Continuum Thermomechanics

433 Pages·2002·10.686 MB·English

by  G. Maugin, et al.

CONTINUUM THERMOMECHANICS
SOLID MECHANICS AND ITS APPLICATIONS
Volume 76
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 undergra-
duates; but essentially the emphasis is on readability and clarity.
Continuum
Thermomechanics
The Art and Science of
Modelling Material Behaviour
Paul Germain’s Anniversary Volume
Edited by
GÉRARD A. MAUGIN (co-ordinator)
Laboratoire de Modélisation en Mécanique,
Université Pierre et Marie Curie,
Paris, France
RAYMONDE DROUOT
Centre de Mécanique de Milieux Continus,
Université de Versailles-St Quentin,
Versailles, France
and
FRANÇOIS SIDOROFF
Laboratoire de Tribologie et Dynamique des Systèmes,
Ecole Centrale de Lyon,
Ecully, France
KLUWER ACADEMIC PUBLISHERS
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Print ISBN: 0-792-36407-4
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CONTENTS
Foreword ix
My Discovery of Mechanics 1
P.Germain
A Selection of Scientific Works and Publications by Paul Germain 25
Contributions
Double Diffusive Aspects of the Convection in Moist-saturated Air 29
P.A.Bois and A. Kubicki
Application of the Theory of Cosserat Media to the Elasto-plastic
Behaviour of Polycrystals 43
M.Brocato, A.Ehrlacher and P. Tamagny
From Clausius to Finite Elasticity, via Bridgman, Eckart and Ziegler 55
L.C.J. Brun
On Viscous Fluid Flow Near a Moving Crack 63
H. D. Bui, C. Guyon and B. Thomas
Elastoplasticity with Aging in Aluminium Alloys 75
G.Cailletaud, C.Depoid,D.Massinon, E.Nicouleau-Bourles
The Application of the Irreversible Thermodynamics to the Development
of Constitutive Equations 87
J.L. Chaboche
On Micromechanics of Martensite Transformation in SMA and TRIP Steels 101
M.Cherkaoui, M.Berveiller and E.Patoor
Modelling of Coupled Effects of Damage by Microcracking and Friction
In Closed Cracks 113
A. Dragon and D. Halm
Structural Plastic Microbuckling and Compressive Strength of Long-fibre
Composite Materials 125
S.Drapier, J.C.Grandidier, JC.Jochum and M.Potier-Ferry
A New Method of Optimisation for Composite Structures 137
G.Duvaut and G. Terrel
Material Evolution in Plasticity and Growth 153
M.Epstein and G.A.Maugin
Thermoelasticity of Second-grade Media 163
S. Forest and J. M. Cardena
The Power of Internal Forces in Solid Mechanics 177
M.Frémond
A Continuum Damage Model in Stress Corrosion 189
A. Gérard
Modelling Wetting Behaviour 197
H. Lanchon-Ducauquis, F. Biguenet, T. Liraud, E.Csapo and Y.Guemeri
Thermodynamics and Phenomenology 209
J.Lemaitre, A.Benallal, R.Billardon and D.Marquis
On the Thermomechanical Modelling of Shape Memory Alloys 225
C.Lexcellent and M.L.Boubakar
Thermo-mechanical Modelling of Nematic Polymers 237
D.Lhuillier
Multiscale Thermomechanical Approaches to SMA Behaviour 247
L.M.G.C.
Regularization of Flutter Ill-posedness in Fluid-saturated Porous Media 265
B.Loret, F.M.F. Simoes and J.A.C.Martins
A 3D-numerical Thermomechanical Approach for Materials Cutting 277
P.Lorong, O.Pontale, R.Rakotomalada and M.Touratier
From Clausius-Duhem and Drucker-Ilyushin Inequalities to Standard Materials 289
J.J.Marigo
Constitutive Relations Involving Internal Variables Based on a
Micromechanical Analysis 301
J. C. Michel, U. Galvanetto and P. Suquet
Adiabatic Shear Banding as an Example of Viscoplastic Flow Instability 313
A.Molinari
On the Evaluation of Damping in a Structure with Viscoelastic Components 331
P.Muller
vii
Standard Dissipative Systems and Stability Analysis 343
Q.S.Nguyen
Enriched Damage Models for Continuum Failure Analyses 355
G.Pijaudier-Cabot and R. de Borst
Constitutive Laws, Relaxation Thermodynamics and Lagrange Formalism 367
R. Rahouadj, J. F. Ganghoffer and C. Cunat
Second-gradient Theory: Application to Cahn-Hilliard Fluids 379
P.Seppecher
Thermodynamics and Duality in Finite Elastoplasticity 389
F. Sidoroff and A. Dogui
Thermodynamical Description of Running Discontinuities 401
C.Stolz
List of invited contributors 413
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FOREWORD
Professor Paul GERMAIN will be 80 years old on August 28, 2000. The day
coïncides with the opening day of the 20th ICTAM in Chicago. This cannot be a
mere coïncidence since Paul GERMAIN is a former President of IUTAM. But if it is
a coïncidence at all, then the scientific children and grandchildren of Paul
GERMAIN have decided to mark that memorable day with a special publication that
reflects his direct influence on a successful scientific trend, the thermomechanics of
materials.
Paul GERMAIN has had an extremely fruitful scientific carreer in which he
contributed to so many various fields, including the study of peculiar partial
differential equations, its application to various regimes of aerodynamics,
transsonics, shock-wave structure, magnetohydrodynamics, the implementation of
asymptotic methods in fluid mechanics, and the general formulation of continuum
mechanics and thermodynamics. This he tells about beautifully in his own
contribution to this volume, a rather easygoing scientific autobiography. What also
emerges from that contribution is not only Paul GERMAIN's deep involvment in
Aeronautical Research at a critical time (1960s-1970s), but also his passion for
teaching, first mathematics, and then mechanics in its various guises. That a single
person should so much influence the teaching of a discipline - continuum mechanics
- in the whole of a medium-size country like France, and that, in turn, that spirit
spread over to a large part of the profession, worldwide, is simply amazing. The
thirty one contributions that make up the rest of this volume, reflect this influence to
the utmost. This is a tribute paid by the contributors to the special talent and
enthusiasm of a person they have tried to imitate, but often in vain. Professors
Monique PIAU, Cristian TEODOSIU and André ZAOUI could not provide a
contribution in time but they fully associate themselves to this hommage.
This volume has been prepared with the efficient help of Jean-Pierre GUIRAUD,
Eleni MAUGIN, and Prof. Graham M.L. GLADWELL. Our heartfelt thanks go to
them for their untiring efforts to improve all manuscripts.
The Editors
ix