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.

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.

Elastic Fields in a Polyhedral Inclusion With Uniform Eigenstrains and Related Problems

2000 ◽  
Vol 68 (3) ◽  
pp. 441-452 ◽  
Author(s):  
H. Nozaki ◽  
M. Taya
Keyword(s):  
Stress Field ◽  
Strain Energy ◽  
Dimensional Space ◽  
Spherical Inclusion ◽  
Three Dimensional ◽  
Elastic Field ◽  
Bounded Region ◽  
Symmetrical Structure ◽  
Elastic Fields ◽  
Three Dimensional Space

In this paper, the elastic field in an infinite elastic body containing a polyhedral inclusion with uniform eigenstrains is investigated. Exact solutions are obtained for the stress field in and around a fully general polyhedron, i.e., an arbitrary bounded region of three-dimensional space with a piecewise planner boundary. Numerical results are presented for the stress field and the strain energy for several major polyhedra and the effective stiffness of a composite with regular polyhedral inhomogeneities. It is found that the stresses at the center of a polyhedral inclusion with uniaxial eigenstrain do not coincide with those for a spherical inclusion (Eshelby’s solution) except for dodecahedron and icosahedron which belong to icosidodeca family, i.e., highly symmetrical structure.

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.

Sliding Inclusions and Inhomogeneities With Frictional Interfaces

1992 ◽  
Vol 59 (4) ◽  
pp. 783-788 ◽  
Author(s):  
R. Furuhashi ◽  
Jin H. Huang ◽  
T. Mura
Keyword(s):  
Exact Solution ◽  
Shear Stress ◽  
Closed Form ◽  
Spherical Inclusion ◽  
Existence Of Solution ◽  
Elastic Fields ◽  
Uniform Shear ◽  
Ellipsoidal Inhomogeneity ◽  
Applied Shear Stress ◽  
Frictional Interface

Elastic fields due to a sliding inclusion and inhomogeneity with the frictional interface are investigated. The exact solution in closed form is presented for three cases: (i) a spherical inclusion which undergoes constant eigenstrains, (ii) a nondegenerate ellipsoidal inclusion with uniform shear eigenstrains and (iii) a nondegenerate ellipsoidal inhomogeneity subjected to an applied shear stress at infinity. Moreover, the existence of solution for a sliding inclusion and inhomogeneity with frictional interface is also demonstrated.

On the dynamic generalization of the anisotropic Eshelby ellipsoidal inclusion and the dynamically expanding inhomogeneities with transformation strain

2016 ◽  
Vol 01 (03n04) ◽  
pp. 1640001 ◽  
Author(s):  
Xanthippi Markenscoff
Keyword(s):  
Spherical Inclusion ◽  
Transformation Strain ◽  
Positive Definiteness ◽  
Equivalent Transformation ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Chemical Phase ◽  
Eshelby Inclusion ◽  
Interior Domain

The self-similarly dynamically (subsonically) expanding anisotropic ellipsoidal Eshelby inclusion is shown to exhibit the constant stress “Eshelby property” in the interior domain of the expanding inclusion on the basis of dimensional analysis, analytic properties and the proof for the static inclusion alone. As an example of this property and the application of the dynamic Eshelby tensor (constant in the interior domain), it is shown that the Eshelby equivalent inclusion method always allows for the determination of the equivalent transformation strain for a self-similarly dynamically expanding inhomogeneous spherical inclusion when the Poisson's ratio is in the real range (positive definiteness of the strain energy). Thus, the solution of dynamically self-similarly expanding inhomogeneities (chemical phase change) with transformation strain can be obtained, as well as the driving force per unit area of the expanding inhomogeneity.

Elastic fields about a perturbed spherical inclusion

1985 ◽  
Vol 33 (6) ◽  
pp. 985-989 ◽  
Author(s):  
P.H. Leo ◽  
J. Iwan ◽  
D. Alexander ◽  
R.F. Sekerka
Keyword(s):  
Spherical Inclusion ◽  
Elastic Fields
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