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Advanced 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