Fracture of concrete and rock editorial

Editorial Fracture of concrete and rock Fracture of concrete and rock has proven dicult to be modelled using linear elastic fracture mechanics LEFM)±±as attempted by Kaplan and other researchers in the 1960sÐdue to the non-negligible size of the process zone, which in turn avoided characterisation of local stress and strain ®elds with only one parameter, be it K or J. Modelling the process zone as a cohesive crack±±pioneered by Hillerborg in 1976±±allowed accurate predictions of peak loads and full load±displacement behaviour of concrete structural components. This powerful model has been applied successfully to other cementitious and ®bre reinforced cementitious materials. More recently, it has been recognised that there are strong similarities between some aspects of the process zone of a wide range of materials; not only cementitious materials, but also rocks, ceramics, polymers and even some brittle metals. Modelling the process zone as a cohesive crack appears as a possible generalisation of LEFM, particularly in two directions; when the process zone is no longer negligible and when no pre-existing cracks are present±±as is the case for notches. This is one of the reasons for airing this topic outside the realm of practitioners. In this special issue, a collection of paper±±written by renowned specialists in the ®eld±±presents an overview of the techniques for modelling fracture of concrete and cementitious materials with special emphasis, particularly in some papers, on cohesive models with the aim that these techniques may prove useful for modelling fracture of other materials as well. A brief description of the contributions is as fol- lows. The ®rst six papers are reviews of the state of the art, re¯ecting the bias of the authors and, thus, en- riching the picture of the present state of the subject: Rene de Borst oers an overview of some important developments in smeared ®nite element analyses of fracture in quasi-brittle materials. A concise summary is given of recent ®nite element concepts for cohesive models. Javier Oliver and collaborators deal with the strong discontinuity approach and shows the links with the cohesive models. The undersigned and co-workers show the advantages, limitations and chances of the cohesive models, based on numerical and experimental evidence, and explores its applications to polymers and some steels. Zdenek Bazant reviews the existing fracture models for concrete and testing methods for fracture energy measurement, with special emphasis on size eect, and discusses the limitations of the cohesive model. Alberto Carpinteri and collaborators generalise the cohesive model through a scale-independent cohesive law, by assuming that damage occurs in a fractal band. By varying the scaling exponents of the kinematic quantities, a transition from discrete to smeared cracking is obtained. Finally, Yiu-Wing Mai reviews the fracture mechanics of cementitious materials, concretes and their ®bre composites, in the light of the cohesive model. The last four papers deal with experimental techniques for the measurement of the key parameters of the cohesive model and with numerical techniques for implementing the model: Jan van Mier and M. van Vliet oer an overview of methods to uniaxial tension. Such procedures can be transferred to other cohesive geomaterials. Hirozo Mihashi and collaborators describe an experimental study to ®nd out material Engineering Fracture Mechanics 69 2002) 93±94 www.elsevier.com/locate/engfracmech 0013-7944/02/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII:S0013-794401)00081-9

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Fracture of concrete and rock editorial