Weak interface in long ®ber composites Stefano Lenci a, b, *, Giovanni Menditto a a Istituto di Scienza e Tecnica delle Costruzioni, Universita Á di Ancona, via Brecce Bianche, Monte D'Ago, 60131, Ancona, Italy b Laboratoire de Mode Âlisation en Me Âcanique, Universite  Pierre et Marie Curie (Paris 6), Tour 66, Case 162, 4 Place Jussieu, 75252, Paris, Cedex 05, France Received 18 September 1998; in revised form 20 April 1999 Abstract The problem of the diusion of load from a ®ber to an embedding matrix is considered in a three dimensional context. It is assumed that the ®ber-matrix interface allows sliding, which is assumed to be proportional to the interface tangential stress. The close-form solution is obtained for generic loads applied to the ®ber, and the case of a concentrated force is studied in detail. The main eects of the interface stiness, such as avoiding the stress singularities and increasing the length of the zone of in¯uence, are discussed and illustrated by some numerical examples. Successively, the problem of the broken ®ber is considered and solved with the same method as the previous case. Three dierent situations are discussed: no interaction between ®bers, very close neighboring ®bers and an intermediate case. It is shown that both problems have the same equations apart from a given function which plays the role of the constitutive equation and which characterizes the considered model. The eect of the neighboring ®bers on the interfacial stress is discussed and it is shown that it has a non-monotonic dependence on the distance between the ®bers. 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Elastic interface; Fiber-reinforced composites; Load diusion; Stress analysis 1. Introduction The problems related to the diusion of load from an elastic bar to its surrounding matrix arise in the ®eld of ®ber-reinforced composites and in many other branches of engineering. Since the pioneering work of Melan (1932), a great deal of attention has been paid to the determination of interface stresses (Grigolyuk and Tolkachev, 1987), responsible for many characteristic phenomena such as interface delamination, breaking of ®bers and so on. International Journal of Solids and Structures 37 (2000) 4239±4260 0020-7683/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S0020-7683(99)00140-7 www.elsevier.com/locate/ijsolstr * Corresponding author. Fax: +390-71-220-4576. E-mail address: m.lenci@fastnet.it (S. Lenci).