Investigation of the Scattering of Harmonic Elastic Waves by Two Collinear Symmetric Cracks Using the Non-Local Theory

ZHOU Zhen-gong; WANG Biao

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Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(7): 682-690

ZHOU Zhen-gong, WANG Biao. Investigation of the Scattering of Harmonic Elastic Waves by Two Collinear Symmetric Cracks Using the Non-Local Theory[J]. Applied Mathematics and Mechanics, 2001, 22(7): 682-690.

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Investigation of the Scattering of Harmonic Elastic Waves by Two Collinear Symmetric Cracks Using the Non-Local Theory

Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, P. R. China

Received Date: 1999-12-14
Rev Recd Date: 2001-02-13
Publish Date: 2001-07-15

Abstract

Abstract

The scattering of harmonic waves by two collinear symmetric cracks is studied using the non-local theory. A one-dimensional non-local kernel was used to replace a two-dimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform was applied and a mixed boundary value problem was formulated. Then a set of triple integral equations was solved by using Schmidt's method. This method is more exact and more reasonable than Eringen's for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of incident wave.
- the non-local theory,
- Schmidt's method,
- the triple-integral equation

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References(22)

References

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