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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 semi-infinite elastic body and a rigid one. It gives solutions in complex form for non-homogeneous 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 crack-tip 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 quasi-elliptical curve. Then we prove that, for an equilibrium crackunder given applied load, the ‘‘energy release rate’’ Gtip; defined at each cracktip by the J-integral along a semi-circular 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 J-integral is path-independent and has the significance of the rate, with respect to the cracklength, of energy dissipated by friction on the crack.
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