scholarly journals Stress singularity due to traction discontinuity on an anisotropic elastic half-plane

2008 ◽  
Vol 45 (1) ◽  
pp. 175-190 ◽  
Author(s):  
J.Y. Liou ◽  
J.C. Sung
Keyword(s):  
Half Plane ◽  
Stress Singularity ◽  
Anisotropic Elastic

The Plane Solution for Anisotropic Elastic Wedges Under Normal and Shear Loading

1972 ◽  
Vol 39 (4) ◽  
pp. 1103-1109 ◽  
Author(s):  
D. B. Bogy
Keyword(s):  
Half Plane ◽  
Complex Function ◽  
Stress Singularity ◽  
Shear Loading ◽  
Elementary Functions ◽  
Linear Elastostatics ◽  
Full Plane ◽  
Plane Solution ◽  
Logarithmic Singularities ◽  
Anisotropic Elastic

The plane traction problem for an anisotropic wedge is solved within the theory of linear elastostatics. The technique employs the complex function representation of the plane solution in conjunction with the Mellin transform. Special attention is given to the orthotropic wedge; the uniform load solution is given in terms of elementary functions for wedge angles less than π, the logarithmic singularities in the stress field resulting from discontinuous loads on the half plane are studied, and the stress singularity at the apex is investigated for the reentrant wedges. Simplified results for the anisotropic half plane and cracked full plane are also presented.

Mixed Mode Stress Singularities in Anisotropic Composites

1999 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Stress Intensity ◽  
Asymptotic Solution ◽  
Stress Intensity Factors ◽  
Stress Singularity ◽  
Free Edge ◽  
Complex Conjugate ◽  
Circular Path ◽  
Intensity Factors ◽  
Element Analysis ◽  
Anisotropic Elastic

Abstract Multi-material wedges composed of fully anisotropic elastic sectors generally show intrinsic coupling of the anti-plane and in-plane modes of deformation. Each anisotropic sector has three complex conjugate pairs of material eigensolutions whose form of expression depends on five distinct types of anisotropic materials. Continuity of the displacements and the tractions across the sector interfaces and the traction-free conditions on two exterior boundary edges determine an infinite sequence of eigenvalues and eigensolutions of the multi-material wedge. These eigensolutions are linearly combined to match the traction-boundary data (generated by global finite element analysis of the structure) on a circular path encircling the singularity. The analysis method is applied to a bimaterial wedge near the free edge of a four-layer angle-ply laminate, and to a trimaterial wedge surrounding the tip of an embedded oblique crack in a three-layer composite. Under a uniform temperature load, the elasticity solution based on the eigenseries yields interfacial stresses that are significantly different from the asymptotic solution (given by the first term of the eigenseries), even as the distance from the singularity decreases to subatomic scales. Similar observations have been found previously for isotropic and orthotropic multi-material wedges. This raises serious questions with regard to characterizing the criticality of stress singularity exclusively in terms of the asymptotic solution and the associated stress intensity factors or generalized stress intensity factors.

Thermal Distortion of an Anisotropic Elastic Half-Plane and its Application in Contact Problems Including Frictional Heating

2005 ◽  
Vol 128 (1) ◽  
pp. 32-39 ◽  
Author(s):  
Yuan Lin ◽  
Timothy C. Ovaert
Keyword(s):  
Heat Flux ◽  
Half Plane ◽  
Frictional Heating ◽  
Contact Problems ◽  
Local Heat ◽  
Extended Version ◽  
Parabolic Profile ◽  
Local Heat Flux ◽  
Anisotropic Elastic ◽  
Thermoelastic Contact Problem

The thermal surface distortion of an anisotropic elastic half-plane is studied using the extended version of Stroh’s formalism. In general, the curvature of the surface depends both on the local heat flux into the half-plane and the local temperature variation along the surface. However, if the material is orthotropic, the curvature of the surface depends only on the local heat flux into the half-plane. As a direct application, the two-dimensional thermoelastic contact problem of an indenter sliding against an orthotropic half-plane is considered. Two cases, where the indenter has either a flat or a parabolic profile, are studied in detail. Comparisons with other available results in the literature show that the present method is correct and accurate.

Thermal Distortion of an Anisotropic Elastic Half-Plane and Its Application in Contact Problems Including Frictional Heating

2004 ◽  
Author(s):  
Yuan Lin ◽  
Timothy C. Ovaert
Keyword(s):  
Heat Flux ◽  
Half Plane ◽  
Frictional Heating ◽  
Contact Problems ◽  
Local Heat ◽  
Extended Version ◽  
Parabolic Profile ◽  
Local Heat Flux ◽  
Anisotropic Elastic ◽  
Thermoelastic Contact Problem

The thermal surface distortion of an anisotropic elastic half-plane is studied using the extended version of Stroh’s formalism. In general, the curvature of the surface depends both on the local heat flux into the half-plane and the local temperature variation along the surface. However, if the material is orthotropic, the curvature of the surface depends only on the local heat flux into the half-plane. As a direct application, the two-dimensional thermoelastic contact problem of an indenter sliding against an orthotropic half-plane is considered. Two cases, where the indenter has either a flat or a parabolic profile, are studied in detail. Comparisons with other available results in the literature show that the present method is correct and accurate.

The Problem of an Elastic Stiffener Bonded to a Half Plane

1971 ◽  
Vol 38 (4) ◽  
pp. 937-941 ◽  
Author(s):  
F. Erdogan ◽  
G. D. Gupta
Keyword(s):  
Mechanical Properties ◽  
Integral Equation ◽  
Contact Problem ◽  
Half Plane ◽  
Elastic Constants ◽  
Infinite System ◽  
Stress Singularity ◽  
Algebraic Equations ◽  
Numerical Example ◽  
Linear Algebraic Equations

The contact problem of an elastic stiffener bonded to an elastic half plane with different mechanical properties is considered. The governing integral equation is reduced to an infinite system of linear algebraic equations. It is shown that, depending on the value of a parameter which is a function of the elastic constants and the thickness of the stiffener, the system is either regular or quasi-regular. A complete numerical example is given for which the strength of the stress singularity and the contact stresses are tabulated.

Asymptotic analysis of an adhered complete contact between elastically dissimilar materials

2014 ◽  
Vol 49 (8) ◽  
pp. 607-617 ◽  
Author(s):  
Hyung-Kyu Kim ◽  
David A Hills ◽  
Robert JH Paynter
Keyword(s):  
Asymptotic Analysis ◽  
Half Plane ◽  
Stress Singularity ◽  
Dissimilar Materials ◽  
Element Model ◽  
Load Combination ◽  
Mode Separation ◽  
Generalized Stress Intensity Factors ◽  
Complete Contact ◽  
Specific Material

A complete contact problem between elastically dissimilar materials is studied using an asymptotic analysis. A quarter plane wedge on a half-plane represents the contact edge geometry. Two eigenvalues are obtained for pairs of contacting materials, and their characteristics are classified on the Dundurs parallelogram. Generalized stress intensity factors, KI and KII, are derived to use a two-term stress equation of dimensionless form with developing a mode separation angle. It is found that the order of stress singularity increases as the wedge becomes more rigid than the half-plane. Slipping characteristics on the contact interface are investigated in detail, especially for the case of KI < 0 < KII that represents a typical adhesive complete contact condition. An example case is given using a finite element model to provide calibration of the stress intensities for a specific material, geometry and load combination.

The Plane Solution for the Elastic Contact Problem of a Semi-Infinite Strip and Half Plane

1976 ◽  
Vol 43 (4) ◽  
pp. 603-607 ◽  
Author(s):  
G. G. Adams ◽  
D. B. Bogy
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Numerical Solutions ◽  
Stress Singularity ◽  
Singular Integral Equations ◽  
Infinite Strip ◽  
Elastic Contact ◽  
Shearing Stress ◽  
Elastic Materials ◽  
Plane Solution

The solution is obtained for both smooth and bonded contact between the strip and half plane of different elastic materials. First, the problems are reduced to singular integral equations of the second kind. Then the order of the stress singularity at the corners is extracted from the integral equations and numerical solutions are obtained. Interface normal and shearing stress are exhibited graphically for several material combinations.

Stress Singularities at Equal Angle Biwedges and Two-Material Composite Half Planes With Rough Interfaces

1976 ◽  
Vol 43 (1) ◽  
pp. 64-68 ◽  
Author(s):  
P. S. Theocaris ◽  
E. E. Gdoutos
Keyword(s):  
Friction Coefficient ◽  
Half Plane ◽  
Elastic Stress ◽  
Stress Singularity ◽  
Complex Variables ◽  
The Other ◽  
Stress Singularities ◽  
Equal Angle ◽  
Common Interface ◽  
Material Composite

The order of the elastic stress singularity developed either at the apex of an equal angle biwedge or at the vertex of a composite half plane is studied for the case when the two wedges adhere along their common interface according to Coulomb’s law of friction. The other two faces of the wedges are considered free from tractions in the vicinity of the apices of both types of biwedges. The study uses the well-known theory of complex variables, and the numerical results obtained for some special geometrical configurations and particular values of the friction coefficient are presented in Dundurs’ parallelograms which cover all physically interesting material combinations of the two wedges.

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