A non-circular Eshelby inclusion near a non-parabolic inhomogeneity admitting internal uniform stresses

2021 ◽  
pp. 108128652110454
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Stress Field ◽  
Circular Inclusion ◽  
Plane Elasticity ◽  
The Other ◽  
Uniform Stress ◽  
Eshelby Inclusion ◽  
Parabolic Shape ◽  
Uniform Stress Field ◽  
Elastic Inhomogeneity ◽  
Open Shape

With the aid of conformal mapping and analytic continuation, we prove that within the framework of anti-plane elasticity, a non-parabolic open elastic inhomogeneity can still admit an internal uniform stress field despite the presence of a nearby non-circular Eshelby inclusion undergoing uniform anti-plane eigenstrains when the surrounding elastic matrix is subjected to uniform remote stresses. The non-circular inclusion can take the form of a Booth’s lemniscate inclusion, a generalized Booth’s lemniscate inclusion or a cardioid inclusion. Our analysis indicates that the uniform stress field within the non-parabolic inhomogeneity is independent of the specific open shape of the inhomogeneity and is also unaffected by the existence of the nearby non-circular inclusion. On the other hand, the non-parabolic shape of the inhomogeneity is caused solely by the presence of the non-circular inclusion.

A hole of irregular shape interacting with a non-parabolic open inhomogeneity with internal uniform anti-plane stresses

2020 ◽  
pp. 108128652097024
Author(s):  
Xu Wang ◽  
Ping Yang ◽  
Peter Schiavone
Keyword(s):  
Free Boundary ◽  
Stress Field ◽  
Conformal Mapping ◽  
Analytic Continuation ◽  
Uniform Stress ◽  
Surrounding Matrix ◽  
Parabolic Shape ◽  
Uniform Stress Field ◽  
Elastic Inhomogeneity ◽  
Mapping Techniques

We use conformal mapping techniques together with analytic continuation to show that a non-parabolic open elastic inhomogeneity continues to admit a state of uniform internal stress when a hole with closed curvilinear traction-free boundary is placed in its vicinity and the surrounding matrix is subjected to uniform remote anti-plane stresses. The internal uniform stress field inside the inhomogeneity is found to be independent of the existence of the nearby hole and the specific non-parabolic shape of the inhomogeneity. In contrast, the non-parabolic shape of the inhomogeneity is influenced solely by the existence of the nearby hole.

A circular Eshelby inclusion interacting with a non-parabolic open inhomogeneity with internal uniform anti-plane stresses

2019 ◽  
Vol 25 (3) ◽  
pp. 573-581 ◽  
Author(s):  
Xu Wang ◽  
Ping Yang ◽  
Peter Schiavone
Keyword(s):  
Stress Field ◽  
Conformal Mapping ◽  
Stress Distributions ◽  
Uniform Stress ◽  
Elastic Deformations ◽  
Surrounding Matrix ◽  
Eshelby Inclusion ◽  
The Matrix ◽  
Uniform Stress Field ◽  
Mapping Techniques

Using conformal mapping techniques and analytic continuation, we prove that when subjected to anti-plane elastic deformations, a non-parabolic open inhomogeneity continues to admit an internal uniform stress field when a circular Eshelby inclusion is placed in its vicinity and the surrounding matrix is subjected to uniform remote stresses. Explicit expressions for the non-uniform stress distributions in the matrix and in the circular Eshelby inclusion are obtained. The internal uniform stress field is independent of the shape of the inhomogeneity and the presence of the circular Eshelby inclusion, whereas the existence of the circular Eshelby inclusion exerts a significant influence on the shape of the non-parabolic open inhomogeneity as well as on the non-uniform stress distributions in the matrix and in the circular Eshelby inclusion itself.

Uniform Stresses Inside an Elliptical Inhomogeneity With an Imperfect Interface in Plane Elasticity

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
X. Wang ◽  
E. Pan ◽  
L. J. Sudak
Keyword(s):  
Stress Field ◽  
Imperfect Interface ◽  
Plane Elasticity ◽  
Uniform Stress ◽  
Uniform Loading ◽  
Elliptical Inhomogeneity ◽  
Interface Function ◽  
Internal Stress Field ◽  
Uniform Stress Field ◽  
Tangential Directions

We consider an elliptical inhomogeneity embedded in an infinite isotropic elastic matrix subjected to in-plane deformations under the assumption of remote uniform loading. The inhomogeneity-matrix interface is assumed to be imperfect, which is simulated by the spring-layer model with vanishing thickness. Its behavior is based on the assumption that tractions are continuous but displacements are discontinuous across the interface. We further assume that the same degree of imperfection on the interface is realized in both the normal and tangential directions. We find a form of interface function, which leads to uniform stress field within the elliptical inhomogeneity. The explicit expressions for the uniform stress field within the elliptical inhomogeneity are derived. The obtained results are verified by comparison with existing solutions. The condition under which the internal stress field is not only uniform but also hydrostatic is also presented.

The 〈111〉 Elliptic Inclusion in an Anisotropic Solid of Cubic Symmetry

1982 ◽  
Vol 49 (2) ◽  
pp. 353-360 ◽  
Author(s):  
H. C. Yang ◽  
Y. T. Chou
Keyword(s):  
Stress Field ◽  
Uniform Stress ◽  
Elliptic Inclusion ◽  
Cubic Symmetry ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Strain Transformation ◽  
Anisotropic Solid ◽  
Uniform Stress Field ◽  
Free Strain

This paper deals with a generalized plane problem in which a uniform stress-free strain transformation takes place in the region of an elliptic cyclinder (the inclusion) oriented in the 〈111〉 direction in an anisotropic solid of cubic symmetry. Closed-form solutions for the elastic fields and the strain energies are presented. The perturbation of an otherwise uniform stress field due to a 〈111〉 elliptic inhomogeneity is also treated including two extreme cases, elliptic cavities and rigid inhomogeneities.

Research on Nonlinear Damping Characteristics of Damping Alloy With Uniform Stress Field

Volume 1 ◽  
2004 ◽  
Author(s):  
Hongzhao Liu ◽  
Ziying Wu ◽  
Lilan Liu ◽  
Daning Yuan ◽  
Zhongming Zhang
Keyword(s):  
Stress Field ◽  
Nonlinear Function ◽  
Nonlinear Damping ◽  
Damping Capacity ◽  
Internal Damping ◽  
Uniform Stress ◽  
Nonlinear Relation ◽  
Uniform Stress Field ◽  
Half Power ◽  
Versus Strain

For the high damping metal material like damping alloy, the damping capacity usually changes with the strain amplitude and frequency nonlinearly. First, to extract the pattern of the internal damping versus strain, two time-domain calculation methods are presented in this paper. One is the moving exponent method (MEM for short) based on FFT (MEM+FFT) and the other is the moving autoregressive model method (MARM). The computing accuracy of the two methods has been compared through numerical simulations. The nonlinear relation curve of loss factor versus strain is achieved by the impulse excitation experiment employing uniform stress field. Then, to extract the pattern of the internal damping versus vibrating frequency, the sine sweep-frequency excitation experiment based on the half-power bandwidth method is carried out. The resulting curve indicates that the internal damping is also a nonlinear function of frequency.

Atomic transport via point defects in crystals III. Migration in a stress field

1985 ◽  
Vol 398 (1814) ◽  
pp. 203-208 ◽  
Keyword(s):  
Stress Field ◽  
Point Defects ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Molecular Volume ◽  
Uniform Stress ◽  
Atomic Transport ◽  
Elastic Dipole ◽  
Uniform Stress Field ◽  
Defect Species

The kinetic theory of isothermal atomic transport via point defects that was presented in two previous papers (Franklin, A. D. & Lidiard, A. B. Proc. R. Soc. Lond . A 389, 405–431 (1983) and Franklin, A. D. & Lidiard, A. B. Proc. R. Soc. Lond . A 392, 457–473 (1984)) has been expanded into a three-dimensional formulation to analyse transport in an applied non-uniform stress field. The fluxes of the various defect species take the general form familiar from non-equilibrium thermodynamics, while the contribution to the force on defect species Y arising from the stress σ αβ is confirmed to be v ∇(λ (Y) αβ σ αβ ), where v is the molecular volume of the solid and λ (Y) αβ is the elastic-dipole strain tensor of the defect species Y (summation over repeated Cartesian indices α, β is here assumed). Full details of these calculations are presented in Lidiard, A. B. A. E. R. E. Rep . no R. 11367 (1984).

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