  
Elastic Properties ◽  
Viscoelastic Properties ◽  
Contact Theory ◽  
Elastic Contact ◽  
Flat Punch ◽  
Linear Elastic ◽  
Contact Models ◽  
Properties Of Materials ◽  
Nonlinear Elastic ◽  
Viscoelastic Contact

Indentation has been widely used to characterize the mechanical properties of biopolymers. Besides Hertzian solution, Sneddon's solution is frequently adopted to interpret the indentation data to deduce the elastic properties of biopolymers, e.g., elastic modulus. Sneddon's solution also forms the basis to develop viscoelastic contact models for determining the viscoelastic properties of materials from either conical or flat punch indentation responses. It is worth mentioning that the Sneddon's solution was originally proposed on the basis of linear elastic contact theory. However, in both conical and flat punch indentation of compliant materials, the indented solid may undergo finite deformation. In this case, the extent to which the Sneddon's solution is applicable so far has not been systematically investigated. In this paper, we use the combined theoretical, computational, and experimental efforts to investigate the indentation of hyperelastic compliant materials with a flat punch or a conical tip. The applicability of Sneddon's solutions is examined. Furthermore, we present new models to determine the elastic properties of nonlinear elastic biopolymers.

Sign in / Sign up

Export Citation Format

Share Document