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Some basic properties of penny‐shaped cracks
Author(s) -
Emery A. F.,
Smith F. W.
Publication year - 1966
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300003934
Subject(s) - mathematics , gravitational singularity , inverse , singularity , square root , isotropy , elasticity (physics) , surface (topology) , displacement (psychology) , mathematical analysis , square (algebra) , linear elasticity , geometry , composite material , materials science , structural engineering , physics , optics , psychology , finite element method , psychotherapist , engineering
The problem of a penny‐shaped crack which is totally embedded in an isotropic material is treated by the theory of linear elasticity. It is shown that for a prescribed crack surface displacement due to compressive stresses on the surface, stress singularities of order higher than the usual inverse square root are possible. It is also demonstrated that for all physically admissible crack surface stresses the singularity can only be of the inverse square root order and that the shape of the crack tip must be elliptical.