Melan’s Problems With Weak Interface

1999 ◽  
Vol 67 (1) ◽  
pp. 22-28 ◽  
Author(s):  
S. Lenci
Keyword(s):  
Closed Form ◽  
Applied Load ◽  
Interface Stress ◽  
Interfacial Stress ◽  
Weak Interface ◽  
Concentrated Force ◽  
Zone Of Influence ◽  
Two Bodies

The problem of a fiber attached to an infinite sheet (Melan’s problem) has been reconsidered under the hypothesis that the adherence between the two bodies is not perfect. We have assumed that the link is guaranteed by the so-called “weak interface,” i.e., we have supposed that the jump of the displacement is linearly proportional to the interface stress. The solutions of (i) the case with a concentrated force acting on the fiber and (ii) the case of the redistribution of stresses as a consequence of the rupture of the fiber have been obtained in closed form. We have discussed how the interface stiffness k influences the solutions and, in particular, the interfacial stress. Emphasis is placed on determining how the zone of influence of the applied load is modified by k. Approximate (though accurate) simple expressions for the length of the zone of influence are given and discussed. [S0021-8936(00)01001-1]

The Elastic Plane With a Circular Insert, Loaded by a Tangentially Directed Force

1962 ◽  
Vol 29 (2) ◽  
pp. 362-368 ◽  
Author(s):  
M. Hete´nyi ◽  
J. Dundurs
Keyword(s):  
Closed Form ◽  
Elastic Properties ◽  
Classical Theory ◽  
Theory Of Elasticity ◽  
Elastic Plane ◽  
Elementary Functions ◽  
Explicit Formulas ◽  
Concentrated Force

The problem treated is that of a plate of unlimited extent containing a circular insert and subjected to a concentrated force in the plane of the plate and in a direction tangential to the circle. The elastic properties of the insert are different from those of the plate, and a perfect bond is assumed between the two materials. The solution is exact within the classical theory of elasticity, and is in a closed form in terms of elementary functions. Explicit formulas are given for the components of stress in Cartesian co-ordinates, and also in polar co-ordinates at the circumference of the insert.

Adhesive Contact of Bodies Having an Elliptical Contact Area

2005 ◽  
Author(s):  
K. L. Johnson ◽  
J. A. Greenwood
Keyword(s):  
Closed Form ◽  
Contact Area ◽  
Adhesive Contact ◽  
Contact Radius ◽  
General Shape ◽  
Elliptical Contact ◽  
Jkr Theory ◽  
Two Bodies

The so-called JKR theory of adhesion between elastic spheres in contact (Johnson, Kendall & Roberts 1971, Sperling 1964) has been widely used in micro-tribology. In this paper the theory is extended to solids of general shape and curvature. It is assumed that the area of contact is elliptical which turns out to be approximately true, though the eccentricity is different from that for non-adhesive contact. Closed form expressions are found for the variation with load of contact radius and displacement, as a function of the ratio of principal relative curvatures of the two bodies in contact. The pull-off force is found to decrease with increasing eccentricity from its value of 3πΔγR/2 in the case of contact of spheres of radius R.

The Axially Loaded Circular Cylinder

1962 ◽  
Vol 29 (2) ◽  
pp. 318-320
Author(s):  
H. D. Conway
Keyword(s):  
Exact Solution ◽  
Fourier Transform ◽  
Circular Cylinder ◽  
Closed Form ◽  
Cross Sections ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Transform Method ◽  
Fourier Transform Method

Commencing with Kelvin’s closed-form solution to the problem of a concentrated force acting at a given point in an indefinitely extended solid, a Fourier transform method is used to obtain an exact solution for the case when the force acts along the axis of a circular cylinder. Numerical values are obtained for the maximum direct stress on cross sections at various distances from the force. These are then compared with the corresponding stresses from the solution for an infinitely long strip, and in both cases it is observed that the stresses are practically uniform on cross sections greater than a diameter or width from the point of application of the load.

Effect of Stress Singularity on Stress Distribution and Initial Debonding of Interface End

2007 ◽  
Vol 334-335 ◽  
pp. 641-644
Author(s):  
Ying Dai ◽  
Xing Ji ◽  
Guo Dong Jiang
Keyword(s):  
Stress Distribution ◽  
Characteristic Length ◽  
Stress Singularity ◽  
Interfacial Stress ◽  
Unique Characteristic ◽  
Concentrated Force

Interfacial stress distribution of bonded quarter planes subjected a concentrated force was re-investigated based on Bogy’s solution [1]. It’s found that the characteristic length of the singularity of interface end (δ), varies with the index of stress singularity at interface end from millimeter to nanometer. This is a unique characteristic of stress singularity at interface end. How the characteristic length of the singularity of interface end (δ) influences the initial de-bonding of the interface end is a new question worth to pay attention. It’s found in the photoelasticity experiments that usually the debonding initiated at the interface end with singularity, but as the index of stress singularity, as well as the characteristic length of singularity of interface end, decrease to some extent, the initial debonding moves to an inner point near the interface end. This phenomenon clearly shows the index of stress singularity has obvious influence on the debonding of interface end.

An Educational Elasticity Problem With Friction, Part 1: Loading, and Unloading for Weak Friction

1981 ◽  
Vol 48 (4) ◽  
pp. 841-845 ◽  
Author(s):  
John Dundurs ◽  
Maria Comninou
Keyword(s):  
Closed Form ◽  
Elasticity Problem ◽  
Concentrated Force ◽  
Initial Loading ◽  
Loading And Unloading

The paper treats an elasticity problem with friction that can be solved in closed form. It involves an unbounded solid with a semi-infinite cut. The solid is compressed in a direction perpendicular to the cut, but the cut is induced to separate and slip locally by applying a concentrated force at the tip of the cut. The first part deals with the initial loading phase and includes unloading for weak friction.

Green’s Functions for Holes/Cracks in Laminates With Stretching-Bending Coupling

2005 ◽  
Vol 72 (2) ◽  
pp. 282-289 ◽  
Author(s):  
Chyanbin Hwu
Keyword(s):  
Closed Form ◽  
Composite Laminates ◽  
Green's Functions ◽  
Green’S Functions ◽  
Continuation Method ◽  
Elliptical Hole ◽  
Arbitrary Point ◽  
Two Dimensional ◽  
Concentrated Force ◽  
Concentrated Forces

Consider an infinite composite laminate containing a traction-free elliptical hole subjected to concentrated forces and moments at an arbitrary point outside the hole. This problem for two-dimensional deformation has been solved analytically in the literature, while for the general unsymmetric composite laminates stretching and bending coupling may occur and due to the mathematical complexity the associated Green’s functions have never been found for complete loading cases. Recently, by employing Stroh-like formalism for coupled stretching-bending analysis, the Green’s functions for the infinite laminates (without holes) were obtained in closed-form. Based upon the nonhole Green’s functions, through the use of analytical continuation method the Green’s functions for holes are now obtained in explicit closed-form for complete loading cases and are valid for the full fields. The Green’s functions for cracks are then obtained by letting the minor axis of ellipse be zero. By proper differentiation, the stress resultants and moments along the hole boundary and the stress intensity factors of cracks are also solved explicitly. Like the Green’s functions for the infinite laminates, only the solutions associated with the in-plane concentrated forces f^1,f^2 and out-of-plane concentrated moments m^1,m^2 have exactly the same form as those of the corresponding two-dimensional problems. For the cases under the concentrated force f^3 and torsion m^3, new types of solutions are obtained.

Roof deformation and collapse of stamps with isolated grooves: a contact mechanics approach

2021 ◽  
pp. 1-22
Author(s):  
Fan Jin ◽  
Changyu Tang ◽  
Xu Guo ◽  
Longteng Bai
Keyword(s):  
Contact Mechanics ◽  
Applied Load ◽  
Full Range ◽  
Applied Pressure ◽  
Elastic Strain Energy ◽  
Interfacial Stress ◽  
Element Analysis ◽  
Strong Adhesion ◽  
Contact Size ◽  
Roof Deformation

Abstract This paper has revisited the roof deformation and collapse of stamps with isolated grooves based on a contact mechanics approach, with emphasis on establishing the non-adhesive and adhesive contact solutions for surfaces containing a shallow rectangular groove with the effects of applied load and interfacial adhesion taken into account. By solving singular integral equations and using the energy release rate approach, closed-form solutions are derived analytically for the deformed groove shapes, interfacial stress distributions and equilibrium relations between load and contact size, which reduce to the previously proposed solutions without adhesion or without applied load. Finite element analysis is performed to validate the non-adhesion solutions, while experiment results of stamp collapse reported in the literature are adopted to examine the adhesion solutions. By introducing the Johnson parameter a to represent a competition between surface energy and elastic strain energy of the groove, four kinds of contact behaviors of the groove roof can be characterized appropriately: non-adhesion, weak adhesion, intermediate adhesion and strong adhesion. Hysteresis loop and energy loss due to distinct load/unloading paths are revealed in the cases of intermediate and strong adhesion. We also provided the critical applied pressure to achieve roof collapse and the corresponding equilibrium contact size for full range of a.

A Concentrated Force Problem of Plane Strain or Plane Stress

1947 ◽  
Vol 14 (3) ◽  
pp. A246
Author(s):  
A. E. Green
Keyword(s):  
Closed Form ◽  
Plane Strain ◽  
Plane Stress ◽  
Complex Variable ◽  
Elliptical Hole ◽  
Minor Axis ◽  
Concentrated Force ◽  
Large Plate ◽  
Force Problem ◽  
Variable Analysis

Abstract The problem in plane strain or plane stress of a large plate containing an elliptical hole, which is loaded by line forces at the ends of the minor axis of the ellipse, is solved in closed form by using complex variable analysis.

Location of Initial Debonding and Stress Singularity at Interface End

2008 ◽  
Vol 33-37 ◽  
pp. 315-320
Author(s):  
Ying Dai ◽  
Li Lang Zhou ◽  
Li Juan Fu ◽  
Xing Ji
Keyword(s):  
Stress Distribution ◽  
Characteristic Length ◽  
Stress Singularity ◽  
Interfacial Stress ◽  
Length Scale ◽  
Test Results ◽  
Characteristic Length Scale ◽  
Concentrated Force ◽  
Size Scale ◽  
Large Size

Interfacial stress distribution of bonded quarter-planes subjected to a concentrated force was re-investigated based on Bogy’s solution[1]. The characteristic length of the singular interface end, δ, was defined, and found varying in a very large size scale with the index of stress singularity from millimeter to nanometer or even smaller scale. The influences the characteristic length scale on the initial debonding of the interface end is a new question worth to pay attention. Photoelasticity experiment was employed to verify whether the initial debonding is always located at interface end with stress singularity. The test results show that the initial debonding does not start from singular interface end if the index of stress singularity is small enough.

Sign in / Sign up

Export Citation Format

Share Document