The Elastic Field in a Half-Space With a Circular Cylindrical Inclusion

1996 ◽  
Vol 63 (4) ◽  
pp. 925-932 ◽  
Author(s):  
L. Z. Wu ◽  
S. Y. Du
Keyword(s):  
Half Space ◽  
Elastic Field ◽  
Elastic Half Space ◽  
Elliptic Integrals ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Function Technique ◽  
Explicit Solutions ◽  
Elastic Fields ◽  
Complete Elliptic Integrals

The problem of a circular cylindrical inclusion with uniform eigenstrain in an elastic half-space is studied by using the Green’s function technique. Explicit solutions are obtained for the displacement and stress fields. It is shown that the present elastic fields can be expressed as functions of the complete elliptic integrals of the first, second, and third kind. Finally, numerical results are shown for the displacement and stress fields.

The Elastic Field Caused by a Circular Cylindrical Inclusion—Part I: Inside the Region x12+x22

1995 ◽  
Vol 62 (3) ◽  
pp. 579-584 ◽  
Author(s):  
Linzhi Wu ◽  
Shanyi Du
Keyword(s):  
Analytical Solutions ◽  
Elastic Field ◽  
Companion Paper ◽  
Elliptic Integrals ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Elastic Fields ◽  
Complete Elliptic Integrals ◽  
Nonsingular Surface ◽  
Surface Integrals

The displacement and stress fields caused by uniform eigenstrains in a circular cylindrical inclusion are analyzed inside the region x12+x22<a2,−∞<x3<∞ and are given in terms of nonsingular surface integrals. Analytical solutions can be expressed as functions of the complete elliptic integrals of the first, second and third kind. The corresponding elastic fields in the region x12+x22>a2,−∞<x3<∞ are solved by using the same technique (by Green’s functions) in the companion paper (Part II).

The Elastic Field Caused by a Circular Cylindrical Inclusion—Part II: Inside the Region x12+x22>a2,−∞

1995 ◽  
Vol 62 (3) ◽  
pp. 585-589 ◽  
Author(s):  
Linzhi Wu ◽  
Shanyi Y. Du
Keyword(s):  
Stress Field ◽  
Elastic Medium ◽  
Analytical Solutions ◽  
Elastic Field ◽  
Numerical Results ◽  
Elliptic Integrals ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Complete Elliptic Integrals

Analytical solutions are presented for the displacement and stress fields caused by a circular cylindrical inclusion with arbitrary uniform eigenstrains in an infinite elastic medium. The expressions obtained and those presented in Part I constitute the solutions of the whole elastic field, −∞<x1,x2,x3<∞. In the present paper, it is found that the analytical solutions within the region x12+x22>a2,−∞<x3<∞ can also be expressed as functions of the complete elliptic integrals of the first, second, and third kind. When the length of inclusion tends towards the limit (infinity), the present solutions agree with Eshelby’s results. Finally, numerical results are shown for the stress field.

On the image of a cylindrical inclusion in the scanning acoustic microscope

1991 ◽  
Vol 435 (1894) ◽  
pp. 393-403 ◽  
Keyword(s):  
Half Space ◽  
Multipole Expansion ◽  
Elastic Half Space ◽  
Cylindrical Lens ◽  
Cylindrical Inclusion ◽  
Subsurface Imaging ◽  
Acoustic Microscope ◽  
Rayleigh Approximation ◽  
Lubricated Contact ◽  
Scanning Acoustic Microscope

An analysis is made of the image produced in the scanning acoustic microscope with a cylindrical lens by a cylindrical inclusion in an elastic half-space. The theory is developed in the Rayleigh approximation in which the characteristic wavelengths in the solid are large relative to the diameter of the cylinder, and when scattered waves can be expressed by the leading terms in a multipole expansion concentrated on the axis of the cylinder. A formula is derived for the acoustic contrast when the inclusion is rigid (but movable) and in fully lubricated contact with the solid. The results are illustrated by consideration of an inclusion in aluminium with water as the coupling fluid. The contrast decreases rapidly when the depth of the inclusion within the solid exceeds the Rayleigh wavelength, in accordance with current views concerning the importance of these waves in subsurface imaging.

Elastic Half Space under Axisymmetric Surface Loading and Influence of Couple Stresses

2020 ◽  
Vol 897 ◽  
pp. 129-133
Author(s):  
Jintara Lawongkerd ◽  
Toan Minh Le ◽  
Suraparb Keawsawasvong ◽  
Suchart Limkatanyu ◽  
Jaroon Rungamornrat
Keyword(s):  
Half Space ◽  
Integral Transform ◽  
Couple Stress Theory ◽  
Elastic Field ◽  
Elastic Half Space ◽  
Small Scale ◽  
Internal Length ◽  
Stress Theory ◽  
Axisymmetric Surface ◽  
Small Scale Effect

This paper presents the complete elastic field of a half space under axisymmetric surface loads by taking the influence of material microstructures into account. A well-known couple stress theory is adopted to handle such small scale effect and the resulting governing equations are solved by the method of Hankel integral transform. A selected numerical quadrature is then applied to efficiently evaluate all involved integrals. A set of results is also reported to not only confirm the validity of established solutions but also demonstrate the capability of the selected mathematical model to simulate the size-dependent characteristic of the predicted response when the external and internal length scales are comparable.

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.

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