Multiple Circular Inclusion Problems in Plane Elastostatics

1974 ◽  
Vol 41 (1) ◽  
pp. 215-221 ◽  
Author(s):  
I.-W. Yu ◽  
G. P. Sendeckyj
Keyword(s):  
Uniaxial Tension ◽  
Elastic Moduli ◽  
Circular Inclusion ◽  
Elastic Matrix ◽  
Schwarz Alternating Method ◽  
Inclusion Problems ◽  
Alternating Method ◽  
Elastic Inclusions ◽  
Plane Bending ◽  
Plane Elastostatics

The problem of an unbounded elastic matrix containing any number of elastic inclusions is considered. The inclusions can have any radii and elastic moduli. Furthermore, the spacing of the inclusions can be arbitrary. The solution for the cases of uniaxial tension and in-plane bending is found by the Schwarz alternating method. Graphical results are presented for a number of examples.

Explicit Solutions of Plane Elastostatics Problems in Heterogeneous Solids

1998 ◽  
Vol 14 (2) ◽  
pp. 67-73 ◽  
Author(s):  
C. K. Chao ◽  
B. Gao
Keyword(s):  
Elastic Moduli ◽  
Homogeneous Problem ◽  
Circular Inclusion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Infinite Matrix ◽  
Heterogeneous Solids ◽  
Arbitrary Loading ◽  
Accuracy Result ◽  
Plane Elastostatics

AbstractThe problem of two circular inclusions of arbitrary radii and of different elastic moduli, which are perfectly bonded to an infinite matrix subjected to arbitrary loading, is solved by the heterogenization technique. This implies that the solution of the heterogeneous problem can be readily obtained from that of the corresponding homogeneous problem by a simple algebraic substitution. Based on the method of successive approximations and the technique of analytical continuation, the solution is formulated in a manner which leads to an approximate, but arbitrary accuracy, result. The present derived solution can be also applied to the problem with straight boundaries. Both the problem of two circular inclusions embedded in an infinite matrix and the problem of a circular inclusion embedded in a half-plane matrix are considered as our examples to demonstrate the use of the present approach.

Effect of Cold Storage on Mechanical Properties of Aorta

2015 ◽  
Author(s):  
Shijia Zhao ◽  
John Lof ◽  
Shelby Kutty ◽  
Linxia Gu
Keyword(s):  
Mechanical Properties ◽  
Uniaxial Tension ◽  
Cold Storage ◽  
Elastic Moduli ◽  
Heart Diseases ◽  
Axial Direction ◽  
Circumferential Direction ◽  
Control Group ◽  
Aortic Tissue ◽  
Tension Tests

Aortic allografts have been widely used in treatments of congenital heart diseases with satisfactory clinical outcomes. They were usually cryopreserved and stored for surgical use. The objective of this work was to investigate the effect of cold storage on mechanical properties of aorta, since the compliance mismatch was one important factor associated with the complication after graft surgery. The segments of porcine descending aorta were divided into two groups: the fresh samples which were tested within 24 hours after harvesting served as control group, and frozen samples which were stored in −20°C for 7 days and then thawed. The uniaxial tension tests along circumferential direction and indentation tests were conducted. The average incremental elastic moduli within each stretch range were obtained from the experimental data obtained during tension tests, and the elastic moduli were also calculated by fitting the force-indentation depth data to Hertz model when the tissue was stretched at 1.0, 1.2, 1.4 and 1.6. In addition, the average incremental elastic moduli of both fresh and frozen aortic tissue along axial direction were also obtained by using uniaxial tension tests. The comparison showed that cold storage definitely increased the average incremental elastic modulus of the aortic tissue along circumferential direction; however, the difference is not significant for the elastic moduli along axial direction.

A Circular Inclusion With Circumferentially Inhomogeneous Sliding Interface in Plane Elastostatics

1998 ◽  
Vol 65 (1) ◽  
pp. 30-38 ◽  
Author(s):  
C. Q. Ru
Keyword(s):  
Circular Inclusion ◽  
Form Solution ◽  
Infinite Matrix ◽  
Rigorous Solution ◽  
First Order ◽  
Sliding Interface ◽  
The Mean ◽  
Plane Elastostatics ◽  
Basic Boundary ◽  
General Method

A general method is presented to obtain the rigorous solution for a circular inclusion embedded within an infinite matrix with a circumferentially inhomogeneous sliding interface in plane elastostatics. By virtue of analytic continuation, the basic boundary value problem for four analytic functions is reduced to a first-order differential equation for a single analytic function inside the circular inclusion. The finite form solution is obtained that includes a finite number of unknown constants determined by the analyticity of the solution and certain other auxiliary conditions. With this method, the exact values of the average stresses within the circular inclusion can be calculated without solving the full problem. Several specific examples are used to illustrate the method. The effects of the circumferential variation of the interface parameter on the mean stress at the interface and the average stresses within the inclusion are discussed.

On Perturbation Solutions for Nearly Circular Inclusion Problems in Plane Thermoelasticity

2001 ◽  
Vol 69 (1) ◽  
pp. 36-44 ◽  
Author(s):  
C.-H. Wang ◽  
C.-K. Chao
Keyword(s):  
Arbitrary Shape ◽  
Perturbation Technique ◽  
Elastic Inclusion ◽  
Circular Inclusion ◽  
Fourier Series Expansion ◽  
Principle Of Superposition ◽  
Variable Theory ◽  
Inclusion Problems ◽  
Complex Variable Theory ◽  
Perturbation Solutions

An approximate analytical solution to the nearly circular inclusion problems of arbitrary shape in plane thermoelasticity is provided. The shape of the inclusion boundary considered in the present study is assumed to have the form r=a0[1+Aθ], where a0 is the radius of the unperturbed circle and Aθ is the radius perturbation magnitude that is represented by a Fourier series expansion. The proposed method in this study is based on the complex variable theory, analytical continuation theorem, and the boundary perturbation technique. Originating from the principle of superposition, the solution of the present problem is composed of the reference and the perturbation terms that the reference term is the known exact solution pertaining to the case with circular inclusion. First-order perturbation solutions of both temperature and stress fields are obtained explicitly for elastic inclusions of arbitrary shape. To demonstrate the derived general solutions, two typical examples including elliptical and smooth polygonal inclusions are discussed in detail. Compared to other existing approaches for elastic inclusion problems, our methodology presented here is remarked by its efficiency and applicability to inclusions of arbitrary shape in a plane under thermal load.

A two-dimensional circular inclusion problem

1969 ◽  
Vol 65 (3) ◽  
pp. 823-830 ◽  
Author(s):  
R. D. List
Keyword(s):  
Edge Dislocation ◽  
Circular Inclusion ◽  
Elastic Matrix ◽  
Inclusion Problem ◽  
Two Dimensional ◽  
Concentrated Force ◽  
Elastic Fields ◽  
The Matrix ◽  
Elastic Circular Inclusion

AbstractThe elastic fields in an elastic circular inclusion and its surrounding infinite dissimilar elastic matrix, are determined when either the matrix or inclusion is subject to a concentrated force or edge dislocation.

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