The sliding interface crack with friction between elastic and rigid bodies
type de publication 
article dans une revue internationale avec comité de lecture 
date de publication 
2005 
auteur(s) 
Bui H.D.; Oueslati Abdelbacet 
journal (abréviation) 
Journal of the Mechanics and Physics of solids (JMPS) 
volume (numéro) 
Volume 53, Issue 6 
 
pages 
1397 – 1421 
résumé 
The paper analyzes the frictional sliding crackat the interface between a semiinfinite elastic
body and a rigid one. It gives solutions in complex form for nonhomogeneous loading at
infinity and explicit solutions for polynomial loading at the interface. It is found that the
singularities at the cracktips are different and that they are related to distinct kinematics at the
cracktips. Firstly, we postulate that the geometry of the equilibrium crackwith cracktip
positions b and a is determined by the conditions of square integrable stresses and continuous
displacement at both cracktips. The crack geometry solution is not unique and is defined by
any compatible pair ðb; aÞ belonging to a quasielliptical curve. Then we prove that, for an
equilibrium crackunder given applied load, the ‘‘energy release rate’’ Gtip; defined at each
cracktip by the Jintegral along a semicircular path, centered at the cracktip, with vanishing
radius ; vanishes. For arbitrarily shaped paths embracing the whole crack, with end points on
the unbroken zone, the Jintegral is pathindependent and has the significance of the rate, with
respect to the cracklength, of energy dissipated by friction on the crack. 
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