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P. Podio-Guidugli
M. Brocato
(Eds)
Rational Continua,
Classical and New
A collection of papers
dedicated to Gianfranco Capriz
on the occasion
of his 75th birthday
, Springer
P. PODIO-GUIDUGLI M. BROCATO
Universita di Roma Tor Vergata IEI-CNR
Roma, Italy Area della Ricerca di Pisa
Pisa, Italy
Springer-Verlag Berlin Heidelberg New York
a member of BertelmannSpringer Science+Business Media GmbH
ISBN-13: 978-88-470-2233-1 e-ISBN-13: 978-88-470-2231-7
DOl: 10.1007/978-88-470-2231-7
© Springer-Verlag ltalia, Milano 2003
Softcover reprint of the hardcover 1st edition
http://www.springer.de
Library of Congress Cataloging-in-Publication Data
Rational continua, classical and new / P. Podio Guidugli, M. Brocato (eds.).
p. cm.
Includes bibliographical references and index.
1. Thermodynamics. 2. Continuum mechanics. r. Podio-Guidugli, Paolo. n. Brocato,
M., 1962-
QC311.2 .R38 2002
536'.7--dc21
2002023679
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Foreword
Gianfranco Capriz was born in Gemona del Friuli on October 16, 1925. After grad
uating summa cum laude in mathematics at the Scuola Normale Superiore in Pisa
(1948) and successfully attending a one-year doctoral course there (1949), he was
appointed by Mauro Picone as a researcher at the Istituto Nazionale per Ie Appli
cazioni del Calcolo in Rome (1951-56). At the Institute, while working at his first
research papers, he also served as a programmer in the staff operating the first general
purpose computer ever installed in Italy.
In Rome he met Barbara, who was shortly to become his wife, and became ac
quainted with Ennio De Giorgi, Gaetano Fichera, Tristano Manacorda, Carlo Pucci,
Michele Sce, and Edoardo Vesentini, with all of whom he was to maintain friendly
and scientific relationships thereafter. In the same period he started his research
activity in rational mechanics under the supervision of Antonio Signorini.
From Rome he moved to Stafford (UK) to work for the English Electric Company
(1956-62) as a research mathematician and a programmer of DEUCE, the engineered
version of the pilot machine ACE, originally designed by Alan Turing. This period
of his life ended when Capriz was asked by Sandro Faedo to return to his country
to contribute to the creation in Pisa of the largest concentration ever in Italy of
research and development activities in computer science and information technology.
As early as 1954, at the suggestion of Enrico Fermi, the construction of the first
Italian scientific computer had been decided, and the task assigned to the Centro
Studi Calcolatrice Elettronica (CSCE), based in Pisa. In 1961, the product of this
effort, the Calcolatrice Elettronica Pisana (CEP), was inaugurated; one year later,
CSCE became part of the Italian National Research Council. For two decades, from
1963 to 1983, Capriz was to serve as the Director of CSCE (later to be transformed
into the Istituto di Elaborazione della Informazione) and then of CNUCE (Centro
Nazionale Universitario di Calcolo Elettronico).
In those busy years, Capriz, who had been given the chair of rational mechanics
at the University of Pisa in 1966, had also a central role in the creation of a school in
continuum physics, which was one of the outcomes of another inspired initiative of
Faedo, namely, the revival at the highest levels of mathematical activities in Pis a, with
the appointments of A. Andreotti, J. Barsotti, E. Bombieri, S. Campanato, G. Prodi,
G. Stampacchia, and Vesentini at the University, and of De Giorgi at the Scuola
Normale.
Capriz never ceased to do research, not even while he was the President of TEC
SlEL (1983-92), a company of the IRI group, where computer networks were studied
and, in particular, the OSI standards first effected and installed (OSIRIDE network,
1984). In addition, he repeatedly served as visiting professor abroad (at the Johns
Hopkins University, the University of Minnesota and the Carnegie Mellon Univer
sity in the US; at the University of Manitoba, in Canada; and as Erskine Professor
at the University of Canterbury, in New Zealand). He was Vice-President of UMI,
the Unione Matematica Italiana (1976-82), President of ISIMM, the International
VI
Society for the Interactions of Mechanics and Mathematics (1997-99), and President
of AIMETA, the Associazione Italiana di Meccanica Teorica ed Applicata (1999-
2001). He is presently a corresponding member of the Accademia dei Lincei and a
professor emeritus at the University of Pi sa.
When he first met Clifford A. Truesdell in the middle sixties, CapIiz had al
ready worked on such diverse subjects as computational mechanics, lubrication,
creep, vibrations and stability of rotating shafts, stability and numerical computations
in hydrodynamics, viscoelasticity, and the manufacture of ceramics. After meeting
Truesdell, his scientific interests were more and more directed toward the analysis of
fundamental and innovative problems in continuum mechanics, especially, mateIials
with memory, problems with live loads, non-linear vibrations of stIings, mixtures,
and a host of problems involving the continuum descIiptions of microstructures: con
tinua' with voids; liquids with bubbles; granular mateIials; continua with vectoIial,
affine, or spheIical structure; bodies with continuous distribution of dislocations;
Cosserat continua; and liquid crystals. The book on Continua with Microstructure
edited by C. Truesdell for Springer in the series Tracts in Natural Philosophy, sum
marizes about fifteen years of his scientific achievements in the field of the title, and
contains innumerable suggestions for further research.
Both CapIiz' broad scientific production and the variety of themes he dealt with
during his career bear witness to the agility and sharpness of his mind, ready to
capture weaknesses and pitfalls, as well as his ability to spot promising possibilities,
sometimes deeply hidden in continuous models, no matter whether classical or just
proposed, and to convert them into new challenging research tasks: whence the title
of this tribute volume.
A mathematician and an engineer, a philosopher and a manager, a leader and a
fIiend: all this Gianfranco CapIiz is to those who have the good fortune, honor and
pleasure to work with him.
Preface
A selected number of prominent researchers, all in close personal and scientific
contact with Gianfranco Capriz, have been invited to contribute to this volume, on a
subject of their choice. They are, in alphabetical order: P. Biscari, G. Cimatti, S. C.
Cowin, C. Davini, R.L. Fosdick, P. Giovine, IT. Jenkins, R.J. Knops, I. Muller, D.R.
Owen, M. Silhavy, G. Vergara Caffarelli, E.G. Virga, K. Wilmanski, and H. Zorski.
It is because of the outstanding quality of their effort, and that of their coauthors,
that this book not only meets to the full its purpose as homage but also offers-so
we believe-a rather unique and variegated collection of papers in modern continuum
mechanics.
Many contributions are in research areas in which Gianfranco Capriz has been
active, but not all. Among the latter papers, those by Biscari and Zorski, the first and
last in the list, exemplify well how useful concepts from continuum mechanics can
be in modeling and analyzing bioaggregates. The papers by Cimatti and Davini are
also rather remote by theme from Gianfranco's own research; yet, they will certainly
appeal to his taste for mathematical analysis, when applied to concrete problems of
continuum physics and structural mechanics. Gianfranco has displayed such taste all
along in his scientific life, first of all in dealing with questions from the theory of
elasticity, linear or non-linear. It is not by mere coincidence that papers in elasticity
comprise a relatively large subgroup in this book, a group including the works by
Cowin, Fosdick (coauthored with Dunn and Zhang), Knops, Silhavy, and Vergara
Caffarelli (with Carillo and Podio-Guidugli). In particular, the paper by Cowin is de
voted to find which response symmetries of a linearly elastic material are compatible
with the presence of a geometrically organized distributed microstructure; for this
reason, this paper may serve as a bridge from elasticity to one ofGianfranco's favorite
subjects, continua with microstructure. Three papers in the book deal with this sub
ject, those by Giovine, Jenkins and LaRagione, and Virga; a fourth paper, by Owen,
discusses the nonstandard type of microstructure due to non smooth sUbmacroscopic
disarrangements. Finally, the paper by Wilmanski, which is about porous media,
another class of micro structured continua, focuses on an issue especially dear to
Gianfranco's heart as a rational mechanist, namely, the role of inertial interactions
in the governing equations of a thermomechanical theory; although the occasion is
a study of heat conduction within the framework of extended thermodynamics, the
theme of Muller's contribution with Barbera is the same.
Rome-Paris, September 2002 Paolo Podio-Guidugli
Maurizio Brocato
List of Contributors
• Elvira Barbera, FB 6, Thermodynamik, Technische Universitat Berlin, 10623
Berlin, Germany
• Paolo Biscari, Dipartimento di Matematica, Politecnico di Milano, Piazza Leo
nardo da Vinci 32, 20133 Milano, Italy and Istituto Nazionale di Fisica della
Materia, Via Ferrata I, 27100 Pavia, Italy
• Sandra Carillo, Dipartimento di Metodi e Modelli Matematici per Ie Scienze
Applicate, Universita di Roma "La Sapienza", Via Scarpa 16,00161 Roma, Italy
• Giovanni Cimatti, Department of Mathematics, Via Buonarroti, 2, 56100 Pisa,
Italy
• Stephen C. Cowin, The Center for Biomedical Engineering and The Department
of Mechanical Engineering, The School of Engineering of The City College and
The Graduate School of The City University of New York, New York, NY 10031,
USA
• Cesare Davini, Dipartimento di Ingegneria Civile, Universita degli Studi di
Udine, via delle Scienze 208, 33100 Udine, Italy
• J. Ernest Dunn, Scientific Consulting, 167 W. Dawn Drive, Tempe, AZ 85284,
USA
• Roger Fosdick, Department of Aerospace Engineering and Mechanics, Univer
sity of Minnesota, Minneapolis, MN 55455, USA
• Pasquale Giovine, Dipartimento di Meccanica e Materiali, U niversita di Reggio
Calabria, Via Graziella, Localita Feo di Vito, 89060 Reggio Calabria, Italy
• James T. Jenkins, Department of Theoretical and Applied Mechanics, Cornell
University, Ithaca, NY 14853, USA
• Robin J. Knops, Department of Mathematics, Heriot-Watt University, Edin
burgh EH14 4AS, Scotland
• Luigi La Ragione, Dipartimento di Ingegneria Civile e Ambientale, Politecnico
di Bari, 70125 Bari, Italy
• Ingo Milller, FB 6, Thermodynamik, Technische Universitat Berlin, 10623
Berlin, Germany
• David R. Owen, Department of Mathematical Sciences, Carnegie Mellon Uni
versity, Pittsburgh, PA 15213, USA
• Paolo Podio-Guidugli, Dipartimento di Ingegneria Civile, Universita di Roma
''Tor Vergata", Via di Tor Vergata 110,00133 Roma, Italy
• Miroslav Silhavy, Mathematicallnstitute of the AV CR, itna 25, 11567 Prague
1, Czech Republic
• Andre M. Sonnet, Dipartimento di Matematica, Istituto Nazionale di Fisica
della Materia, Universita di Pavia, Via Ferrata 1, 27100 Pavia, Italy
• Giorgio Vergara Caffarelli, Dipartimento di Metodi e Modelli Matematici per
Ie Scienze Applicate, Universita di Roma "La Sapienza", Via Scarpa 16,00161
Roma, Italy
x
• Epifanio G. Virga, Dipartimento di Matematica, Istituto Nazionale di Fisica
della Materia, Universita di Pavia, Via Ferrata 1,27100 Pavia, Italy
• Krzysztof Wilmanski, Weierstrass Institute for Applied Analysis and Stochas
tics, Berlin, Germany
• Ying Zhang, Department of Materials Science, Xiamen University, Xiamen,
Fujian 361005, China
• Henryk Zorski, Institute of Fundamental Technological Research, Polish Aca
demy of Sciences, 00-049 Warsaw, Swit(tokrzyska 21, Poland
Contents
Heat Conduction in a Non-Inertial Frame .......................... .
Elvira Barbera, Ingo Muller
Mediated Interactions of Proteins in Lipid Membranes 11
Paolo Biscari
Second-Order Surface Potentials in Finite Elasticity. . . . . . . . . . . . . . . . .. 19
Sandra Carillo, Paolo Podio-Guidugli, Giorgio Vergara Caffarelli
The Thermistor Problem with Thomson's Effect 39
Giovanni Cimatti
Elastic Symmetry Restrictions from Structural Gradients 51
Stephen C. Cowin
Gaussian Curvature and Babuska's Paradox
in the Theory of Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 67
Cesare Davini
Rank 1 Convexity for a Class of Incompressible Elastic Materials. . . . . .. 89
J. Ernest Dunn, Roger Fosdick, Ying Zhang
A Continuum Description of Diatomic Systems 97
Pasquale Giovine
Induced Anisotropy, Particle Spin, and Effective Moduli
in Granular Materials ........................................... 111
James T. Jenkins, Luigi La Ragione
On Uniqueness in Nonlinear Homogeneous Elasticity ................. 119
Robin 1. Knops
Twin Balance Laws for Bodies Undergoing
Structured Motions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 139
David R. Owen
On the Hysteresis in Martensitic Transformations .................... 151
Miroslav Silhavy
Dissipative Fluids with Microstructure ............................. 169
Andre M. Sonnet, Epifanio G. Virga
XII
Some Questions on Material Objectivity Arising in Models
of Porous Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 183
KrzysztoJWilmanski
Simplifield Dynamics of a Continuous Peptide Chain ................. 197
Henryk Zorski
