Table Of ContentAdvanced Structured Materials
Holm Altenbach
Samuel Forest Editors
Generalized
Continua as Models
for Classical and
Advanced Materials
Advanced Structured Materials
Volume 42
Series editors
Andreas Öchsner, Southport Queensland, Australia
Lucas F.M. da Silva, Porto, Portugal
Holm Altenbach, Magdeburg, Germany
More information about this series at http://www.springer.com/series/8611
Holm Altenbach Samuel Forest
(cid:129)
Editors
Generalized Continua
as Models for Classical
and Advanced Materials
123
Editors
HolmAltenbach Samuel Forest
Otto‐von‐Guericke Universität Magdeburg Mines ParisTech
Magdeburg Paris
Germany France
ISSN 1869-8433 ISSN 1869-8441 (electronic)
AdvancedStructured Materials
ISBN978-3-319-31719-9 ISBN978-3-319-31721-2 (eBook)
DOI 10.1007/978-3-319-31721-2
LibraryofCongressControlNumber:2016935580
©SpringerInternationalPublishingSwitzerland2016
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart
of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission
orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar
methodologynowknownorhereafterdeveloped.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom
therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
The publisher, the authors and the editors are safe to assume that the advice and information in this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor
foranyerrorsoromissionsthatmayhavebeenmade.
Printedonacid-freepaper
ThisSpringerimprintispublishedbySpringerNature
TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland
Preface
Generalized Continua have been in the focus of scientists from the end of the
nineteenth century. A first summary was given in 1909 by the Cosserat brothers.
AfterWorldWarII,atruerenaissanceinthisfieldoccurredwiththepublicationof
Ericksen and Truesdell in 1958. Further developments were connected with the
fundamentalcontributionsofscientistsfrom Germany, Russia,andFrance.During
thepastyearsthecentennialoftheCosseratbookwascelebratedbytwocolloquia,
both held in Paris in 2009. In addition, previous trilateral seminars Mechanics of
GeneralizedContinua—fromMicromechanicalBasicstoEngineeringApplications
(Wittenberg 2010, 2012) and the CISM Course Generalized Continua—from the
TheorytotheEngineeringApplications(Udine2011)discussedproblemsrelatedto
the theory and applications. During a new Advanced Seminar (Magdeburg,
September 2015), attention was paid to the most recent research items, i.e., new
generalized models, materials with a significant microstructure, multi-field load-
ings, oridentification of constitutive equations. Last but not least, a comparison of
discrete modeling approaches have been discussed.
This book contains 21 papers submitted to the Advanced Seminar Generalized
Continua as Models for Materials with Multi-Scale Effects or Under Multi-Field
Actions or discussed during the seminar. Finally, after reviewing and acceptance
they were collected as a unique collection of papers. The authors are from France,
Germany, and Russia, the traditional countries of the previous trilateral seminars,
completed by authors from Egypt, Estonia, Finland, Great Britain, Italy, and the
United States.
The editors thank the anonymous reviewers for their carefully performed job,
Mrs. Johanna Eisenträger and Mrs. Barbara Renner for proofreading, Mr. Marcus
Aßmusforthetechnicalsupportinlatexprocessingandcompilingthewholebook.
Special thanks to Christoph Baumann from Springer Publisher for supporting this
project.
Magdeburg, Germany Holm Altenbach
Paris, France Samuel Forest
February 2016
v
Contents
On Strain Rate Tensors and Constitutive Equations of Inelastic
Micropolar Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Holm Altenbach and Victor A. Eremeyev
On the Modelling of Carbon Nano Tubes as Generalized Continua. . . 15
Hossein Aminpour and Nicola Rizzi
Isogeometric Analysis of Gradient-Elastic 1D and 2D Problems . . . . . 37
Viacheslav Balobanov, Sergei Khakalo and Jarkko Niiranen
A Fast Fourier Transform-Based Approach for Generalized
Disclination Mechanics Within a Couple Stress Theory . . . . . . . . . . . 47
Stéphane Berbenni, Vincent Taupin, Claude Fressengeas
and Laurent Capolungo
Some Cases of Unrecognized Transmission of Scientific Knowledge:
From Antiquity to Gabrio Piola’s Peridynamics and Generalized
Continuum Theories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Francesco dell’Isola, Alessandro Della Corte, Raffaele Esposito
and Lucio Russo
Computational Analysis of the Size Effects Displayed in Beams
with Lattice Microstructures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Martin A. Dunn and Marcus A. Wheel
Inelastic Interaction and Splitting of Strain Solitons Propagating
in a One-Dimensional Granular Medium with Internal Stress. . . . . . . 145
Vladimir I. Erofeev, Vladimir V. Kazhaev and Igor S. Pavlov
The Eigenmodes in Isotropic Strain Gradient Elasticity . . . . . . . . . . . 163
Rainer Glüge, Jan Kalisch and Albrecht Bertram
Limit Analysis of Lattices Based on the Asymptotic Homogenization
Method and Prediction of Size Effects in Bone Plastic Collapse. . . . . . 179
Ibrahim Goda, Francisco Dos Reis and Jean-François Ganghoffer
vii
viii Contents
An Improved Constitutive Model for Short Fibre Reinforced
Cementitious Composites (SFRC) Based on the Orientation
Tensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Heiko Herrmann
Isogeometric Static Analysis of Gradient-Elastic
Plane Strain/Stress Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Sergei Khakalo, Viacheslav Balobanov and Jarkko Niiranen
Applications of Higher-Order Continua to Size Effects
in Bending: Theory and Recent Experimental Results . . . . . . . . . . . . 237
Christian Liebold and Wolfgang H. Müller
Classification of Gradient Adhesion Theories Across Length Scale . . . 261
Sergey Lurie, Petr Belov and Holm Altenbach
Eigenvalue Problems of a Tensor and a Tensor-Block Matrix
(TMB) of Any Even Rank with Some Applications in Mechanics . . . . 279
Mikhail U. Nikabadze
Analytical Solutions in the Theory of Thin Bodies . . . . . . . . . . . . . . . 319
Mikhail U. Nikabadze and Armine R. Ulukhanyan
Method for Calculating the Characteristics of Elastic
State Media with Internal Degrees of Freedom . . . . . . . . . . . . . . . . . 363
Sergey N. Romashin, Victoria Yu. Presnetsova, Larisa Yu. Frolenkova
and Vladimir S. Shorkin
Variational Theories of Two-Phase Continuum Poroelastic Mixtures:
A Short Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
Roberto Serpieri, Alessandro Della Corte, Francesco Travascio
and Luciano Rosati
Buckling of Sandwich Tube with Foam Core Under Combined
Loading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
Denis N. Sheydakov and Nikolay E. Sheydakov
Frequency-Dependent Attenuation and Phase Velocity Dispersion
of an Acoustic Wave Propagating in the Media with Damages . . . . . . 413
Anatoli Stulov and Vladimir I. Erofeev
A Statistically-Based Homogenization Approach for Particle
Random Composites as Micropolar Continua . . . . . . . . . . . . . . . . . . 425
Patrizia Trovalusci, Maria Laura De Bellis and Martin Ostoja-Starzewski
Paradoxical Size Effects in Composite Laminates and Other
Heterogeneous Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443
Marcus A. Wheel, Jamie C. Frame and Philip E. Riches
Contributors
Holm Altenbach Lehrstuhl für Technische Mechanik, Institut für Mechanik,
FakultätfürMaschinenbau,Otto-von-Guericke-UniverstätMagdeburg,Magdeburg,
Germany
Hossein Aminpour Università Degli Studi Roma Tre, Rome, Italy
Viacheslav Balobanov Department of Civil and Structural Engineering, Aalto
University, Aalto, Espoo, Finland
Petr Belov Institute of Research, Development and Technology Transfer,
Moscow, Russia
StéphaneBerbenni Laboratoired’EtudedesMicrostructuresetdeMécaniquedes
Matériaux, LEM3, UMR CNRS 7239, University of Lorraine, Metz, France
Albrecht Bertram Lehrstuhl für Festigkeitslehre, Institut für Mechanik, Fakultät
für Maschinenbau, Otto-von-Guericke-Universität Magdeburg, Magdeburg,
Germany
Laurent Capolungo George Woodruff School of Mechanical Engineering,
Georgia Institute of Technology, Metz, France
Maria Laura De Bellis Department of Innovation Engineering, University of
Salento, Lecce, Italy
Alessandro Della Corte Department of Mechanical and Aerospace Engineering,
University La Sapienza of Rome, Rome, Italy
Francesco dell’Isola Department of Structural and Gentechnical Engineering,
University La Sapienza of Rome, Rome, Italy; International Research Center on
Mathematics and Mechanics of Complex Systems (M&MoCS), University of
L’Aquila, L’Aquila, Italy
Francisco Dos Reis LEMTA, Université de Lorraine, Vandoeuvre-lès-Nancy
Cedex, France
ix
x Contributors
Martin A. Dunn Department of Mechanical and Aerospace Engineering,
University of Strathclyde, Glasgow, UK
Victor A. Eremeyev Faculty of Mechanical Engineering, Rzeszów University of
Technology, Rzeszów, Poland
Vladimir I. Erofeev Mechanical Engineering Research Institute of Russian
Academy of Sciences, Nizhny Novgorod Lobachevsky State University, Nizhny
Novgorod, Russia
Raffaele Esposito International Research Center on Mathematics and Mechanics
of Complex Systems (M&MoCS), University of L’Aquila, L’Aquila, Italy
Jamie C. Frame Department of Biomedical Engineering, University of
Strathclyde, Glasgow, UK
Claude Fressengeas Laboratoire d’Etude des Microstructures et de Mécanique
des Matériaux, LEM3, UMR CNRS 7239, University of Lorraine, Metz, France
Larisa Yu. Frolenkova StateUniversity-Education-Science-ProductionComplex,
Orel,Russia
Jean-François Ganghoffer LEMTA, Université de Lorraine, Vandoeuvre-lès-
Nancy Cedex, France
Rainer Glüge Lehrstuhl für Festigkeitslehre, Institut für Mechanik, Fakultät für
Maschinenbau, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany
Ibrahim Goda LEMTA, Université de Lorraine, Vandoeuvre-lès-Nancy Cedex,
France; Faculty of Engineering, Department of Industrial Engineering, Fayoum
University, Fayoum, Egypt
HeikoHerrmann CentreforNonlinearStudies,InstituteofCyberneticsatTallinn
University of Technology, Tallinn, Estonia
Jan Kalisch Graduiertenkolleg 1554 “Micro-Macro-Interactions in Structured
Media and Particle Systems”, Otto-von-Guericke-Universität Magdeburg,
Magdeburg, Germany
Vladimir V. Kazhaev Mechanical Engineering Research Institute of Russian
Academy of Sciences, Nizhny Novgorod Lobachevsky State University, Nizhny
Novgorod, Russia
Sergei Khakalo Department of Civil and Structural Engineering, Aalto
University, Aalto, Espoo, Finland
Christian Liebold Institute of Mechanics, Berlin University of Technology,
Berlin, Germany
SergeyLurie InstituteforProblemofMechanicsofRASandInstituteofApplied
Mechanics of RAS, Moscow, Russia
