IUTAM Symposium on Analytical and Computational Fracture Mechanics of Non-Homogeneous Materials: Proceedings of the IUTAM Symposium held in Cardiff, U.K., 18–22 June 2001 PDF
Preview IUTAM Symposium on Analytical and Computational Fracture Mechanics of Non-Homogeneous Materials: Proceedings of the IUTAM Symposium held in Cardiff, U.K., 18–22 June 2001
IUTAM Symposium on Analytical and Computational Fracture Mechanics of Non-Homogeneous Materials SOLID MECHANICS AND ITS APPLICATIONS Volume 97 Series Editor: G.M.L. GLADWELL Department of Civil Engineering University of Waterloo Waterloo, Ontario, Canada N2L 3GI Aims and Scope of the Series The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids. The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and structures; dynamical systems and chaos; the theories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design. The median level of presentation is the first year graduate student. Some texts are mono graphs defining the current state of the field; others are accessible to final year under graduates; but essentially the emphasis is on readability and clarity. For a list of related mechanics titles, see final pages. IUTAM Symposium on Analytical and Computational Fracture Mechanics of Non-Homogeneous Materials Proceedings of the IUTAM Symposium held in Cardiff, U.K., 18-22 June 2001 Edited by B.L. KARIHALOO Cardiff University, School of Engineering, Cardiff, u.K. .... " SPRINGER-SCIENCE+BUSINESS MEDIA. B.V. A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-90-481-5977-2 ISBN 978-94-017-0081-8 (eBook) DOl 10.1007/978-94-017-0081-8 Printed on acid-free paper All Rights Reserved © 2002 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2002 Softcover reprint of the hardcover 1st edition 2002 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. CONTENTS Preface IX Features and ellipticity analysis ofa discrete constitutive equation H L Schreyer Finite fracture mechanics -Application to the onset of a crack at a bimaterial comer 11 D Leguillon and K Siruguet Elastic-plastic stress singularity near a bonded interface 19 D H Chen and K Ushijima Viscosity-dominated regime of a fluid-driven fracture in an elastic medium 25 D Garagash and E Detournay Modelling failure mechanisms in laminated composites 31 L N McCartney The influence of fiber on the structural response of reinforced concrete beams 41 A Carpinteri, G Ferro and G Ventura Materials with novel architectonics: assemblies of interlocked elements 51 Y Estrin, A V Dyskin, A J Kanel-Belov and E Pasternak Asymptotics of elastic field near the tip of interface crack under nonclassical 57 transmission conditions G Mishuris and G Kuhn Scaling in multiple fracture and size effect 63 F M Borodich Mechanics of fractal materials 73 A V Dyskin Fractal aspects of fracture simulation 83 M M Davydova Filling of a circular crack with two non-miscible fluids 89 A Feraille-Fresnet and A Ehrlacher Effect of inhomogeneous rock properties on the stability of wellbores 95 C Atkinson and I Bradford The interplay of material and geometric instabilities in large deformations of viscous 105 rock H-B Miihlhaus, L Moresi, F Dufour and R Hobbs A displacement rate dependent softening model applied to the unstable propagation of 117 shear crack in soft rock Y Nakagawa, E Puntel and H Horii Fractures and defects in Cosserat continua modelling layered materials 127 E Pasternak, H B Miihlhaus and A V Oyskin VI Modeling thin inclusions in poroelastic medium by line discontinuities 133 L Germanovich and R Chanpura Cleavage fracture in "heterogeneous" steel microstructures 143 J F Knott Modelling delayed hydride cracking in zirconium alloys 155 D A Scarth and E Smith Multiscale modeling of crack growth in polycrystals 167 E Iesulauro, T Cretegny, C S Chen, K Dodhia, C Myers and A R Ingraffea The viscoelastic fracture and indentation of sea ice 177 J P Dempsey An enriched finite element method for dynamic crack propagation 187 H Chen and T Belytschko Modeling of early-age fracture of shotcrete: application to tunneling 197 R Lackner and H A Mang Modelling of progressive interface failure under monotonic and cyclic loading 211 Z Mroz and N Bialas Crack kinking from an initially closed interface crack in the presence of friction 223 J Frelat and J-B Leblond Elasto-plastic interface laws for non-homogeneous materials: formulation, sensitivity 233 analysis and parameter identification A Corigliano Analytical and discrete modeling of transformation toughening 243 D Zeng, P Shrotriya, M Li, N Katsube and W 0 Soboyejo The influence of boundary conditions on the non-local response of a randomly 249 heterogeneous medium R Luciano and J R Willis Dynamic crack growth along interfaces 261 A Needleman, D Cocker and A J Rosakis A thermodynamic plasticity formulation with local and non-local internal variables 271 G Borino, B Failla and C Polizzotto Multi-scale energy release rate in dynamic crack growth of strain-softening materials 28 I X Zhang and Y W Mai Analysis of cohesive cracks under quasi-static and dynamic loading 293 G N Wells, R de Borst and L J Sluys Material forces in computational fracture mechanics 303 F J Barth, D Ackermann and P Steinmann Shear localisation in thick-walled cylinders under internal pressure based on gradient 313 elastoplasticity A Zervos, P Papanastasiou and I Vardoulakis vii Damage and fracture study of non-homogeneous materials by image correlation 323 computations J Fang, J X Wang, M Li, J Zhang and C Y Xiong Fibre failure due to thermal residual stresses in model polymer based composites 333 A S Nielsen and R Pyrz A new method to obtain crack surface areas from electromagnetic radiation emitted in 343 fracture: a string of pulses A Rabinovitch, V Frid, D Bahat and J Goldbaum Determination of cohesive laws for materials exhibiting large scale damage zones 349 E K Gamstedt, T K Jacobsen and B F Sorensen A bio-chemo-mechanics approach to bone resorption and fracture 355 E C Silva and F J Ulm Numerical study of mixed-mode fracture in concrete 367 J Ozbolt and H W Reinhardt Thermodynamics of a multi component crack model 377 A D Jefferson Failure assessment of anchor bolts by means of nonlinear finite element analysis 387 D Pivonka, R Lackner and H A Mang An interface model for fibre reinforced concrete 395 M Cuomo Gradual degradation of initially porous polycrystalline ceramics subjected to quasi- 401 static tension T Sadowski, S Samborski and Z Mroz 3 D studies of ductile failure in particulate reinforced metals 407 V Tvergaard Modeling deformation and damage in particle-reinforced composites: the effect of 417 superposed hydrostatic pressure C Gonzalez and J Llorca Understanding failure of heterogeneous materials from the analysis of discrete 427 disordered systems A Delaplace, S Roux and G Pijaudier-Cabot Photonic band gaps for fields in continuous and lattice structures 437 A B Movchan, V V Zalipaev and N V Movchan Effects of shear and rotation on the mechanical behaviour of interphase 447 S W Yu, G F Wang, X Q Fen and Y L Kang Modelling of R-curves from measured bridging laws 453 T K Jacobsen, B F Sorensen and E K Gamstedt Interfacial crack depinning 459 S Roux, D Vandembroucq and R Skoe viii Analysis of 3D crack propagation in random lattice structures with particle overlay 471 G Lilliu and J G M van Mier A novel technique for the generation of failure criteria for jointed rock 481 N Madhusudhan and T N Singh Nonlinear wave propagation in porous materials 487 A Pegushin and V I Erofeyev An improved lattice model for fracture and size effect of concrete structures 493 B L Karihaloo, R Ince and A Arslan APPENDIX: The Scientific Programme 507 PREFACE This volume constitutes the Proceedings of the IUTAM Symposium on "Analytical and Computational Fracture Mechanics of Non-homogeneous Materials", held in Cardiff from 18th to 22nd June 2001. The Symposium was convened to address and place on record topical issues in analytical and computational aspects of the fracture of non-homogeneous materials as they are approached by specialists in mechanics, materials science and related fields. The expertise represented in the Symposium was accordingly very wide, and many of the world's greatest authorities in their respective fields participated. Given the extensive range and scale of non-homogeneous materials, it had to be focussed to enhance the quality and impact of the Symposium. The range of non-homogeneous materials was limited to those that are inhomogeneous at the macroscopic level and/or exhibit strain softening. The issues of micro to macro scaling were not excluded even within this restricted range which covered materials such as rock, concrete, ceramics and composites on the one hand, and, on the other, those metallic materials whose ductile fracture is strongly influenced by the presence of inhomogeneities. The Symposium remained focussed on fundamental research issues of practical significance. These issues have many common features among seemingly disparate non-homogeneous materials. Presentations emphasized many aspects, including experimental observation, ranging from the role of inhomogeneities, interfaces, scaling laws and non-local effects. Micromechanical modelling, macroscopic analysis and meso-scale lattice modelling that reveal underlying micromechanisms of fracture, and methods based on non-local and higher-order gradient theories were expounded. These Proceedings address all of these different aspects and more, and provide a reasonable picture of understanding as it exists at present. The Symposium consisted of forty-one lectures, all of which were invited and accorded equal time in the programme. In addition, twenty presentations of shorter duration were made by younger contributors. This is reflected in this volume by a briefer version of their written contributions. Full record of the programme appears as an Appendix. A few of the lectures are not represented, mainly because of prior commitments to publish elsewhere. The International Scientific Committee responsible for the Symposium comprised the following: Professor B.L. Karihaloo (UK) Chairman Professor Z.P. Baz ant (USA) Professor J.-B. Leblond (France) Professor R. de Borst (Netherlands) Professor G. Maier (Italy) Professor L.B. Freund (USA) Professor Z. Mroz (Poland) Professor K.-C. Hwang (PR China) Professor H.-B. Muhlhaus (Australia) Professor A.R. Ingraffea (USA) Professor J.R. Willis (UK) The Committee gratefully acknowledges financial support for the Symposium from the International Union of Theoretical and Applied Mechanics and the Innovation Centre of Welsh Development Agency. The smooth running of the Symposium owes much to the efforts of Cherrie Summers, Aderyn Reid, Farshid Alaee, Sharon Benson, Sinan Caliskan, Tony Jefferson, Qizhi Xiao, and it would not have happened at all without a great deal of work before by Sheila Foley. To all of them many thanks. B.L. Karihaloo Cardiff, August 200 I IX FEATURES AND ELLIPTICITY ANALYSIS OF A DISCRETE CONSTITUTIVE EQUATION H.L. SCHREYER Depanment ofM echanical Engineering The University of New Mexico Albuquerque, NM 87131 [email protected] Abstract One approach for describing material failure is that of using a discrete constitutive equation which relates traction to displacement discontinuity on a failure surface. Here we propose a failure function that might be considered a generalization of the Mohr Coulomb criterion. One of the unique features is the capability for predicting axial splitting under uniaxial compression. Other experimentally plausible aspects of the model are shown. If the discontinuity is smeared over a shell, then a conventional ellipticity analysis can be performed. For a particular choice of material parameters, it is shown that ellipticity holds provided the thickness of the shell is sufficiently small. 1. Introduction Failure of inhomogeneous materials is often exhibited as a physical separation at the interface of two distinct phases. Under certain loading conditions, the failure is a gradual process involving a decrease in traction capability with an increase in displacement discontinuity. Constitutive equations that attempt to represent this process are called discrete, cohesive crack or decohesive models. There are numerous attempts at using such models with numerical procedures and the results in the literature range from somewhat discouraging to highly promising. Because there is such a wide range of problems for which material failure is one of the distinguishing features, it is essential that attempts be made to understand the reasons why numerical solutions sometimes fail to display convergence with mesh refinement. A solid mechanics problem based on a continuum formulation is well-posed until ellipticity is lost. Under certain restrictions, loss of ellipticity is identical to loss of B.L. Karihaloo (ed.), IUTAM Symposium on Analytical and Computational Fracture Mechanics ofN on-Homogeneous Materials, 1-10. © 2002 Kluwer Academic Publishers.
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