David Natroshvili; Shota Zazashvili : The Interface Crack Problem for Anisotropic Bodies

Author(s) :

David Natroshvili; Shota Zazashvili

Title :

The Interface Crack Problem for Anisotropic Bodies

Electronic source :

[gzipped dvi-file] 33 kB
[gzipped ps-file] 80 kB

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-4, 1998

Mathematics Subject Classification :

31A10 [ Integral representations of harmonic functions (two-dimensional) ]

35J55 [ Systems of elliptic equations, boundary value problems ]

73B40 [ Anisotropic materials ]

73C35 [ Mixed boundary value problems in elasticity ]

73M25 [ Fracture mechanics ]

Abstract :

The two-dimensional interface crack problem is investigated for anisotropic bodies in the Comninou formulation. It is established that, as in the isotropic case, properly incorporating contact zones at the crack tips avoids contradictions connected with the oscillating asymptotic behaviour of physical and mechanical characteristics leading to the overlapping of material. Applying the special integral representation formulae for the displacement field the problem in question is reduced to the scalar singular integral equation with the index equal to -1. The analysis of this equation is given. The comparison with the results of previous authors shows that the integral equations corresponding to the interface crack problems in the anisotropic and isotropic cases are actually the same from the point of view of the theoretical and numerical analysis.

Keywords :

anisotropic body, interface crack problem

Language :

english

Publication time :

2/1998