Handbook of Materials Behavior Models

1183 Pages·2001·17.935 MB·English

by  Jean Lemaitre (Eds.)

FOREWORD
We know that there is an abundance of models for particular materials and for
specific types of mechanical responses. Indeed, both the developers of models
and their users sometimes criticize this situation, for different reasons. The
presence of different models that attempt to describe the same material and
response is due not only to the personal style of their inventors, but also to a
desirable element of competition that drives the progress in the field.
Given this situation, the selection of the proper constitutive model from all
the available ones can be difficult for users or even materials modelers when
they are not experts in the field. This Handbook is the first attempt to organize
a wide range of models and to provide assistance in model selection and
actual application. End-users will find here either potential models relevent
for their application and ready to be used for the problem at hand, or an
entrance to the specific technical literature for more details.
Recognizing the breadth of the field as well as the unavoidable personal
touch of each approach, Jean Lemaitre has chosen to include in this
Handbook the writings of as many as 130 authors. Drawing on his wide
experience developing and using constitutive models for many materials, he
has addressed his worldwide network of colleagues, all experts in their
pertinent subject, to accomplish this difficult task. Yet, even though the
Handbook covers an unprecedented range of materials and types of behavior,
it is only a sample of currently available models, and other choices would
have been possible. Indeed, more choices will become possible as the
development of novel and improved material models continues.
Erik van der Giessen
Koiter Institute Delft
Delft University of ygolonhceT
ehT Netherlands
ivx
INTRODUCTION
Why a Handbook of models? Handbooks are often compilations of
characteristic numbers related to well-established laws or formulae that are
ready to apply. In this case of the behavior of materials, no unique law exists
for any phenomenon, especially in the range of nonlinear phenomena. This is
why we use the term model instead of law. During the past thirty years many
models have been proposed, each of them having its own domain of validity.
This proliferation is partly due to advances in computers. It is now possible to
numerically simulate the "in-service life" of structures subjected to plasticity,
fatigue, crack propagation, shock waves and aging for safety and economy
purposes. The time has come to try to classify, compare, and validate these
models to help users to select the most appropriate model for their applications.
How is the Handbook organized? All solid materials are considered,
including metals, alloys, ceramics, polymers, composites, concrete, wood,
rubber, geomaterials such as rocks, soils, sand, clay, and biomaterials. But the
Handbook is organized first by phenomena because most engineering
mesomodels apply to different materials.
(cid:12)9 In the first volume: "Deformation of Materials," the first chapter is an
attempt to give general methodologies in the "art" of modeling with
special emphasis, on domains of validity in order to help in the choice of
models, in the selection of the appropriate materials for each specific
application, and in the consideration of the so-called "size effect" in
engineering structures. Chapter 2 to 5 deal, respectively, with elasticity
and viscoelasticity, yield limit, plasticity, and viscoplasticity.
(cid:12)9 The second volume is devoted to "Failure of Materials": continuous
damage in Chapter 6, cracking and fracture in Chapter 7, friction and
wear in Chapter 8.
(cid:12)9 In the third volume "Multiphysics Behaviors" are assembled. The
different possible couplings are described in Chapter 9. Chapters 10
and 11 are devoted to special classes of materials: composites and
xvii
xviii Introduction
geomaterials, respectively, because they each corresponds to a particular
modeling typed and moreover to a self-organized community of people.
(cid:12)9 In each chapter the different sections written by different authors
describe one model with its domain of validity, its background, its
formulation, the identification of material parameters for as many
materials as possible, some advice on implementation or use of the
model, and some references. The order of the sections follows as much as
possible from physical and micromechanical oriented models to more
phenomenological and engineering oriented ones.
How to use the Handbook?
(cid:12)9 Search by phenomena: This is the normal order of the Handbook
described in the "Contents".
(cid:12)9 Search by model name: Unfortunately, not all models have a name, and
some of them have several. Look in the list of contributors, where the
names of all authors are given.
(cid:12)9 Search by type of application: Each chapter begins with a chapter
introduction in which a few words are written on each section.
If you do not find exactly what you are looking for, please remember that the
best model is the simplest which gives you what you need and nothing more!
In case of any difficulty, get in touch with the author(s), whose address is
given after the title of each section.
Some personal comments. This Handbook has been initiated by the editor of
"Academic Press" who gave me much freedom to organize the book. It took
me two years to prepare the contents, to obtain the agreement of more than
100 authors, to ask for manuscripts, to ask again and again (and again for
some of them!) to review and to obtain the final material. It was an exciting
experience for which all actors must be thanked: the editors Z. Ruder, G.
Franklin, and M. Filion, all the authors who are still my friends, my
colleagues and friends from the LMT-Cachan who often advised me on
subjects and authors and particularly Erik van der Giessen, who helped me in
the selection of the subjects, who corrected the chapter introductions, and
who agreed to write the foreword, Catherine Genin who was so kind and so
efficient with letters, fax, e-mail, telephone, disks and manuscripts and
answered so many questions in order to obtain the materials in due time. I must
also mention Annie, my wife, who accepted 117 articles on the table at home!
Merci d tous,
Jean Lemaitre
Septembre 2000
CONTRIBUTORS
Numbers in parentheses indicate eht section of authors' contributions.
ELIAS C. AIFANTIS (4.12), Aristotle University of Thessaloniki, Thessaloniki,
54006 Greece, and Michigan Technological University, Houghton, Michigan
HOLM ALTENBACH (3.6), Fachbereich Ingenieurwissenschaften, Martin-
Luther-Universitat Halle-Wittenberg, D-06099 Halle (Saale), Germany
E ARCHAMBAULT (9.12), Laboratoire de Science et GSnie des Mat~riaux et
de M~tallurgie, UMR 7584 CNRS/INPL, Ecole des Mines de Nancy, Parc de
Saurupt, 54042 Nancy Cedex, France
ELLEN .M ARRUDA (5.12), Department of Mechanical Engineering, University
of Michigan, Ann Arbor, Michigan
C. BATHIAS (6.11), Laboratoire de M~canique de la Rupture, CNAM/ITMA,
2 rue Conte, 75003 Paris, France
ZDENEK .P BAZANT (1.3), Northwestern University, Evanston, Illinois, ASU
AHMED BENALLAL (4.11, 9.2), Laboratoire de M~canique et Technologie,
SNE de Cachan/CNRS/Universit~ Paris 6, 61 avenue du President Wilson, 94235
Cachan, France
ALBRECHT BERTRAM (5.2), Otto-von-Guericke-University Magdeburg, Uni-
versit/~tsplatz 2, 39106 Magdeburg, Germany
YVES BERTHIER (8.2), Laboratoire de M~canique des Contacts, UMR CNRS-
INSA de Lyon 5514, Batiment 113, 20, Avenue Albert Einstein, 69621
Villeurbanne Cedex, France
xix
XX Contributors
.B J. BESSON (7.8), Ecole des Mines de Paris, Centre des Mat~riaux, RMU
CNRS 7533, PB 87, 91003 Evry Cedex, France
J. E BESSELING (5.5), [email protected]
M. BERVEILLER (4.2), Laboratoire de Physique et M&anique des Mat~riaux,
elI du Saulcy, 57045 Metz Cedex, France
RENt~ BILLARDON (9.16), SNE de Cachan/CNRS/Universit~ Paris ,6 16
avenue du President Wilson, 94235 Cachan Cedex, France
SOL .R BODNER (5.7), Technion Israel Institute of Technology, Haifa 32000,
Israel
MARY C. BOYCE (5.12), Department of Mechanical Engineering, Center for
Materials Science and Engineering, Massachusetts Institute of Technology,
Cambridge, Massachusetts, ASU
YVES BRECHET (1.2), L.T.EC.M. BP75, Institut National Polytechnique de
Grenoble, 38402 tS Martin d'Heres Cedex, France
DAVID BROEK (7.14), 263 Dogwood Lane, Westerville, Ohio, ASU
HUY DUONG BUI (7.3, 8.5), Laboratoire de M&anique des Solicles, Ecole
Polytechnique, 91128 Palaiseau, France Electricit4 de France, R&D, Clamart,
France
ALAIN BURR (10.7), Laboratoire de Physico-Chimie Structurale et Macro-
mol&ulaire, RMU 7615, ESPCI, 01 rue Vauquelin, 75231 Paris Cedex 05,
France
ESTEBAN .P BUSSO (9.7), Department of Mechanical Engineering, Imperial
College, University of London, London, SW7 2BX, United Kingdom
GEORGES CAILLETAUD (5.3), Centre des Mat4riaux de l't~cole des Mines de
Paris, UMR CNRS 7633, PB 87, F91003 Evry Cedex, France
VALTER CARVELLI (10.8), Department of Structural Engineering, Technical
University (Politecnico) of Milan, Piazza Leonardo Da Vinci 32, 20133 Milano,
Italy
SERGE CESCOTTO (4.3, 9.3), D4partement MSM, Universit4 de Liege, ,1
chemin des Chevreuils bfit.B52/3, 4000 Liege, Belgique
J. .L CHABOCHE (5.8), O.N.E.R.A., DMSE, PB 72, 92322 ChStillon Cedex,
France and ,SIMSAL Troyes University of Technology, PB 2060, 10010 Troyes
Cedex, France
.A H. C. CHAN (11.10), School of Engineering, University of Birmingham,
United Kingdom
srotubirtnoC xxi
C.L. CHOW (6.4), Department of Mechanical Engineering, University of
Michigan-Dearborn
TRAIAN CICONE (8.4), Dept. of Machine Elements and Tribology, Polytechnic
University of Bucharest, Romania
N.D. CRISTESCU (2.3), 231 Aerospace Building, University of Florida,
Gainesville, Florida
OLIVIER COUSSY (11.7), Laboratoire Central des Ponts et Chaussees, Paris,
France
STEPHEN C. COWIN (10.10), New York Center for Biomedical Engineering,
School of Engineering, The City College, New York
CHRISTIAN CUNAT (2.6, 9.17), ,ATMEL UMR CNRS 7563, ENSEM INPL ,2
avenue de la Foret-de-Haye, 54500 Vandoeuvre-les-Nancy, France
PATRICK DANGLA (11.7), Laboratoire Central des Ponts et Chaussees, Paris,
France
XIL~IF DARVE (11.2), EINP Grenoble, L3S-BP 53 38041 Grenoble, France
YANNIS E DAFALIAS (4.8, 11.11), Civil and Environmental Engineering, The
George Washington University, Washington, D.C.
.S DENIS (9.12), Laboratoire de Science et G~nie des Mat~riaux et de
M~tallurgie, RMU 7584 CNRS/INPL, Ecole des Mines de Nancy, Parc de
Saurupt, 54042 Nancy Cedex, France
CHANDRA .S DESAI (9.10), Department of Civil Engineering and Engineering
Mechanics, The University of Arizona, Tucson, Arizona, ASU
RODRIGUE DESMORAT (6.14, 6.15), Universite Paris 6-LMS, 8, Rue du
Capitaine Scott, F-75015 Paris, France
MARTA DRAGON-LOUISET (8.5), Laboratoire de M~canique des Solides,
Ecole Polytechnique, 91128 Palaiseau, France
DANIEL C. DRUCKER (3.2, 3.7), Department of Aerospace Engineering,
Mechanics Engineering Service, University of Florida, 231 Aerospace Building,
Gainesville, Florida 32611
GEORGE J. DVORAK (10.5), Rensselaer Polytechnic Institute, ,yorT New York
.L DUCHENE (4.3), D6partement MSM, Universit8 de Liege, ,1 chemin des
chevreuils b~t.B52/3, 4000 Liege, Belgique
FERNAND ELLYIN (5.10), Department of Mechanical Engineering, University
of Alberta, Edmonton, ,BA Canada
xxii srotubirtnoC
E D. FISCHER (9.13), Montanuniversit. at Leoben, Franz-Josef-Strasse ,81
A-8700 Leoben, Austria
DOMINIQUE FRAN~;OIS (7.5), eloc21 Centrale de Paris, Chfitenay-Malabry,
F92 295, France
JEAN EN.SIRF (8.4), Laboratoire de M~canique des Solides, Universit~ de
Poitiers, France
.E GAUTIER (9.12), Laboratoire de Science et G~nie des Mat~riaux et de
M~tallurgie, RMU 7584 CNRS/INPL, t~cole des Mines de Nancy, Parc de
Saurupt, 54042 Nancy Cedex, France
.A GODINAS (4.3), D~partement MSM, Universit~ de Liege, ,1 chemin des
Chevreuils bfit.B52/3, 4000 Liege, Belgium
DIETMAR GROSS (7.6), Institute of Mechanics, UT Darmstadt, Hochschul-
strasse ,1 D 64289 Darmstadt
ANNE MARIE HABRAKEN (4.3, 9.3), D~partement MSM, Universit~ de Liege,
,1 chemin des Chevreuils b~t.B52/3, 4000 Liege, Belgique
JEAN-MARC HAUDIN (4.9), CEMEF- PB 207, 06904 Sophia Antipolis,
France
.D .R HAYHURST (9.4), Department of Mechanical Engineering, UMIST,
9(cid:14)P xoB 88, Manchester M60 1QD, United Kingdom
FRANCOIS HILD (7.4, 10.7), LMT-Cachan, 16 avenue du Pr4sident Wilson,
F-94235 Cachan Cedex, France
LAURENT HIRSINGER (9.16), SNE de Cachan/CNRS/Universit4 Paris ,6 16
avenue du Pr4sident Wilson, 94235 Cachan Cedex, France
.K HO (5.6), Yeungnam University, Korea
GERHARD .A HOLZAPFEL (10.11), Institute for Structural Analysis,
Computational Biomechanics, Graz University of Technology, 8010 Graz, Austria
KOZO IKEGAMI (2.5), Tokyo Denki University, Kanda-Nishikicho 2-2,
Chiyodaku, Tokyo 101-8457, Japan
TATSUO INOUE (9.11), Department of Energy Conversion Science, Graduate
School of Energy Science, Kyoto University, Yoshida-Honmachi, Sakyo-ku,
Kyoto, Japan
HIROMASA ISHIKAWA (4.7), Hokkaido University, N13, W8, Kita-ku,
Sapporo 060-8628, Japan
srotubirtnoC xxiii
HENRIK MYHRE JENSEN (7.7), Department of Solid Mechanics, 404,
Technical University of Denmark, DK-2800 Lyngby, Denmark
KOJI KATO (8.7), Tohoku University, Aramaki-Aza-Aoba 01, Sendal 980-8579,
Japan
JANUSZ .R KLEPACZKO (4.10), Metz University, Laboratory of Physics and
Mechanics of Materials, lie du Saulcy, 57045 Met7, France
.W G. KNAUSS (7.13), California Institute of Technology, Pasadena, California
DUSAN KRAJCINOVIC (6.3), Arizona State University, Tempe, Arizona
.E KREMPL (5.6), Mechanics of Materials Laboratory, Rensselaer Polytechnic
Institute, Troy, New York
TADEUSZ KURTYKA (3.5), CERN- European Organization for Nuclear
Research, CH-1211 Geneve 23, Switzerland
PIERRE LADEVI~ZE (10.6), LMT-Cachan, SNE de Cachan/CNRSAJniversit6
Paris 6, 61 avenue du President Wilson, 94235 Cachan Cedex, France
FREDERICK .A LECKIE (10.7), Department of Mechanical and Environmental
Engineering, University of California, Santa Barbara, California
J-B. LEBLOND (7.3, 9.14), Laboratoire de Mod~lisation en M~canique,
Universit~ de Pierre et Marie Curie, Paris, France
JEAN LEMAITRE (1.1, 2.1, 3.1, 4.1, 5.1, 6.1, 6.2, 6.14, 6.15, 7.1, 8.1, 9.1,
10.1, 11.1), Universit~ Paris 6, LMT-Cachan, 61, avenue du Pr6sident Wilson,
F-94235 Cachan Cedex, France
GIULIO MAIER (10.8), Department of Structural Engineering, Technical
University (Politecnico) of Milan, Piazza Leonardo Da Vinci 32, 20133 Milano,
Italy
DIDIER MARQUIS (4.4), Laboratoire de M~canique et Technologie, Ecole
Normale Sup~rieure de Cachan, 16 avenue du President Wilson, 94230 Cachan,
France
MAJID .T MANZARI (11.11), Department of Mechanics, National Technical
University of Athens, 15773, Hellas, and Civil and Environmental Engineering,
University of California, Davis, California
JACKY MAZARS (6.13, 7.2), LMT-Cachan, Ecole Normale Superieure
de Cachan, 61, avenue du President Wilson, 94235 Cachan, France and
L35-Institut National Polytechniquede Grenoble, F38041 Grenoble Cedex 9,
France
xxiv srotubirtnoC
FREDERIC MESLIN (10.9), LMT-Cachan, SNE de Cachan, Universit6 Paris 6,
16 avenue du Pr6sident Wilson, 94235 Cachan Cedex, France
ALAIN MOLINARI (5.4), Laboratoire de Physique et M&anique des Mat6riaux,
eloc~l Nationale d'Ing4nieurs, Universit~ de Metz, elI du Saulcy, 57045 Metz-
Cedex, France
BERNARD MONASSE (4.9), CEMEF- PB 207, 06904 Sophia Antipolis,
France
HAEL MUGHRABI (7.11), Universit~it Erlangen-Nfirnberg, Institut rl~f
Werkstoffwissenschaften, Martensstr. ,5 D-91058 Erlangen, Germany
N. STALIN-MULLER (7.3), Laboratoire de M4canique des Solides, eloc21
Polytechnique, 91128 Palaiseau, France
.Z MROZ (4.5), Institute of Fundamental Technological Research, Warsaw, Poland
SUMIO MURAKAMI (6.7), Nagoya University, Furo-cho, Chikusa-ku, Nagoya,
464-8603 Japan
ROBERTO NOVA (11.9), Milan University of Technology (Politecnico),
Department of Structural Engineering, Milan, Italy
.A NEEDLEMAN (6.5), Brown University, Division of Engineering, Providence,
Rhode Island and Department of Mechanical Engineering, Solid Mechanics,
Technical University of Denmark, 2800 Lyngby, Denmark
SIA NEMAT-NASSER (5.11, 11.5), Center of Excellence for Advanced
Materials, Department of Mechanical and Aerospace Engineering, University of
California, San Diego, California
.R .W OGDEN (2.2, 2.4), Department of Mathematics, University of ,wogsalG
Glasgow G12 8QW, United Kingdom
NOBUTADA OHNO (4.6), Department of Mechanical Engineering, Nagoya
University, Chikusa-ku, Nagoya 464-8603, Japan
J. URGEN OLSCHEWSKI (5.2), BAM-V2, Unter den Eichen 87, 12200 Berlin,
Germany
FLORENCE OSSART (9.16), SNE de Cachan/CNRS/Universit~ Paris 6, 16
avenue du President Wilson, 94235 Cachan Cedex, France
.M PASTOR (11.10), Centro de Estudios y Experimentaci6n de Obras P~blicas
and STE de Ingenieros de Caminos, Madrid, Spain
PIOTR PERZYNA (9.5), Institute of Fundamental Technological Research,
Polish Academy of Sciences, Swir 21, 00-049 Warsaw, Poland
Contributors XXV
GILLES PIJAUDIER-CABOT (6.13), Laboratoire de G~nie Civil de Nantes Saint-
Nazaire, eloc~t Centrale de Nantes, PB 92101, F-44321 Nantes Cedex 03, France
.A PINEAU (7.8), eloc~ des Mines de Paris, Centre des Mat~riaux, UMR CNRS
7533, PB 87, 91003 Evry Cedex, France
ARNAUD POITOU (10.9), LMT-Cachan, SNE de Cachan, Universit8 Paris ,6 16
avenue du President Wilson, 94235 Cachan Cedex, France
RACHID RAHOUADJ (2.6, 9.17), ,ATMEL RMU CNRS 7563, ENSEM INPL 2,
Avenue de la For~t-de-Haye, 54500 Vandoeuvre-l~s-Nancy, France
MICHEL RAOUS (8.6), Laboratoire de Mecanique et d'Acoustique, 31, chemin
Joseph Aiguier, 13402 Marseille Cedex 20, France
GILLES ROUSSELIER (6.6), EDF/R&D Division, seL Renardi~res, 77818
Moret-sur-Loing Cedex, France
J. .W RUDNICKI (11.6), Department of Civil Engineering, Northwestern
University, Evanston, Illinois, ASU
KATSUHIKO SASAKI (4.7), Hokkaido University, N13, W8, Kita-ku, Sapporo
060-8628, Japan
.A .R SAVKOOR (8.3), Vehicle Research Laboratory, Delft University of
Technology, Delft, The Netherlands
.R .A SCHAPERY (2.7), Department of Aerospace Engineering and Engineering
Mechanics, The University of Texas, Austin, Texas
ROBERT SCHIRRER (6.12), Institut Charles Sadron, 6 rue Boussingault,
F-67083 Strasbourg, France
SABINE .M SCHLOGL (9.8), Koiter Institute Delft, Delft University of
Technology, The Netherlands
.B .A SCHREFLER (11.8), Department of Structural and Transportation
Engineering, University of Padua, Italy
.L SIMONI (11.8), Department of Structural and Transportation Engineering,
University of Padua, Italy
PETROS SOFRONIS (9.9), Department of Theoretical and Applied Mechanics,
University of Illinois at Urbana-Champaign, 104 South Wright Street, Urbana,
Illinois
DARRELL SOCIE (6.8), Department of Mechanical Engineering, University of
Illinois, Urbana, Illinois
CLAUDE STOLZ (8.5), Laboratoire de M~canique des Solides, Ecole
Polytechnique, 91128 Palaiseau, France