Eigenfunction Expansion and Higher Order Weight Functions of Interface Cracks

1994 ◽  
Vol 61 (4) ◽  
pp. 843-849 ◽  
Author(s):  
Yi-Zhou Chen ◽  
Norio Hasebe
Keyword(s):  
Weight Function ◽  
Interface Crack ◽  
Eigenfunction Expansion ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Reciprocal Theorem ◽  
Weight Functions ◽  
J Integral ◽  
Expansion Form ◽  
Eigenfunction Expansion Form

In this paper the properties of the eigenfunction expansion form in the interface crack problem of plane elasticity are discussed in detail. After using the Betti’s reciprocal theorem to the cracked dissimilar bonded body, several path-independent integrals are obtained. All the coefficients in the eigenfunction expansion form, including the K1 and K2 values, and the J-integral can be related to corresponding path independent integrals. Possibility for formulating the weight function is also suggested.

Some Properties of J-Integral in Plane Elasticity

2001 ◽  
Vol 69 (2) ◽  
pp. 195-198 ◽  
Author(s):  
Y. Z. Chen ◽  
K. Y. Lee
Keyword(s):  
Function Method ◽  
Infinite Plate ◽  
Scalar Function ◽  
Plane Elasticity ◽  
Reciprocal Theorem ◽  
J Integral ◽  
Large Circle ◽  
Complex Variable Function ◽  
Variable Function ◽  
Complex Variable Function Method

Some properties of the J-integral in plane elasticity are analyzed. An infinite plate with any number of inclusions, cracks, and any loading conditions is considered. In addition to the physical field, a derivative field is defined and introduced. Using the Betti’s reciprocal theorem for the physical and derivative fields, two new path-independent D1 and D2 are obtained. It is found that the values of Jkk=1,2 on a large circle are equal to the values of Dkk=1,2 on the same circle. Using this property and the complex variable function method, the values of Jkk=1,2 on a large circle is obtained. It is proved that the vector Jkk=1,2 is a gradient of a scalar function Px,y.

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