Analysis of the Reflection of Point Force-Induced Crack Surface Waves by a Crack Edge

1985 ◽  
Vol 52 (1) ◽  
pp. 57-61 ◽  
Author(s):  
L. M. Brock ◽  
H. P. Rossmanith
Keyword(s):  
Surface Waves ◽  
Crack Surface ◽  
Crack Edge ◽  
Stress Fields ◽  
Surface Reflection ◽  
Reflection Process ◽  
Point Forces ◽  
Analytical Expressions ◽  
Insight Into ◽  
Component Parallel

Dynamic stress fields near cracks follow in part from the reflection of crack surface waves by the crack edges. To gain insight into the reflection process, the problem of stationary normal and tangential point forces applied to one surface of a stationary semi-infinite crack is considered, and analytical expressions for the crack surface reflection-generated particle velocity waves presented. Study of these expressions shows that the dominant reflected wave is singular at its wave front, travels at the Rayleigh speed, and is generated by the reflection of a singular Rayleigh wave. However, the reflection process “moves” the singularity from the velocity component parallel to the particular force to the component normal to it.

scholarly journals Interior-stress fields produced by a general axisymmetric punch

Friction ◽  
2021 ◽  
Author(s):  
Longxiang Yang ◽  
Zhanjiang Wang ◽  
Weiji Liu ◽  
Guocheng Zhang ◽  
Bei Peng
Keyword(s):  
Hankel Transform ◽  
Elastic Half Space ◽  
Stress Fields ◽  
Dual Integral Equations ◽  
Total Load ◽  
Interior Stress ◽  
Von Mises ◽  
Von Mises Stresses ◽  
Relationship Of ◽  
Analytical Expressions

AbstractThis work is a supplement to the work of Sneddon on axisymmetric Boussinesq problem in 1965 in which the distributions of interior-stress fields are derived here for a punch with general profile. A novel set of mathematical procedures is introduced to process the basic elastic solutions (obtained by the method of Hankel transform, which was pioneered by Sneddon) and the solution of the dual integral equations. These processes then enable us to not only derive the general relationship of indentation depth D and total load P that acts on the punch but also explicitly obtain the general analytical expressions of the stress fields beneath the surface of an isotropic elastic half-space. The usually known cases of punch profiles are reconsidered according to the general formulas derived in this study, and the deduced results are verified by comparing them with the classical results. Finally, these general formulas are also applied to evaluate the von Mises stresses for several new punch profiles.

Колебания слоя с расслоением в рамках градиентной теории упругости

2021 ◽  
pp. 3-15
Author(s):  
А.О. Ватульян ◽  
О.В. Явруян
Keyword(s):  
Boundary Integral Equations ◽  
Relative Length ◽  
Theory Of Elasticity ◽  
Boundary Integral ◽  
Stress Fields ◽  
Gradient Theory ◽  
Main Attention ◽  
Asymptotic Approach ◽  
Crack Tips ◽  
Analytical Expressions

The direct problem of antiplane oscillations of a layer with delamination in the context of the gradient theory of elasticity is considered. The gradient model proposed by Aifantis is taken as a mathematical model. The main attention has been paid to the analysis of mechanical fields at the crack bank and at its tips - stress concentrators. The study is carried out using the method of boundary integral equations (BIE). The BIE for the gradient of displacement field on the crack is constructed. The analysis of the constructed BIE is carried out and the cubic singularity is explicitly revealed. The solution of singular BIE is constructed using approximating Chebyshev polynomials. A study for cracks of small relative length - asymptotic approach is carried out, simple semi-analytical expressions for constructing the crack swap function are obtained, the range of efficiency of the asymptotic approach is obtained. The stress fields in the area of the crack tips are constructed. Numerical results of computational experiments are presented.

Contours for Planar Cracks Growing in Three Dimensions: Influence of Kinetic Energy

2015 ◽  
Vol 82 (11) ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Kinetic Energy ◽  
Crack Edge ◽  
Three Dimensions ◽  
Crack Plane ◽  
Infinite Plane ◽  
Brittle Crack ◽  
Elastic Solids ◽  
Point Forces ◽  
State Growth ◽  
Subcritical Speed

Dynamic steady-state growth in 3D of a semi-infinite plane brittle crack in isotropic elastic solids is considered. Loads cause growth by translating on the crack surfaces at constant, subcritical speed. An analytical solution is obtained and subjected to a criterion for brittle crack growth based on dynamic energy release rate, with kinetic energy included. The result is a nonlinear differential equation for the crack contour, i.e., the curve formed by the crack edge in the crack plane. The equation is studied for the case of compression loading by translating point forces. At large distances from the forces, the crack edge asymptotically approaches the rectilinear and kinetic energy effects can be negligible. A bulge forms around the forces, however, the effect of kinetic energy on its size can be pronounced.

scholarly journals New Exact Solutions for an Oldroyd-B Fluid in a Porous Medium

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
I. Khan ◽  
M. Imran ◽  
K. Fakhar
Keyword(s):  
Porous Medium ◽  
Shear Stress ◽  
Exact Solutions ◽  
Strong Influence ◽  
Stress Fields ◽  
Porous Space ◽  
New Exact Solutions ◽  
Laplace Transform Technique ◽  
Similar Solutions ◽  
Analytical Expressions

New exact solutions for unsteady magnetohydrodynamic (MHD) flows of an Oldroyd-B fluid have been derived. The Oldroyd-B fluid saturates the porous space. Two different flow cases have been considered. The analytical expressions for velocity and shear stress fields have been obtained by using Laplace transform technique. The corresponding solutions for hydrodynamic Oldroyd-B fluid in a nonporous space appeared as the limiting cases of the obtained solutions. Similar solutions for MHD Newtonian fluid passing through a porous space are also recovered. Graphs are sketched for the pertinent parameters. It is found that the MHD and porosity parameters have strong influence on velocity and shear stress fields.

Analytical Solutions for Crack-Tip Higher Order Stress Fields in Thermal Barrier Coating

2008 ◽  
Vol 47-50 ◽  
pp. 1023-1026
Author(s):  
Yao Dai ◽  
Chang Qing Sun ◽  
Sun Qi ◽  
Wei Tan
Keyword(s):  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Stress Fields ◽  
Thermal Barrier ◽  
Barrier Coating ◽  
Graded Material ◽  
Stress Functions ◽  
Order Stress ◽  
Analytical Expressions

Analytical expressions for crack-tip higher order stress functions for a plane crack in a special functionally graded material (FGM), which has an variation of elastic modulus in 1 2 power form along the gradient direction, are obtained through an asymptotic analysis. The Poisson’s ratio of the FGM is assumed to be constant in the analysis. The higher order fields in the asymptotic expansion display the influence of non-homogeneity on the structure of crack-tip fields obviously. Furthermore, it can be seen from expressions of higher order stress fields that at least three terms must be considered in the case of FGMs in order to explicitly account for non-homogeneity effects on the crack- tip stress fields. These results provide the basis for fracture analysis and engineering applications of this FGM.

Surface Waves Guided by a Slit in an Elastic Solid

1972 ◽  
Vol 39 (4) ◽  
pp. 1027-1032 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Surface Waves ◽  
Crack Surface ◽  
Body Wave ◽  
Elastic Solid ◽  
Dispersion Relations ◽  
Finite Width ◽  
Infinite Length ◽  
Open Crack ◽  
Oblique Reflection ◽  
Rate Of Decay

Wave propagation in an isotropic elastic solid containing a slit is studied. The slit is viewed as an open crack of finite width and infinite length. In particular, the propagation of surface waves on the faces of the slit is considered. Making use of a reflection law for the oblique reflection of a Rayleigh wave from the tip of an open half-plane crack, surface waves are superimposed to form guided surface waves in the slit. In order to carry out the construction of dispersion relations, an assumption on the rate of decay of body wave modes localized in the vicinity of the edges of the guide is made, and the range of validity of the assumption is discussed. The dispersion relations are obtained by geometrical construction, and representative dispersion curves are shown.

A Mathematical Model of Blood Flow in a Catheterized artery with multiple stenoses

2020 ◽  
Vol 1 (1) ◽  
pp. 1-5
Author(s):  
B. Basu Mallik ◽  
Saktipada Nanda
Keyword(s):  
Mathematical Model ◽  
Shear Stress ◽  
Stress Distribution ◽  
Flow Resistance ◽  
Wall Stress ◽  
Symmetric Flow ◽  
Catheterized Artery ◽  
Impedance Wall ◽  
Analytical Expressions ◽  
Insight Into

A mathematical model is developed in this investigation for studying the axi-symmetric flow of blood through a catheterized artery with multiple stenoses. Consideration of Newtonian character of blood is described following the report of Young (1968) and Srivastava (2009) with the appropriate constitutive equation governing the flow. The boundary conditions appropriate to the problem under study are the standard no slip conditions at the artery and the catheter wall. Analytical expressions for impedance (flow resistance), the wall stress distribution in the stenotic region and the shear stress at the stenosis throat in their non dimensional form are derived by using the model. The derived expressions are computed numerically and the results are presented graphically for different values of the rheological and other parameters. The study provides an insight into the effects of catheter radius and stenosis height on impedance, wall stress distribution in the stenotic region and the shear stress at the stenotic throat.

Dislocation models and seismomagnetic calculations for California 1906 and Alaska 1964 earthquakes

1969 ◽  
Vol 59 (4) ◽  
pp. 1435-1448
Author(s):  
Sabiha Shamsi ◽  
Frank D. Stacey
Keyword(s):  
San Francisco ◽  
Stress Fields ◽  
Maximum Value ◽  
Dislocation Models ◽  
Vertical Displacements ◽  
Dislocation Stress ◽  
Fault Displacement ◽  
Analytical Expressions ◽  
Best Fit ◽  
Fault Length

Abstract For eathquakes occurring on fault planes whose horizontal dimensions are very much greater than the vertical dimensions, the assumption of infinite fault length allows the dislocation stress fields to be expressed by simple analytical equations. This facilitates an important generalization of the dislocation theory of earthquakes, in which the fault displacement is graded to zero at the edges of the fault planes, thus avoiding singularities in the stress fields, which are still represented by straightforward analytical expressions. This development is necessary for realistic calculations of seismomagnetic anomalies, due to the piezomagnetic effect in rocks above the Curie point isotherm. The best fit to geodetic observations on the San Francisco earthquake of 1906 is given by a model in which a horizontal slip of 5m at the surface grades either linearly or sinusoidally to zero at (5 ± 1.5) km depth. Vertical displacements of the Alaskan earthquake of 1964 are represented by a compound dislocation having a vertical slip with a maximum value of 40m at 65m depth, graded to zero at 5km and 125km. Maximum total magnetic field anomalies for these models are respectively 2 gammas and 1 gamma per 10−3 e.m.u. of rock magnetization.

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