Spheroidal Sliding Inclusion in an Elastic Half-Space

1991 ◽  
Vol 44 (11S) ◽  
pp. S143-S149 ◽  
Author(s):  
Iwona Jasiuk ◽  
Eiichiro Tsuchida ◽  
Toshio Mura
Keyword(s):  
Half Space ◽  
Integral Form ◽  
Transformation Strain ◽  
Elastic Half Space ◽  
Elasticity Solution ◽  
Numerical Examples ◽  
Hydrostatic Loading ◽  
Displacement Potentials ◽  
Infinite Integral ◽  
Uniform Plane

An analytical elasticity solution for a half-space having a spheroidal sliding inclusion is obtained. The inclusion is subjected to either a uniform plane hydrostatic loading applied at infinity or a uniform transformation strain (eigenstrain). The interface between the inclusion and the surrounding material allows sliding and does not sustain shear tractions. Boussinesq’s displacement potentials in infinite integral form and in infinite series form are used in the analysis. Numerical examples are included.

A Spherical Inclusion in an Elastic Half-Space Under Shear

1997 ◽  
Vol 64 (3) ◽  
pp. 471-479 ◽  
Author(s):  
I. Jasiuk ◽  
P. Y. Sheng ◽  
E. Tsuchida
Keyword(s):  
Half Space ◽  
Spherical Inclusion ◽  
Transformation Strain ◽  
Elastic Half Space ◽  
Elastic Fields ◽  
Surrounding Matrix ◽  
Uniform Shear ◽  
The Matrix ◽  
Displacement Potentials ◽  
Space Matrix

We find the elastic fields in a half-space (matrix) having a spherical inclusion and subjected to either a remote shear stress parallel to its traction-free boundary or to a uniform shear transformation strain (eigenstrain) in the inclusion. The inclusion has distinct properties from those of the matrix, and the interface between the inclusion and the surrounding matrix is either perfectly bonded or is allowed to slip without friction. We obtain an analytical solution to this problem using displacement potentials in the forms of infinite integrals and infinite series. We include numerical examples which give the local elastic fields due to the inclusion and the traction-free surface.

Plane Strain Sliding Contact Between a Rigid Cylinder and a Pseudoelastic Shape Memory Alloy Half-Space

2018 ◽  
Author(s):  
Ralston Fernandes ◽  
James G. Boyd ◽  
Dimitris C. Lagoudas ◽  
Sami El-Borgi
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Half Space ◽  
Maximum Stress ◽  
Transformation Strain ◽  
Elastic Half Space ◽  
Sliding Contact ◽  
Temperature Dependent ◽  
Rigid Cylinder ◽  
Parametric Studies

This study uses the finite element method to analyze the sliding contact behavior between a rigid cylinder and a shape memory alloy (SMA) semi-infinite half-space. An experimentally validated constitutive model is used to capture the pseudoelastic effect exhibited by these alloys. Parametric studies involving the maximum recoverable transformation strain and the transformation temperatures are performed to analyze the effects that these parameters have on the stress fields during indentation and sliding contact. It is shown that, depending on the amount of recoverable transformation strain possessed by the alloy, a reduction of almost 40 % of the maximum stress in the pseudoelastic half-space is achieved when compared to the maximum stress in a purely elastic half-space. The studies also reveal that the sliding response is strongly temperature dependent, with significant residual stress present in the half-space at temperatures below the austenitic finish temperature.

Response of an Elastic Half Space to Uniformly Moving Circular Surface Load

1970 ◽  
Vol 37 (1) ◽  
pp. 109-115 ◽  
Author(s):  
S. K. Singh ◽  
J. T. Kuo
Keyword(s):  
Half Space ◽  
Hypergeometric Functions ◽  
Integral Form ◽  
Elastic Half Space ◽  
Point Load ◽  
Surface Load ◽  
Static Part ◽  
Circular Load ◽  
Circular Surface ◽  
Velocity Effect

The problem of a uniformly moving circular surface load of a general orientation on an elastic half space for two types of load distribution, viz., “uniform” and “hemispherical,” is considered. The solutions have been obtained in integral form. The displacements on the surface of the half space, in the case in which the load velocity V is smaller than the transverse wave velocity of the medium CT are expressed in a closed form as a sum of two terms by using properties of Gauss’ hypergeometric functions. One of these terms gives the static part of the solution, whereas the other term represents the velocity effect part. At distances greater than about five radii from the center of the moving circular load, a moving point load is found to be a good approximation.

The Hemispheroidal Inhomogeneity at the Free Surface of an Elastic Half Space

1989 ◽  
Vol 56 (1) ◽  
pp. 70-76 ◽  
Author(s):  
D. Kouris ◽  
E. Tsuchida ◽  
T. Mura
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Series Solution ◽  
Elastic Half Space ◽  
Numerical Calculations ◽  
Displacement Potentials ◽  
Axis Of Symmetry ◽  
Elastic Inhomogeneity

A series solution is presented for a hemispheroidal elastic inhomogeneity at the free surface of an elastic half space. The loading is either all around tension at infinity, perpendicular to the axis of symmetry of the inhomogeneity, or uniform, nonshear type eigenstrains sustained by the inhomogeneity. The displacement potentials of Boussinesq are used to represent the solution and several numerical calculations are performed to illustrate the results.

scholarly journals Reconstruction of round voids in the elastic half-space: Antiplane problem

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Mezhlum A. Sumbatyan ◽  
Vincenzo Tibullo ◽  
Vittorio Zampoli
Keyword(s):  
Half Space ◽  
Finite Length ◽  
Boundary Surface ◽  
Elastic Half Space ◽  
Point Force ◽  
Good Stability ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Numerical Examples ◽  
Antiplane Problem

We study the reconstruction of geometry (position and size) of round voids located in the elastic half-space, in frames of antiplane two-dimensional problem. We assume that a known point force is applied to the boundary surface of the half-space, and we can measure the shape of the surface over a certain finite-length interval. Then, if the geometry of the defect is unknown, we construct an algorithm to restore its position and size. Some numerical examples demonstrate a good stability of the proposed algorithm.

The efficiency of application of virtual cross-sections method and hypotheses MELS in problems of wave signal propagation in elastic waveguides with rough surfaces

2016 ◽  
pp. 3564-3575 ◽  
Author(s):  
Ara Sergey Avetisyan
Keyword(s):  
Half Space ◽  
Cross Sections ◽  
Classical Method ◽  
Signal Propagation ◽  
Elastic Half Space ◽  
Layered Systems ◽  
Surface Layers ◽  
Inhomogeneous Surface ◽  
Wave Signal ◽  
The Impact

The efficiency of virtual cross sections method and MELS (Magneto Elastic Layered Systems) hypotheses application is shown on model problem about distribution of wave field in thin surface layers of waveguide when plane wave signal is propagating in it. The impact of surface non-smoothness on characteristics of propagation of high-frequency horizontally polarized wave signal in isotropic elastic half-space is studied. It is shown that the non-smoothness leads to strong distortion of the wave signal over the waveguide thickness and along wave signal propagation direction as well.  Numerical comparative analysis of change in amplitude and phase characteristics of obtained wave fields against roughness of weakly inhomogeneous surface of homogeneous elastic half-space surface is done by classical method and by proposed approach for different kind of non-smoothness.

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