Fully Developed Sliding of Rough Surfaces

1989 ◽  
Vol 111 (3) ◽  
pp. 445-451 ◽  
Author(s):  
C. Liu ◽  
B. Paul
Keyword(s):  
Closed Form ◽  
Contact Region ◽  
Tangential Force ◽  
Normal Pressure ◽  
Shear Stresses ◽  
Closed Form Solutions ◽  
Pressure Distributions ◽  
The Coefficient Of Friction ◽  
Force Components ◽  
Instantaneous Center

Given the contact region between two bodies, the normal pressure distribution over the contact region, and the coefficient of friction, we seek to find all combinations of tangential forces and twisting moment (about the normal to the contact surface) for which fully developed sliding impends. As part of the solution we must determine the distribution of the surface tractions (shear stresses) and the location of the instantaneous center (IC) of the impending motion. New closed form solutions of the stated problem are found for circular contact patches with pressure distributions corresponding to (a): a flat stamp; and (b): elastic spheroids with Hertzian pressure distributions. For contact regions other than circular, no closed form solutions are known. We have developed numerical procedures to solve for arbitrary contact patches, with arbitrary distributions of normal pressure, and present carpet plots of tangential force components (Fx, Fy) and IC coordinates for the following cases: flat ellipsoidal stamps; ellipsoidal indenters (Hertzian pressure); and a non-Hertzian, nonelliptical contact of a rail and wheel. Level curves of twisting moment Mz versus tangential force components are provided. Given any two of the three quantities (Fx, Fy, Mz), the algorithms and the plots in this paper make it possible and convenient to find the remaining force or moment which will cause gross sliding to impend, for virtually arbitrary contact regions and arbitrary pressure distributions.

Elasticity Approach to Load Transfer in Cord-Composite Materials

2009 ◽  
Vol 76 (6) ◽  
Author(s):  
Anthony J. Paris
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Axial Force ◽  
Load Transfer ◽  
Axial Loading ◽  
Shear Stresses ◽  
Matrix Interface ◽  
Closed Form Solutions ◽  
Apparent Modulus ◽  
Reinforced Composite

An elasticity approach to the mechanics of load transfer in cord-reinforced composite materials is developed. Finite cords embedded in an elastic matrix and subjected to axial loading is considered, and the extension-twist coupling of the cords is taken into account. Closed form solutions for the axial force and twisting moment in the cord, the shear stresses at the cord-matrix interface in the axial and circumferential directions, the effective axial modulus of the cord, and the apparent modulus of the cord composite are presented. An example of a cord composite typical of what can be found in steel-belted-radial tires is used to illustrate the results. It was found that large shear stresses occur at the cord-matrix interface in both the axial and circumferential directions at the cord ends and that the effective modulus of the cords may be greatly reduced. As a result, the apparent modulus of the composite may be significantly less than that found by a conventional application of the rule-of-mixtures approach.

scholarly journals Closed-Form Solutions for a Mode-III Moving Interface Crack at the Interface of Two Bonded Dissimilar Orthotropic Elastic Layers

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
B. M. Singh ◽  
J. Rokne ◽  
R. S. Dhaliwal
Keyword(s):  
Closed Form ◽  
Integral Transform ◽  
Practical Importance ◽  
Leading Edge ◽  
Shear Stresses ◽  
Mode Iii ◽  
Closed Form Solutions ◽  
Moving Interface ◽  
Elastic Layers ◽  
Physical Quantities

An integral transform technique is used to solve the elastodynamic problem of a crack of fixed length propagating at a constant speed at the interface of two bonded dissimilar orthotropic layers of equal thickness. Two cases of practical importance are investigated. Firstly, the lateral boundaries of the layers are clamped and displaced in equal and opposite directions to produce antiplane shear resulting in a tearing motion along the leading edge of the crack, and secondly, the lateral boundaries of the layers are subjected to shear stresses. The analytic solution for a semi-infinite crack at the interface of two bonded dissimilar orthotropic layers has been derived. Closed-form expressions are obtained for stressing the intensity factor and other physical quantities in all cases.

scholarly journals Effect of skin hydration on the dynamics of fingertip gripping contact

2011 ◽  
Vol 8 (64) ◽  
pp. 1574-1583 ◽  
Author(s):  
T. André ◽  
V. Lévesque ◽  
V. Hayward ◽  
P. Lefèvre ◽  
J.-L. Thonnard
Keyword(s):  
Coefficient Of Friction ◽  
Contact Region ◽  
Tangential Force ◽  
Normal Component ◽  
Specific Effect ◽  
Skin Hydration ◽  
Skin Area ◽  
Force Component ◽  
Dry Skin ◽  
The Coefficient Of Friction

The dynamics of fingertip contact manifest themselves in the complex skin movements observed during the transition from a stuck state to a fully developed slip. While investigating this transition, we found that it depended on skin hydration. To quantify this dependency, we asked subjects to slide their index fingertip on a glass surface while keeping the normal component of the interaction force constant with the help of visual feedback. Skin deformation inside the contact region was imaged with an optical apparatus that allowed us to quantify the relative sizes of the slipping and sticking regions. The ratio of the stuck skin area to the total contact area decreased linearly from 1 to 0 when the tangential force component increased from 0 to a maximum. The slope of this relationship was inversely correlated to the normal force component. The skin hydration level dramatically affected the dynamics of the contact encapsulated in the course of evolution from sticking to slipping. The specific effect was to reduce the tendency of a contact to slip, regardless of the variations of the coefficient of friction. Since grips were more unstable under dry skin conditions, our results suggest that the nervous system responds to dry skin by exaggerated grip forces that cannot be simply explained by a change in the coefficient of friction.

scholarly journals Closed-form solutions of hole distortion for use in deep-hole drilling measurements of residual stress in orthotropic plates

2016 ◽  
Vol 52 (2) ◽  
pp. 77-82 ◽  
Author(s):  
Carlos Garza ◽  
Anton Shterenlikht ◽  
Martyn J Pavier ◽  
David J Smith
Keyword(s):  
Residual Stress ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Hole Drilling ◽  
Shear Stresses ◽  
Deep Hole ◽  
Element Analysis ◽  
Deep Hole Drilling ◽  
Closed Form Solutions

The measurement of residual stress using the deep-hole drilling method relies on the evaluation of the distortion of a hole in a plate under the action of far-field direct and shear stresses. While closed-form solutions exist for the isotropic materials, in previous work for orthotropic materials, finite element analysis has been used to find the distortion. In this technical note, Lekhnitskii’s analysis is used to find closed-form solutions for the distortion of a circular hole in an orthotropic plate. The results are compared with those of finite element analysis for a range of material properties with excellent agreement.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
Sign in / Sign up

Export Citation Format

Share Document