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.

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.

The Elastic Field of an Elliptic Inclusion With a Slipping Interface

1986 ◽  
Vol 53 (1) ◽  
pp. 103-107 ◽  
Author(s):  
E. Tsuchida ◽  
T. Mura ◽  
J. Dundurs
Keyword(s):  
Closed Form ◽  
Infinite Series ◽  
Elastic Field ◽  
Elliptic Inclusion ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Bonded Interface ◽  
The Matrix ◽  
Displacement Potentials ◽  
Uniform Expansion

The paper analyzes the elastic fields caused by an elliptic inclusion which undergoes a uniform expansion. The interface between the inclusion and the matrix cannot sustain shear tractions and is free to slip. Papkovich–Neuber displacement potentials are used to solve the problem. In contrast to the perfectly bonded interface, the solution cannot be expressed in closed form and involves infinite series. The results are illustrated by numerical examples.

On the Dynamic Growth of a Spherical Inclusion With Dilatational Transformation Strain in Infinite Elastic Domain

1999 ◽  
Vol 66 (4) ◽  
pp. 879-884 ◽  
Author(s):  
B. Wang ◽  
Q. Sun ◽  
Z. Xiao
Keyword(s):  
Hydrostatic Stress ◽  
Spherical Inclusion ◽  
Reduction Rate ◽  
Dynamic Effect ◽  
Propagation Speed ◽  
Transformation Strain ◽  
Elastic Fields ◽  
Initiation And Propagation ◽  
Dynamic Growth ◽  
Basic Ideas

In this paper, the dynamic effect was incorporated into the initiation and propagation process of a transformation inclusion. Based on the time-varying propagation equation of a spherical transformation inclusion with pure dilatational eigenstrain, the dynamic elastic fields both inside and outside the inclusion were derived explicitly, and it is found that when the transformation region expands at a constant speed, the strain field inside the inclusion is time-independent and uniform for uniform eigenstrain. Following the basic ideas of crack propagation problems in dynamic fracture mechanics, the reduction rate of the mechanical part of the free energy accompanying the growth of the transformation inclusion was derived as the driving force for the move of the interface. Then the equation to determine the propagation speed was established. It is found that there exists a steady speed for the growth of the transformation inclusion when time is approaching infinity. Finally the relation between the steady speed and the applied hydrostatic stress was derived explicitly.

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.

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.

Alternative Formulation of Elastic Fields due to Inhomogeneous Isotropic Spherical Inclusions Undergoing Shape-Conserving Volume Change

1992 ◽  
Vol 59 (4) ◽  
pp. 1026-1027
Author(s):  
S. Schmauder ◽  
W. Mader
Keyword(s):  
Shear Modulus ◽  
Elastic Constants ◽  
Volume Change ◽  
Spherical Inclusion ◽  
Infinite Medium ◽  
Alternative Formulation ◽  
Elastic Fields ◽  
Spherical Inclusions ◽  
The Matrix ◽  
Initial Strains

In this Note alternative formulae are derived for the elastic fields due to homogeneous initial strains in an isotropic spherical inclusion embedded in an isotropic infinite medium, assuming a shape conserving volume change of the inclusion. The bulk modulus of the inclusion and the shear modulus of the matrix are the only physically relevant elastic constants necessary to describe analytically displacements, strains, and stresses in the inclusion and the matrix.

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