The Elastic Potentials for Coplanar Interaction Between an Infinitesimal Prismatic Dislocation Loop and a Circular Crack for Transverse Isotropy

1992 ◽  
Vol 59 (2S) ◽  
pp. S72-S78 ◽  
Author(s):  
M. T. Hanson
Keyword(s):  
Isotropic Material ◽  
Transverse Isotropy ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Internal Crack ◽  
Elementary Functions ◽  
Elastic Potentials ◽  
Title Problem ◽  
Dislocation Crack ◽  
In The Beginning

This paper gives a closed-form evaluation in terms of elementary functions for the title problem of coplanar dislocation—crack interaction. The two cases of an external and internal crack are considered and the potential for each is found for an isotropic material. The similarity between isotropy and transverse isotropy is discussed in the beginning sections and is used to write the corresponding potential for a transversely isotropic material from the isotropic result.

The Elastic Field for Spherical Hertzian Contact Including Sliding Friction for Transverse Isotropy

1992 ◽  
Vol 114 (3) ◽  
pp. 606-611 ◽  
Author(s):  
M. T. Hanson
Keyword(s):  
Coulomb Friction ◽  
Sliding Friction ◽  
Contact Region ◽  
Transverse Isotropy ◽  
Elastic Field ◽  
Hertzian Contact ◽  
Elementary Functions ◽  
Elastic Bodies ◽  
Title Problem ◽  
Equivalent Expressions

This paper gives closed-form expressions in terms of elementary functions for the title problem of spherical Hertzian contact of elastic bodies possessing transverse isotropy. Traction in the contact region is also included in the form of Coulomb friction; thus the shear stress is proportional to the contact pressure. The present expressions derived here by integration of the point force Green’s functions are simpler and easier to apply than equivalent expressions which have previously been given.

The Elastic Field for Conical Indentation Including Sliding Friction for Transverse Isotropy

1992 ◽  
Vol 59 (2S) ◽  
pp. S123-S130 ◽  
Author(s):  
M. T. Hanson
Keyword(s):  
Shear Stress ◽  
Coulomb Friction ◽  
Sliding Friction ◽  
Contact Region ◽  
Transverse Isotropy ◽  
Elastic Field ◽  
Elementary Functions ◽  
Elastic Bodies ◽  
Title Problem ◽  
Conical Indentation

This paper gives closed-form expressions in terms of elementary functions for the title problem of conical indentation of elastic bodies possessing transverse isotropy. Traction in the contact region is also included in the form of Coulomb friction; thus, the shear stress is taken proportional to the contact pressure. The present expressions are derived here by integration of the point force Green’s functions.

Dynamic Response to Normal Stresses in a Transversely Isotropic Material Containing an External Circular Crack

1992 ◽  
Vol 114 (2) ◽  
pp. 208-212 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Isotropic Material ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Transversely Isotropic Material ◽  
External Circular Crack

The dynamic response of an external circular crack to a harmonic longitudinal wave in a transversely isotropic material is investigated using the techniques of Hankel transform. The wave impinges normally onto the crack surfaces. The inversion integral is evaluated and simplified through a complete contour integration. An exact expression for the dynamic stress intensity factor is obtained in terms of the wave frequency and the anisotropic material constants. The maximum value of the normalized dynamic stress-intensity factor is shown to occur at different wave frequencies for different sample composite and metallic materials. The dynamic effect on the crack surface displacement is also shown to be a function of the wave frequency and the material anisotropy.

Stress Concentration Around Spheroidal Inclusions and Cavities in a Transversely Isotropic Material Under Pure Shear

1970 ◽  
Vol 37 (1) ◽  
pp. 85-92 ◽  
Author(s):  
W. T. Chen
Keyword(s):  
Exact Solution ◽  
Shear Stress ◽  
Isotropic Material ◽  
Pure Shear ◽  
Transversely Isotropic ◽  
Transversely Isotropic Material ◽  
Elementary Functions ◽  
Stress Concentrations ◽  
Spheroidal Cavity ◽  
Hexagonal Crystals

This paper presents an exact solution for the stress distribution around an elastic spheroidal inclusion in an infinite transversely isotropic elastic body which is otherwise under a pure shear stress. The stresses and displacements are expressed in terms of elementary functions. The technically important consideration of the stress concentrations around a spheroidal cavity is discussed. Numerical results are given for a number of hexagonal crystals.

On: “Long‐wave elastic anisotropy in transversely isotropic media” by James G. Berryman (GEOPHYSICS, May 1979, p. 896–917).

Geophysics ◽  
1980 ◽  
Vol 45 (5) ◽  
pp. 977-980
Author(s):  
K. Helbig
Keyword(s):  
Isotropic Material ◽  
Significant Contribution ◽  
Elastic Anisotropy ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Homogeneous Material ◽  
Long Wave ◽  
Transversely Isotropic Media ◽  
Horizontal Stratification ◽  
Isotropic Media

Berryman shows elegantly that the “inequality [Formula: see text] is true for any horizontally stratified, homogeneous material whose constituent layers are isotropic…” However, the final clause of this sentence “…, i.e., any homogeneous, transversely isotropic material,” is, if taken at face value, misleading. It is clear from the proof in the section “A fundamental inequality” that this statement is only shown to hold for lamellated media with isotropic lamellae, and that Berryman chooses arbitrarily and without any warning the phrase homogeneous, transversely isotropic to stand as a synonym for what Backus (1962) painstakingly describes as “smoothed, transversely isotropic, long‐wave equivalent (STILWE).” In view of the fact that even within the context of exploration seismics transverse isotropy can be due to causes other than horizontal stratification with isotropic constituents (e.g., schists can be intrinsically anisotropic, anisotropy might be due to preferential orientation of sandgrains or joints), I believe this choice to be unfortunate. It leads the unsuspecting reader to assume a wider applicability of the fundamental inequality than Berryman really intends to claim, and thus makes it unnecessarily difficult to understand this significant contribution.

External Circular Crack Under Normal Load: A Complete Solution

1994 ◽  
Vol 61 (4) ◽  
pp. 809-814 ◽  
Author(s):  
V. I. Fabrikant ◽  
B. S. Rubin ◽  
E. N. Karapetian
Keyword(s):  
Normal Load ◽  
Complete Solution ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Elementary Functions ◽  
Normal Loading ◽  
Method Of Solution ◽  
External Circular Crack ◽  
Concentrated Loading ◽  
Crack Faces

For the first time, a complete solution in terms of elementary functions is given to the problem of a transversely isotropic elastic space weakened by an external circular crack and subjected to arbitrary normal loading applied symmetrically to both crack faces. A complete field of displacements and stresses due to a concentrated loading is given for both transversely isotropic and purely isotropic cases. The method of solution is based on the results published earlier by the first author.

On the General Solution for Piezothermoelasticity for Transverse Isotropy With Application

2000 ◽  
Vol 67 (4) ◽  
pp. 705-711 ◽  
Author(s):  
W. Q. Chen
Keyword(s):  
General Solution ◽  
Transverse Isotropy ◽  
Crack Problem ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Static Case ◽  
Elementary Functions ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Basic Equations

This paper derives a general solution of the three-dimensional equations of transversely isotropic piezothermoelastic materials (crystal class, 6 mm). Two displacement functions are first introduced to simplify the basic equations and a general solution is then derived using the operator theory. For the static case, the proposed general solution is very simple in form and can be used easily in certain boundary value problems. An illustrative example is given in the paper by considering the symmetric crack problem of an arbitrary temperature applied over the faces of a flat crack in an infinite space. The governing integro-differential equations of the problem are derived. It is found that exact expressions for the piezothermoelastic field for a penny-shaped crack subject to a uniform temperature can be obtained in terms of elementary functions. [S0021-8936(00)01704-9]

THE ANALYSIS OF DYNAMICAL RESPONSE OF TRANSVERSELY ISOTROPIC MATERIAL UNDER BLASTING LOAD

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1443-1448
Author(s):  
YUE-XIU WU ◽  
QUAN-SHENG LIU
Keyword(s):  
Isotropic Material ◽  
Peak Velocity ◽  
Transversely Isotropic ◽  
Normal Direction ◽  
Dynamical Response ◽  
Transversely Isotropic Material ◽  
Peak Acceleration ◽  
Loading Direction ◽  
Blasting Load ◽  
Explosion Load

To understand the dynamic response of transversely isotropic material under explosion load, the analysis is done with the help of ABAQUS software and the constitutive equations of transversely isotropic material with different angle of isotropic section. The result is given: when the angle of isotropic section is settled, the velocity and acceleration of measure points decrease with the increasing distance from the explosion borehole. The velocity and acceleration in the loading direction are larger than those in the normal direction of the loading direction and their attenuation are much faster. When the angle of isotropic section is variable, the evolution curves of peak velocity and peak acceleration in the loading direction with the increasing angles are notching parabolic curves. They get their minimum values when the angle is equal to 45 degree. But the evolution curves of peak velocity and peak acceleration in the normal direction of the loading direction with the increasing angles are overhead parabolic curves. They get their maximum values when the angle is equal to 45 degree.

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