IUTAM Symposium on Non-linear Singularities in Deformation and Flow: Proceedings of the IUTAM Symposium held in Haifa, Israel, 17–21 March 1997

365 Pages·1999·16.36 MB·English

by  J. R. A. Pearson (auth.), D. Durban, J. R. A. Pearson (eds.)

IUTAM SYMPOSIUM ON
NON-LINEAR SINGULARITIES IN DEFORMATION AND FLOW
IUTAM Symposium on
Non-linear Singularities
Deformation and Flow
Proceedings of the IUTAM Symposium
held in Haifa, Israel,
17-21 March 1997
Edited by
D. DURBAN
Faculty of Aerospace Engineering,
Israel Institute of Technology,
Technion, Haifa, Israel
and
J.R.A. PEARSON
Fluid Mechanics Department,
Schlumberger Cambridge Research,
Cambridge, U.K.
SPRINGER SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging-in-Publication Data
ISBN 978-94-010-5991-6 ISBN 978-94-011-4736-1 (eBook)
DOI 10.1007/978-94-011-4736-1
Printed on acid-free paper
All Rights Reserved
© 1999 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1999
Softcover reprint of the hardcover 1st edition 1999
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
Committees and Sponsors xi
Introduction
Length Scales, Asymptotics and Non-Linear Singularities 1
A. Pearson
Corner Flows
High Weissenberg Number Asymptotics and Corner Singularities
in Viscoelastic Flows 13
M. Renardy
Comer Singularities in Three-Dimensional Stokes Flow 21
H.K. Moffatt and V. Mak
Hydraulic Fracturing
Fluid and Solid Singularities at the Tip of a Fluid-Driven Fracture 27
E. Detoumay
Inverse Problems in Hydraulic Fracturing 43
D.P. Alekseenko, A.M. Vaisman and A.F. Zazovsky
Fracture Mechanics I
The Bimaterial Notch Problem 55
L. Banks-Sills
VI
Crack Development in Spatially Random Stress Fields
Generated by Point Defects. Fracture in Compression 63
A.V. Dyskin
Elastic Interaction of Edge Dislocations with a Crack in a Disk 75
S. Vigdergauz
The Asymptotic Solution of Anisotropic Gradient Elasticity with
Surface Energy for a Mode II Crack 87
1. Vardoulakis and G. Exadaktylos
Interfacial Effects in Fluids
The Unsteady Motion of Three Phase Contact Lines 99
J. Billingham
Singularities on Viscous Interfaces 111
S.H. Davis
Spirals, Jets and Pinches 119
M.J. Shelley
Penetration Phenomena
Localization of Strain and the Melting Wave in
High-Speed Penetration 129
M. V. Ayzenberg and L.1. Slepyan
Friction and Singularities in Steady Penetration 141
D. Durban
Fracture Mechanics II
Creep Induced Cohesive Crack Propagation in Mixed Mode 155
F. Barpi, S. Valente, F. Chilli and L. Imperato
\"11
Asymptotic Analysis of a Spontaneous Crack Growth.
Application to a Blunt Crack 169
D. Leguillon
Experimental Investigation of Dynamic Failure Mode Transitions 181
D. Rittel
Energy Release in Fracture of Rate-Dependent Materials 193
L.l. Slepyan
Numerical Methods
A Combined Element-Free Galerkin Method/Arbitrary
Lagrangian-Eulerian Formulation for Dynamic Crack Propagation 205
l.-P. Ponthot and T. Belytschko
Boundary Element and Discrete Vortices Method for Ideal Fluid
Flow Calculations 217
D. V. Yevdokymov
Method of Numerical Analysis of Stress Singularity
at Singular Points in Two- and Three-Dimensional Bodies 231
V.P. Matveyenko, S.M. Borzenkov and S.G. Minakova
Capillary Breakup and Instabilities
Capillary-Elastic Instabilities with an Oscillatory
Forcing Function 243
D. Halpern, 1.A. Moriarty and I. Grotberg
Singularities and Similarity Solutions in Capillary Breakup 257
I.R. Lister, M.P. Brenner, R.F. Day, E.J. Hinch and H.A. Stone
The Linear Stability of a Two-Phase Compound Jet 271
A. Chauhan, C. Maldarelli, D. Papageorgiou
and D. Rumschitzki
VlIl
Cusps and Contact Lines
Free-Surface Deformation and Formation of Cusps at Low
Reynolds Number Flow 283
J.-T. Jeong
Free-Surface Cusps and Moving Contact Lines. A Common
Approach to the Problems 297
Y.D. Shikhmurzaev
Applications
Effects of Time-Periodic Fields on the Rheology of Suspensions
of Brownian Dipolar Spheres 309
I. Puyesky and I. Frankel
A Molecular Theory for Dynamic Contact Angles 321
A. Indeikina and H.-c. Chang
Regularization of Singularities in the Theory of Thin
Liquid Films 339
A. Oron and S.G. Bankoff
Bounds on the Endurance Limit in Fatigue of Dilute Fibrous
Composites by the Shakedown Theorems 349
J. Tirosh
Preface
The IUTAM Symposium on "Non-Linear Singularities in Defonnation
and Flow" took place from March 17 to 21, 1997, at the Technion in
Haifa, Israel, with 70 participants from 12 countries.
The leitmotif of this Symposium brought together scientists working on
singularity-dominated local fields in various branches of continuum
mechanics, covering traditional solid and liquid behaviour as well as that
of more complex non-linear materials; non-linearities arise either from
the constitutive equations for the material or from the presence of
interfaces or both. The scientific committee invited speakers who
presented 34 papers in 12 sessions. Topics covered in the lectures
included near tip fields of cracks, notches and wedges; flow around
comers, wedges and cones; interfacial phenomena; moving contact lines
in multiphase systems; cusps in fluid interfaces and shocks and
localization. There was a general consensus among the participants that
singularities induced by non-linearities provide a challenging and
currently important area of research in mechanics, engineering and
applied mathematics. Presentation and discussions during the symposium
initiated further studies of problems in these interesting areas.
This volume contains 30 full length papers, submitted by the lecturers
after the symposium and reviewed to the standards of international
scientific periodicals.
It is our pleasure to acknowledge the efficient and tireless help of Mrs.
Alice Goodman and Mr. Gideon Wachsman of the Faculty of Aerospace
Engineering at the Technion.
David Durban Anthony Pearson
Haifa Cambridge
April 1998
IX
International Scientific Committee
C. Atkinson (UK)
G.I. Barenblatt (USA)
H.-c. Chang (USA)
D. Durban (Israel, Chairman)
E.J. Hinch (UK)
J.-T. Jeong (Korea)
D.D. Joseph (USA)
H.K. Moffatt (UK)
J.R.A. Pearson (UK, Chairman)
E. Sanchez-Palencia (France)
I. V ardoulakis (Greece)
Local Organizing Committee
D. Durban (Chairman)
I. Frankel
D. Givoli
B. Greenberg
Y. Tirosh
A. Goodman (Secretary)
Sponsors of the IUTAM Symposium on Non-Linear Singularities in
Deformation and Flow
International Union of Theoretical and Applied Mechanics (JUT AM)
The Institute of Advanced Studies in Mathematics at the Technion
Technion-Israel Institute of Technology
The S. Neaman Institute for Advanced Studies in Science and
Technology
Faculty of Aerospace Engineering, Technion
International Association for Computational Mechanics (JACM)
Kluwer Academic Publishers
xi
LENGTH SCALES, ASYMPTOTICS AND
NON-LINEAR SINGULARITIES
J.R.A. PEARSON
23 Chaucer Road, Cambridge CB2 2EB, England
1. Introduction
This short introductory paper will try to give a common perspective to
many of the problems and techniques covered in later papers. We shall
draw attention to those common features that lead to singularities, and
to any similarities in the techniques used to deal with them. Continuum
mechanical theories for elasto-plastic solids, for materials with memory and
for purely viscous or ideal fluids have tended to be treated separately lead
ing to unnecessary and unhelpful specialisation. The mechanics of porous or
fractured media have developed as almost independent subjects, while wave
propagation is often studied in isolation. It is hoped that this symposium
will help to restore the universality inherent in continuum mechanics.
It is well known that singular solutions exist for many of the sets of equa
tions (mathematical models) describing the bulk continuum mechanics of
deformable and fluid materials. In the case of linear models, these sim
ple singular solutions have fundamental mathematical (rather than phys
ical) significance and can be used in a formal fashion to provide gen
eral solutions to geometrically-complex boundary-value problems. In cases
with smooth boundaries, superposition of these isolated singular solutions
can lead to physically acceptable (everywhere) smooth solutions. However,
when boundaries have corners or include finite cracks, these singularities
(specifically in the stress tensor) remain as localised features ofthe full solu
tion. Examples are provided later in this volume (Banks-Sills, Matveyenko
et al., Leguillon).
The question then arises as to how these physically unacceptable sin
gularities can best be removed (regularised) so as to make the solutions
correspond to physical reality. There are several ways in which this can be
done.
D. Durban and J.R.A. Pearson (eds.),
IUTAM Symposium on Non-Linear Singularities in Deformation and Flow, 1-20.
© 1999 Kluwer Academic Publishers.