scholarly journals Closure to “Discussion of ‘The Elastic Field in a Half-Space With a Circular Cylindrical Inclusion’” (1997, ASME J. Appl. Mech., 64, p. 721)

1997 ◽  
Vol 64 (3) ◽  
pp. 721-721 ◽  
Author(s):  
Lin Zhi Wu
Keyword(s):  
Half Space ◽  
Elastic Field ◽  
Cylindrical Inclusion

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.

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.

Influence of Cylindrical Inclusion on the Elastic Field of Soft Material Loaded by Wedge Indenter

2014 ◽  
Vol 670-671 ◽  
pp. 664-667
Author(s):  
Xiao Hua Tan ◽  
Wei Qiu ◽  
Xia Xiao
Keyword(s):  
Rigid Inclusion ◽  
Elastic Field ◽  
Contact Stresses ◽  
Soft Material ◽  
Experimental Results ◽  
Cylindrical Inclusion ◽  
Experimental Procedure ◽  
Soft Matrix

In this work, the influence of a rigid cylindrical inclusion on the elastic field in a transparent soft material is studied by an embedded-grating technique. The same experimental procedure was implemented on two specimens, a homogeneous bulk soft material and the same material containing a rigid cylindrical inhomogeneity. Under the indentation of a rigid wedge, two kinds of deformation sectors underneath the contacting boundary are observed from experimental results. Furthermore, the shape of the deformation sectors is horizontally expanded due to the inclusion. A local fluctuation of contact stresses between the soft matrix and rigid inclusion are discussed.

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).

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.

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