Uniform stresses inside both a non-parabolic inhomogeneity and a non-elliptical inhomogeneity located in the vicinity of a circular Eshelby inclusion

2021 ◽  
pp. 108128652110134
Author(s):  
Ping Yang ◽  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Conformal Mapping ◽  
Connected Domain ◽  
Mapping Function ◽  
Elliptical Inhomogeneity ◽  
Surrounding Matrix ◽  
Eshelby Inclusion ◽  
Doubly Connected Domain ◽  
The Matrix ◽  
Uniformity Property ◽  
Complex Cases

We establish the uniformity of stresses inside both a non-parabolic open inhomogeneity and a non-elliptical closed inhomogeneity interacting with a nearby circular Eshelby inclusion undergoing uniform anti-plane eigenstrains when the surrounding matrix is subjected to uniform remote anti-plane stresses. Our procedure involves the introduction of a conformal mapping function for the doubly connected domain occupied by the matrix and the circular Eshelby inclusion. Two conditions are established in order to achieve the uniformity property inside each of the two inhomogeneities. Our results indicate that: (a) the internal uniform stresses are independent of the specific shapes of the two inhomogeneities and the existence of the nearby circular Eshelby inclusion; (b) the open and closed shapes of the respective inhomogeneities are significantly affected by the presence of the circular Eshelby inclusion. We also consider the two more complex cases involving: (a) an arbitrary number of circular Eshelby inclusions undergoing uniform eigenstrains; (b) a circular Eshelby inclusion undergoing linear eigenstrains. Detailed numerical results demonstrate the feasibility and effectiveness of the proposed theory.

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.

Constructing a conformal mapping for a complex doubly connected domain

1968 ◽  
Vol 4 (4) ◽  
pp. 5-9 ◽  
Author(s):  
E. A. Kolchanova ◽  
A. V. Shvetsov ◽  
A. V. Shvetsov
Keyword(s):  
Conformal Mapping ◽  
Connected Domain ◽  
Doubly Connected Domain

Uniform stress state inside a non-elliptical inhomogeneity near an irregularly shaped hole in antiplane shear

2019 ◽  
Vol 25 (2) ◽  
pp. 362-373 ◽  
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Antiplane Shear ◽  
Shear Stresses ◽  
Uniform Stress ◽  
Elliptical Inhomogeneity ◽  
Surrounding Matrix ◽  
The Matrix ◽  
Shaped Hole ◽  
Mapping Techniques ◽  
Hole Boundary ◽  
High Level

Analytic continuation and conformal mapping techniques are applied to establish that the state of stress inside a non-elliptical elastic inhomogeneity can remain uniform despite the presence of a nearby irregularly shaped hole when the surrounding matrix is subjected to uniform remote antiplane shear stresses. The hole boundary is assumed to be either traction-free or subjected to antiplane line forces. Detailed numerical results are presented to demonstrate the resulting analytical solutions. Our results indicate that in maintaining a uniform stress distribution inside the inhomogeneity, it is permissible for the stresses in the matrix to exhibit either a square root singularity at sharp corners of a hole boundary or a high level of stress concentration at rounded corners of a hole.

scholarly journals Approximate Conformal Mappings and Elasticity Theory

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Pyotr N. Ivanshin ◽  
Elena A. Shirokova
Keyword(s):  
Conformal Mapping ◽  
Elasticity Theory ◽  
Unit Disk ◽  
Connected Domain ◽  
Smooth Boundary ◽  
Mapping Function ◽  
Conformal Mappings ◽  
New Method ◽  
Taylor Polynomial ◽  
Elasticity Problems

Here, we present the new method of approximate conformal mapping of the unit disk to a one-connected domain with smooth boundary without auxiliary constructions and iterations. The mapping function is a Taylor polynomial. The method is applicable to elasticity problems solution.

ANALYSIS OF PROTEOGLYCAN GENE EXPRESSION IN CONNECTIVE TISSUES BY SEMI-QUANTITATIVE RT-PCR

2001 ◽  
Vol 05 (02) ◽  
pp. 79-88
Author(s):  
K. Dobra ◽  
A. Hjerpe
Keyword(s):  
Rt Pcr ◽  
Connective Tissues ◽  
Surrounding Matrix ◽  
Cell Proliferation And Differentiation ◽  
Extracellular Matrix Components ◽  
Proliferation And Differentiation ◽  
The Matrix ◽  
Quantitative Changes ◽  
Regulatory Functions ◽  
Multiple Samples

Proteoglycans (PGs) are cell-membrane and extracellular matrix components with a wide variety of different functions. In the matrix, they are mainly of structural importance, although some of them have been ascribed specific regulatory functions, such as in the assembly of collagen fibers. PGs on the cell surface act as essential modulators of specific ligand-binding reactions, involving interactions between adjacent cells and between cells and surrounding matrix. Through these interactions they participate in different processes, including cell proliferation and differentiation. Qualitative and quantitative changes in PG expression can therefore be associated with various physiological and pathological conditions. We have optimized the conditions for semi-quantitative evaluation of proteoglycan expression by RT-PCR reaction, using glyceraldehyde-3-phosphate dehydrogenase (GAPDH) as reference gene. The relative fluorescence of analyte to reference amplimers can — within certain limits — be used to estimate the amount of target RNA and allows direct comparison of multiple samples. The profile of PG expression obtained in this way can be used to extend our current understanding of the possible functions that can be associated with these complex molecules.

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