Table Of ContentIUTAM SYMPOSIUM ON ANISOTROPY, INHOMOGENEITY AND
NONLINEARITY IN SOLID MECHANICS
SOLID MECHANICS AND ITS APPLICATIONS
Volume 39
Series Editor: G.M.L. GLADWELL
Solid Mechanics Division, F acuity ofE ngineering
University ofWaterloo
Waterloo, Ontario, Canada N2L 3G1
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 research
ers 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
monographs defining the current state of the field; others are accessible to final
year undergraduates; but essentially the emphasis is on readability and clarity.
For a list of related mechanics titles, see final pages.
IUTA M Symposium on
Anisotropy,
Inhomogeneity and
Nonlinearity in
Solid Mechanics
Proceedings of the IUTAM-ISIMM Symposium
held in Nottingham, U.K.,
30 August- 3 September 1994
Edited by
D. F. PARKER
Department ofM athematics and Statistics,
University ofE dinburgh,
Edinburgh, U.K.
and
A. H. ENGLAND
Department of Theoretical Mechanics,
University ofN ottingham,
Nottingham, 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 978-90-481-4589-8 ISBN 978-94-015-8494-4 (eBook)
DOI 10.1007/978-94-015-8494-4
Printed on acid-free paper
All Rights Reserved
© 1995 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1995
Softcover reprint of the hardcover 1s t edition 1995
No part of the material protected by this copyright notice may be reproduced or
utilized in any fonn or by any means, electronic or mechanical,
including photocopying, recording or by any infonnation storage and
retrieval system, without written permission from the copyright owner.
CONTENTS
Preface xt
Foreword xiii
1. Characterisation of Anisotropic Materials 1
Optimization of Direct Biaxial Testing of Anisotropic Materials 3
J.P. Boehler and S. Demmerle
Anisotropy and Proper States of Materials 19
J. Rychlewski
Characterising a 2D Elasticity Tensor by Two Orientation
Distribution Functions 25
Q.-C. He and A. Curnier
The Mirror Symmetries of Anisotropic Elasticity 31
S.C. Cowin and M.M. Mehrabadi
Integrity Bases for a Fourth-rank Tensor 37
J. Betten and W. Helisch
On Anisotropy at the Actual Configuration and the Adequate
Formulation of a Free Energy Function 43
C. Sansour
A Continuum Model for Induced Anisotropy with Application
to Natural Ice 51
B. Svendsen and K. Hutter
On the Roles of Initial and Induced Anisotropies 57
Q.-S. Zheng
Higher Grade Material Structures 63
M. Elianowski and S. Prishepionok
Local Atomic Level Elastic Moduli of Surface ·Regions 69
Y. Shibutani, V. Vitek and J.L. Bassani
"'
2. Large Deformations and Flow 75
Description of Finite Plastic Deformations in Single Crystals
by Material Isomorphisms 77
A. Bertram and M. Kraska
vi TABLE OF CONTENTS
Modelling of Textured Materials 91
W. Gambin
Sensitivity Analysis of Fibre-reinforced Composites with
Interphase Unilateral Constraints 97
C. Alessandri and A. Tralli
Effective Local Properties for Modelling of Functionally
Graded Composite Materials 103
G.J. Dvorak and J.R. Zuiker
A Dislocation Solution for a Nonlinear Material with a Yield
Stress 109
R. V. Craster
The Application of Hyperelastic and Rate Dependent Models
to the Multiaxial Deformation of Polymers 115
J. Sweeney and I.M. Ward
Squeezing Flow of Fibre-reinforced Viscoelastic Composites 121
P. Watson, I.F. Collins and D. Bhattacharyya
Nonlinear Thermo-visco-elastic Behaviour 127
A.D. Irving, B.R. Clayton and T. Dewson
Damped Periodic Fluctuations in Certain Smectic Liquid
Crystals 133
F.M. Leslie and S.P.A. Gill ·
3. Numerical Studies in Plasticity 139
Dynamic Flow Localization in Plane-Strain Blocks Obeying
a Thermo-elasto-viscoplastic Constitutive Equation 141
Y. Tomita and K. Mimura
Numerical and Experimental Assessment of the Size and Boundary
Conditions Effects for the Overall Properties of Granular
Composite Bodies Smaller than the Representative Volume 149
M. Amieur A. Hazanov and C. Huet
1
Out-of-plane Deformation in Laminated Sheet Metals 155
S. Imatani, T. Saito and K. Yamaguchi
A New Model of Nonlinear Dynamic Creep 161
D. Breslavsky and 0. Morachkovsky
TABLE OF CONTENTS vii
4. Plasticity and Granular Materials 167
Double-shearing Theory for Dilatant Granular Materials 169
J.M. Hill
Equations Governing Plane Plastic Deformation in Anisotropic
Materials 183
D. Harris
Bounds for the Effective Yield Surface of Polycrystals 191
A.A. Kirillov, jr. and E. T. Onat
Analysis of the Influence of Anisotropy Effects on Adiabatic
Shear Band Localization Phenomena 201
P. Perzyna
An Analytical Investigation of Inhomogeneous Straining,
Subgrain Formation, and the Initiation of Microshear
Bands in Bicrystals 211
K.S. Havner and S.-C. Wu
On the Stability of Shear Bands 217
R. W. Ogden and P. Connor
Phase Inhomogeneities in Deformed Superalloy Single Crystals:
Numerical Estimates 223
R. Estevez, P. Franciosi, A. Hazotte and S. Denis
Material Symmetry in Solid Crystals 229
G.P. Parry
On the Volume Changes of Granular Materials and
their Consequences for Plasticity Theory 235
H. W. Chandler
Dynamic Deformations in the Theory of Fluid-saturated
Porous Solid Materials 241
W. Ehlers and S. Diebels
5. Fracture and Damage 247
Fracturing in Anisotropic Solids 249
S. Nemat-Nasser
Analysis of Anomalous Microcrack Growth in a Brittle Porous
Material Prior to Compression Failure 263
M. Hori and E. Mao
viii TABLE OF CONTENTS
Influence of Subcritical Propagation of Initial Flaws on the
Reliability of Brittle Structures 269
F. Hild and D. Marquis
Effect of Dynamic Strain Ageing and Portevin-le-Chatelier
Instabilities on the Tearing Failure of 2091 Al-Li Sheets 275
D. Delafosse and L.P. Kubin
Modelling of Semi-brittle Ceramics Behaviour under
a Quasi-static Deformation Process 281
T. Sadowski
Interactions between Cracks and Inclusions 287
C. Hwu, Y.K. Liang and W.J. Yen
Multi-fracture Processes in Ceramic Composites 293
Y.J. Weitsman
Three-dimensional Buckling Analysis of Orthotropic Cylinders
Subjected to Thermo-mechanical Loading 299
K.P. Soldatos and J.Q. Ye
6. Anisotropic Media 305
3-D Elastodynamic Green's Functions for BEM Applications
to Anisotropic Solids 307
C.-Y. Wang, A. Saez and J.D. Achenbach
Green's Functions for an Anisotropic Elliptic Inclusion under
Antiplane Deformations 321
T.C.T. Ting
Boundary Layer Problem in a Piezoelectric Composite 327
B. Gambin and A. Galka
Relaxed Energy Densities for Anisotropic Membranes 333
A.C. Pipkin
Qualitative Estimates for Laminate-like Elastic Materials 339
J.N. Flavin
Configurational Forces and Coherent Phase-transition Fronts
in Thermoelastic Solids 345
G.A. Maugin and C. Trimarco
The Formulation of Constitutive Equations for Anisotropic
Materials with Different Behaviour in Tension
and Compression 351
A. Zolochevsky
TABLE OF CONTENTS ix
7. Composites 357
An Application of the IFRM Theory to Evaluation of
Interlaminar Shear Stresses in a Fibre-reinforced Laminate 359
M. Kurashige, K. Watanabe and T. Kuriyama
Ideal Fibre-reinforced Materials and the Deformation of
Real Composites 371
J.T. Evans
Constitutive Equation for a Fiber-reinforced Lamina 379
R.S. Rivlin
Elastic and Elastic-plastic Deformations of Ideal
Fibre-reinforced Materials 385
A.H. England and P. W. Gregory
Micro-mechanics of a Segmented Embedded Fibre 391
A.P.S. Selvadurai
A One-dimensional Discrete Model of a Na nolayered Structure 397
W.A. Green
Morphological n-Layered Cylindrical Pattern-based
Micromechanical Modelling 403
E. Herve and A. Zaoui
Upper and Lower Bounds for the Overall Properties of a
Nonlinear Elastic Composite 409
D.R.S. Talbot and J.R. Willis
Effective Yield Surfaces for Anisotropic Composite Materials 415
M. Zaidman and P. Ponte Castaneda
8. Waves and Vibrations 423
Waves in Dissipative Anisotropic Solids 425
A. Morro and G. Caviglia
Inhomogeneous Plane Waves in Anisotropic Elastic
Materials 431
P. Boulanger and M. Hayes
Interfacial Phonons and the Existence of Elastic Interfacial Waves 437
E.S. Alber, J.L. Bassani, V. Vitek and G.J. Wang
Nonlinear Waves in Soils and Rocks 443
V.N. Nikolaevskiy
