The Stress Field Caused by a Circular Cylindrical Inclusion in a Transversely Isotropic Elastic Solid

2003 ◽  
Vol 70 (6) ◽  
pp. 825-831 ◽  
Author(s):  
H. Hasegawa ◽  
M. Kisaki
Keyword(s):  
Stress Field ◽  
Strain Energy ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Cylindrical Inclusion ◽  
Stress Distributions ◽  
Axisymmetric Stress ◽  
Displacement Fields ◽  
Isotropic Solid ◽  
Stress And Displacement Fields

Exact solutions are presented in closed form for the axisymmetric stress and displacement fields caused by a circular solid cylindrical inclusion with uniform eigenstrain in a transversely isotropic elastic solid. This is an extension of a previous paper for an isotropic elastic solid to a transversely isotropic solid. The strain energy is also shown. The method of Green’s functions is used. The numerical results for stress distributions are compared with those for an isotropic elastic solid.

The Stress Fields Caused by a Circular Cylindrical Inclusion

1992 ◽  
Vol 59 (2S) ◽  
pp. S107-S114 ◽  
Author(s):  
Hisao Hasegawa ◽  
Ven-Gen Lee ◽  
Toshio Mura
Keyword(s):  
Exact Solutions ◽  
Strain Energy ◽  
Elastic Solid ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Axisymmetric Stress ◽  
Displacement Fields ◽  
Elastic Fields ◽  
Stress And Displacement Fields ◽  
Interior Points

Exact solutions are presented in closed forms for the axisymmetric stress and displacement fields caused by a solid or hollow circular cylindrical inclusion (with uniform axial eigenstrain prescribed) in an infinite elastic solid. The same expressions are obtained for the elastic fields for interior and exterior points of the inclusion. Although Eshelby’s solutions for ellipsoidal inclusions are uniform in the interior points, the present solutions do not show the uniformity. When the length of inclusion becomes infinite, the present solutions agree with Eshelby ’s results. The strain energy is also shown. The method of Green’s function is used.

Axisymmetric Stress Field Around Spheroidal Inclusions and Cavities in a Transversely Isotropic Material

1968 ◽  
Vol 35 (4) ◽  
pp. 770-773 ◽  
Author(s):  
W. T. Chen
Keyword(s):  
Stress Field ◽  
Linear Elasticity ◽  
Isotropic Material ◽  
Transversely Isotropic ◽  
Transversely Isotropic Material ◽  
Axisymmetric Stress ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
The Matrix ◽  
Classical Linear Elasticity

A spheroidal inclusion is embedded in an elastic matrix composed of a different material. Both materials are transversely isotropic with the material property axes parallel to the geometric axis of the spheroid. At the interface, the two materials are bonded. The matrix is subjected to a uniform axisymmetric stress field at infinity. Explicit expressions for the stress and displacement fields in the inclusion and the matrix will be presented. The analysis is within the realm of classical linear elasticity.

True bounds on Poisson's ratios for transversely isotropic solids

1992 ◽  
Vol 27 (1) ◽  
pp. 43-44 ◽  
Author(s):  
P S Theocaris ◽  
T P Philippidis
Keyword(s):  
Energy Density ◽  
Basic Principle ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Linear Elastic ◽  
Positive Strain ◽  
Transversely Isotropic Solids ◽  
Isotropic Solids

The basic principle of positive strain energy density of an anisotropic linear or non-linear elastic solid imposes bounds on the values of the stiffness and compliance tensor components. Although rational mathematical structuring of valid intervals for these components is possible and relatively simple, there are mathematical procedures less strictly followed by previous authors, which led to an overestimation of the bounds and misinterpretation of experimental results.

Penetration of a Half Space by a Rectangular Cylinder

1979 ◽  
Vol 46 (3) ◽  
pp. 587-591 ◽  
Author(s):  
A. Cemal Eringen ◽  
F. Balta
Keyword(s):  
Half Space ◽  
Stress Singularity ◽  
Elastic Solid ◽  
Interatomic Interaction ◽  
Elastic Half Space ◽  
Rigid Block ◽  
Field Equations ◽  
Displacement Fields ◽  
Rectangular Cylinder ◽  
Stress And Displacement Fields

The stress and displacement fields are determined in an elastic half space loaded by a rectangular frictionless, rigid block normally at its surface. The semi-infinite solid is considered to be an elastic solid with nonlocal interatomic interaction. The field equations of the nonlocal elasticity and boundary conditions are employed to treat this contact problem. Interestingly the classical stress singularity at the edges of the block are not present in the nonlocal solutions. Consequently the critical applied load for the initiation of penetration of the rigid cylinder into the semi-infinite solid can be determined without recourse to any criterion foreign to the theory. The stress field obtained is valid even for penetrators of submicroscopic width.

scholarly journals The critical influence of some “tiny” geometrical details on the stress field in a Brazilian Disc with a central notch of finite width and length

2021 ◽  
Vol 16 (59) ◽  
pp. 405-422
Author(s):  
Stavros K Kourkoulis ◽  
Christos Markides ◽  
Ermioni Pasiou ◽  
Andronikos Loukidis ◽  
Dimos Triantis
Keyword(s):  
Stress Field ◽  
Finite Width ◽  
Notch Radius ◽  
Displacement Fields ◽  
Geometrical Characteristics ◽  
Numerical Studies ◽  
Stress And Displacement Fields ◽  
Geometrical Features ◽  
Actual Stress

The role of some geometrical characteristics of the notches ma­chined in circular discs, in order to determine the mode-I fracture tough­ness of brittle materials, is discussed. The study is implemented both analyti­cally and numerically. For the analytic study advantage is taken of a recently intro­duced solution for the stress- and displacement-fields developed in a finite disc with a central notch of finite width and length and rounded corners. The vari­ation of the stresses along strategic loci and the deformation of the peri­me­ter of the notch obtained analytically are used for the calibration/validation of a flexible nu­mer­ical model, which is then used for a parametric investiga­tion of the role of geometrical features of the notched disc (thickness of the disc, length and width of the notch, radius of the rounded corners of the notch). It is con­cluded that the role of the width of the notch is of critical im­port­ance. Both the ana­lytic and the numerical studies indicate definitely that ignoring the ac­curate geo­metric shape of the notch leads to erroneous results concerning the actual stress field around the crown of the notch. Therefore, it is possible that misleading values of the fracture toughness of the material of the disc may be obtained.

Hollow Circular Cylindrical Inclusion at the Surface of a Half-Space

1993 ◽  
Vol 60 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Hisao Hasegawa ◽  
Ven-Gen Lee ◽  
Toshio Mura
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Half Space ◽  
Strain Energy ◽  
Analytical Form ◽  
Cylindrical Inclusion ◽  
Displacement Fields ◽  
Elastic Fields

Exact solutions are presented in closed form for the axisymmetric stresses and displacement fields caused by a solid or hollow circular cylindrical inclusion in the present of uniform eigenstrain in a half space. The elastic fields for interior and exterior points are expressed by one analytical form. The strain energy is also obtained in closed forms.

Three-dimensional stress distributions in hexagonal aeolotropic crystals

1948 ◽  
Vol 44 (4) ◽  
pp. 522-533 ◽  
Author(s):  
H. A. Elliott ◽  
N. F. Mott
Keyword(s):  
Harmonic Functions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Quadratic Equation ◽  
Stress Distributions ◽  
Third Order ◽  
Isotropic Solid ◽  
Single Stress ◽  
Image Position ◽  
Special Case

The conditions for equilibrium in an elastically stressed hexagonal aeolotropic medium (transversely isotropic) are formulated, and solutions are found in terms of two ‘harmonic’ functions ø1, ø2, which are solutions ofν1, ν2 being the roots of a certain quadratic equation.It is also shown that in the case of axially symmetrical stress systems the solution may be expressed in terms of the third-order differential coefficients of a single stress function Φ.The solutions for an isotropic medium may be deduced as a special case.The problems of nuclei of strain in such a hexagonal solid are solved, and the results for zinc and magnesium contrasted with those for an isotropic solid.

Characteristics of the Elastic Field of a Rigid Line Inhomogeneity

1985 ◽  
Vol 52 (4) ◽  
pp. 818-822 ◽  
Author(s):  
Z. Y. Wang ◽  
H. T. Zhang ◽  
Y. T. Chou
Keyword(s):  
Stress Field ◽  
Elastic Field ◽  
Square Root ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
Rigid Line ◽  
Square Root Singularity ◽  
Inclined Loading ◽  
Explicit Expressions

Explicit expressions are obtained for the stress and displacement fields near the tip of a rigid line inhomogeneity subjected to an inclined loading. It is shown that the tip stress field, with a square-root singularity, differs in characteristics from that of a slit crack. New designations for the mode of deformation based on the fracture concept are presented and the inhomogeneity extension forces are calculated and discussed.

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