Proceedings of the Ninth International Symposium

on

CONTINUUM MODELS AND DISCRETE SYSTEMS 29 June - 3 July 1998

Istanbul, Turkey

Editors

Esin inan Faculty of Science and Letters Istanbul Technical University Turkey

Konstantin Z. Markov Faculty of Mathematics and Informatics

UN1VER5ITATS318UOTHEK HANNOVER TGCHN1SCHE INFORMAT'ONSBIBLIOTHEK

World Scientific Singapore »New Jersey London* Hong Kong

IX

CONTENTS Preface

V

PART I. THERMODYNAMICS, TRANSPORT THEORY AND STATISTICAL MECHANICS IN THE CONTEXT OF CONTINUUM MODELLING OF DISCRETE SYSTEMS * GL

Statistical Mechanics of Vortex Matter G. Blatter*. M. Dodgson, V. Geshkenbein & H. Nordborg

. . 2

RC

Continuum Modelling of Flows with Nucleation and Condensation C. Delale 14

RC

Non-commutative Geometry, Irreversibility and Log-Periodicity A. Erzan & A. Gorbon

22

RC

Evolution of Snow-Firn Properties: A Thermomechanical Approach E. Guseva-Lozinski 29

RC

Nonpolynomial Expansion Near Fixed Points A. Hacmhyan, N. Perdahgi & F. Firat Acar

39

Endoreversible Thermodynamics: A Tool for Simulating Discrete Systems W. Muschik

47

RC

GL

Order-Disorder and Phase Separation: Modeling Grain Sintering A. Novick-Cohen 56

RC

Thermodynamics and Wellposedness of Constitutive Differential Equations in Continuum Mechanics (Abstract) E. Romensky 69

*GL — General Lecture, RC — Research Communication tNames underlined — Lecturers

RC

Microstructural Models for the Spin (Abstract) C. Trimarco

RC

71

The Mechanical Foundations of the Fokker-Planck Equation and its Generalizations (Abstract) S. Sellers & E. Fried

72

PART II. CONTINUUM MECHANICS OF COMPLEX FLUIDS AND DEFORMABLE SOLIDS WITH MICROSTRUCTURE RC

RC

On the Determination of the Theoretical Strength Limit in Compression of Unidirectional Composite Materials S. Akbarov & A. Cilli

74

The Theory of Deformable Porous Media Applied to Composite Materials Manufacturing (Abstract) D. Ambrosi, A. Farina & L. Preziosi

81

RC

The Mass Transport by Convection and Diffusion in a Multiporous Medium D. Baltean, T. Levy & S. Balint 82

RC

Rheology of Suspensions; Continuous Water/AOT/Oil Microemulsions D. Bedeaux. G. Koper & J. Smeets

RC RC

RC

RC RC

91

Composites with Superconducting Interfaces Y. Benveniste & T. Miloh

100

Equilibrium States in Volume Scattering of Acoustic Waves in a Channel (Abstract) M. Beran & A. Whitman

109

Duality Transformation and a New Kind of Phase Transition in the Magnetoresistive Response of a Composite Conductor with a 2D Microstructure D. Bergman & Y. Strelniker

110

Unstable Variational Problems in Solid Mechanics (Abstract) A. Cherkaev

120

Continuum Models of Plane Elastic Cellular Media I. Cielecka, M. Wozniak & C. Wozniak

121

XI

RC

RC RC

RC GL

GL

RC

GL RC

RC

RC

RC RC

Higher Order Continuum Model for Incompressible Viscous Flow and Application to the Modeling of Thermal Vibrational Convection A. Fedoseyev & B. Alexeev Sedimentation Phenomena and Structure in Suspensions F. Feuillebois. L. Talini & J. Leblond Exact Relations for Composites: Towards a Complete Solution (Abstract) Y. Grabovsky, G. Milton & D. Sage

130 138

146

Bounds of Physical Properties of Some Random Structures Models D. Jeulin 147 Some Basic Problems in Micromechanics of Solids with Pores of Various Shapes (Dry and Fluid-filled) (Abstract) M. Kachanov 155 Self-Consistent Schemes in the Problem of Wave Propagation Through Inhomogeneous Media S. Kanaun 156 The Elastic Wave Propagation in the Piezoelectric Fiber Reinforced Composites V. Levin Fluid Dynamics of Particulate Suspensions: Selected Topics D. Lhuillier & A. Nadim Material Mixing in Space-Time: The Problem of Bounds for Effective Parameters K. Lurie On a Two-point Correlation Function in Random Dispersions and an Application K. Markov Effects of Densely Packed Substructures on the Response of a Core Structure (Abstract) J. McCoy Micromechanics and Stochastic Finite Elements M. Ostoja-Starzewski Efficient Dielectric Constant Calculation for Periodic Composites (Abstract) Ping Sheng & H. Ma

171 180

198

206

216 217

226

XII

RC RC RC

Nonlinear Polycrystals with Microstructure Evolution P. Ponte Castaneda

228

Transport and Diffusion in Porous Media (Abstract) L. Schwartz

236

On the Status of the Beavers and Joseph Condition in the Mechanics of Porous Media A. Soliman & A. Ghaleb

237

RC

Induced Anisotropic Magneto-Resistance in a Composite Medium with a Periodic Microstructure: A New Effect in Classical Transport Y. Strelniker & D. Bergman 247

RC

Third-Order Bounds for the Effective Properties of a Nonlinear Dielectric Polycrystal D. R. S. Talbot & J. Willis

260

Self-heating of Some Viscoelastic Fluids V. Tigoiu

268

RC

P A R T III. CONTINUUM THEORY OF LIVING STRUCTURES RC

Biological Polymers: Dynamics and Solitons A. Askar

278

GL

Communication and Cooperation in Complex Bacterial Colonies (Abstract) E. Ben-Jacob 287

RC

Mathematical Modeling of Soft Biological Tissues and Solitary Waves in Arteries H. Demiray

288

Simulations of Polymeric Systems B. Erman & I. Bahar

297

Effect of Interfacial Bonding on the Mechanical Properties of Bone Tissue N. Giizelsu

304

The Renewal and Statistical Equilibrium of the Epidermis: Biomechanics of Tissues (Abstract) N. Rivier & B. Dubertret

318

RC GL

RC

XIII

RC RC

Continuum Kinematics, of Volumetric Growth R. Segev & G. Rodnay

321

Micromechanical Design of Materials for Bone Implants /. Sevostianov

329

PART IV. DEFECT DYNAMICS, DYNAMICAL SYSTEMS, SYNERGETICS, SOLITONS, COHERENT STRUCTURES RC GL RC RC RC

GL

Dissipation in Solids: Thermal Oscillations of Atoms A. Akay & C. Celik

340

Thermodynamics of Chaos V. Berdichevsky

348

A Model of Pulse Neural Networks B. Cavicchia, B. Tirozzi, D. Brown & J. Feng

353

An Asymptotic Theory of Thin Micropolar Plates H. Erbay

358

Multi-Scale Expansion of the Coupled Modified KadomtsevPetviashvili Equations 5. Erbay

366

Self-Organized Criticality in a Creep-Slip Model of Earthquake Faults P. Hdhner & Y. Drossinos

374

RC

Scattering of Transverse Elastic Waves from a Thin Defect Layer A. Kosevich & A. Tutov 388

RC

Wave Propagation in Bounded Media without Using Boundary Conditions D. Nelson

396

Solitons as Quasiparticles (Abstract) D. Pushkarov

404

Waves in Piezoelectric Random Media F. Sabina

405

Propagation of Nonlinear Surface SH Waves in a Layered Hyperelastic Half-Space M. Teymur & H. Var

413

RC RC RC

RC

Bayen-Flato Mechanics and Symmetries of Dynamical Systems G. final

421

PART V. DISLOCATIONS AND PLASTICITY RC

Experimental Approach to Continuum Dislocation Fields in Polycrystalline Materials B. Adams. S. Sun & W. Yang 428

RC

Anisotropic Models of Multiplicative Finite Elastoplasticity 5. Cleja-Tigoiu

437

Overall Modelling of Periodic Heterogeneous Cosserat Media 5. Forest & K. Sab

445

Mesomechanics of PSB Ladder Structure Formation V. Gregor & J. Kratochvil

454

Micromechanics of Plastic Deformation, Continuum Damage and Necking V. Kafka

462

Generalized Plasticity: Theory and Application J. Lubliner

470

An End Effect Model for Fibre-Reinforced Composites /. Mihovsky

483

RC RC RC

GL RC GL

Observations of Strain Localization and Instabilities in Plastic Deformation of Metals H. N e u h a u s e r . A . Z i e g e n b e n , M. A l e x & C. E n g e l k e

RC

RC RC

. . . .

491

Continuum Dynamic Theory of Elastoplastic Medium with Microstructure V. Popov & E. Kroner

503

The Mechanics of Defective Crystals (Abstract) 5. Sellers & P. Cermelli

511

Statistical Characterization of Inhomogeneous Dislocation Distributions M. Zaiser & P. Hahner

512

XV

PART VI. NEW DEVELOPMENTS IN CONTINUUM THEORY, NON CLASSICAL MODELS RC

RC GL RC RC RC

The Local and Nonlocal Nonsmooth Pseudoparabolic Systems, Their Fundamental Solutions and Applications S. Akhiev & E. Inan

522

Lagrange Formalism and Dissipation in Material Systems K.-H. Anthony

530

The Flux-Line Lattice in Superconductors E. Brandt Energetics of Fine Domain Structures (Abstract) A. De Simone Elements of a Theory of Growth M. Epstein & G. Maugin Diffusion in Non-Crystalline Solids, Particularly Metallic Glasses and Quasicrystals W. Frank, P. Scharwaechter & R. Bliiher

540 554 555

562

RC

On Optimal Systems of Subalgebras Admitted by Karman-Howarth Equations S. Khabirov & G. Unal 570

RC

Hardening Treated as Phase Transition: A Model Based on Superconductivity J.-L. Marques 576 Mesoscopic Modelling of Magnetization Process and Magnetostriction 5. Motogi 584

RC GL RC

GL RC

Some Microscopic Perspectives in Continuum Modelling A. Murdoch

592

A Non-Conventional Gauge Approach Towards Continuum Theories of Dissipative Deformation Processes M. Scholle

608

Equivalence Groups for Second Order Balance Equations E. Suhubi

617

Real-Time Behavior Control of Deformable Bodies 5. Utku & M. Suner

632

XVI

RC

The Microscopic Stress Tensor for Systems with Spin-Dependent Many-Body Interactions H. Wagner 644

RC

On Mechanics of Deformable Superconductors Shu-Ang Zhou

652

PART VII. DISCRETE MATERIAL STRUCTURES IN ENGINEERING SCIENCE, FATIGUE AND CRACK DYNAMICS ON DIFFERENT MICROLEVELS RC RC RC

GL

Elasticity and Fracture in Polyacrylamide Gels L. Benguigui

662

Nonlinear Scattering of Waves by Cracks D. Capuani & J. Willis

669

Statistical Aspects and Size Effect in Toughness of Concrete (Abstract) A. Chudnovsky, M. Issa & M. Gorelik

677

Towards a Unified Approach to Fracture Yielding, and Damage G. Del Piero

679

RC

Stress Singularity Exponent at the Vertex of a Three-Dimensional Conical Notch D. Esparza & N. Movchan 693

RC

Impact Damage Mechanisms in Laminated Composites (Abstract) A. Filippov 701

RC

Micromechanics of Cracking in Composite Materials Z. Hashin

702

Asymptotic Crack Tip Fields for Dynamic Crack Growth in Ductile-Porous Solids K. Herrmann & B. Potthast

710

Thermo-Microstretch Model of Damage Mechanics E. Inan

719

Variational Formulation of the Crack Problem with a Virtual Crack Kinking K. C. Le & H. Schutte

727

RC

RC RC

XVII

RC

RC

RC

GL RC RC

Continual, Discrete and Hybrid Models in Rupture Mechanics (Abstract) N. Morozov & M. Paukshto On the Nature of Fractal Crack Interfaces and the Evolution of Fractality P. Panagiotopoulos Recent Advances in the Modeling of Failure Phenomena of Piezoelectric Ceramics H. Sosa & N. Khutoryansky On Micro-Macro Transition in Nonlinear Mechanics C. Stolz Microstructural Effects on the Fracture of Concrete M. Tasdemir, C. Ta§demir, B. Barr & F. Lydon On the Interaction between a Crack and Inclusions in Materials D. Weichert & A. Haddi

736

737

745 753 767 775

PART VIII. GRANULAR MATERIALS AND INTERFACIAL PHENOMENA RC RC RC RC

A Kinetic Model for Granular Materials (Abstract) G. Capriz Remarks on Equations for Fast Granular Flows P. Giovine. G. Mullenger & F. Oliveri Junctions between Several Thin Bodies A. Movchan & 6. Selsil A Model for Granular Material Mechanics Combining Double-Shearing and Critical State Concepts A. J. M. Spencer

786 787 795

803

PART IX. SPECIAL POSTER SESSION (SP) (ABSTRACTS) SP SP

Nonlinear Wave Modulation in a Two-layered Elastic Medium 5. Ahmetolan & M. Teymur Nonlinear Wave Modulation in a Prestressed Viscoelastic Thin Tube Filled with an Inviscid Fluid G. Akgiin & H. Demiray

812

815

XVIII

SP

SP

SP SP

Weakly Nonlinear Waves in a Prestressed Thin Elastic Tube Containing a Viscous Fluid N. Antar & H. Demiray Approximate Constants of Motion for the Modified Henon-Heiles Problem E. Atilgan

817

819

An Investigation of Pulsatile Flow in a Slowly Tapered Tube I. Bahrta§ & H. Demiray

820

Analysis of Three Dimensional Non-linear Systems Using Trigonometric Transformations F. Firat Acar

822

SP

Buckling of Composite Plates which the Material has Periodically Curved Structure Z. Kutug 824

SP

Elasticity of a Continuum with Extra-Matter and Dislocation Defects F. Miri. N. Rivier & R. Khajehpour

826

SP

The Stability of Poiseuille Flow of a Second Order Incompressible Rivlin-Ericksen Fluid S. Ozer & E. Suhubi 827

SP

Nonpolynomial Normal Forms in Dynamical Systems Near Equilibrium N. Perdahci, A. Hacmhyan & G. Firat Acar

SP

The Stability Loss of the Strip Fabricated from the Multilayered Composite Material with Periodically Curved Structure N. Yahnioglu & S. Selim

830

832

Author Index

837

List of Participants

841