Table Of ContentAdvanced Structured Materials
Holm Altenbach
Arkadi Berezovski
Francesco dell’Isola
Alexey Porubov Editors
Sixty Shades
of Generalized
Continua
Dedicated to the 60th Birthday of
Prof. Victor A. Eremeyev
Advanced Structured Materials
Volume 170
Series Editors
Andreas Öchsner, Faculty of Mechanical Engineering, Esslingen University of
Applied Sciences, Esslingen, Germany
Lucas F. M. da Silva, Department of Mechanical Engineering, Faculty of
Engineering, University of Porto, Porto, Portugal
Holm Altenbach , Faculty of Mechanical Engineering, Otto von Guericke
University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany
Common engineering materials are reaching their limits in many applications, and
new developments are required to meet the increasing demands on engineering
materials. The performance of materials can be improved by combining different
materials to achieve better properties than with a single constituent, or by shaping
the material or constituents into a specific structure. The interaction between
materialandstructurecanoccuratdifferentlengthscales,suchasthemicro,meso,
or macro scale, and offers potential applications in very different fields.
This book series addresses the fundamental relationships between materials and
theirstructureonoverallproperties(e.g.,mechanical,thermal,chemical,electrical,
or magnetic properties, etc.). Experimental data and procedures are presented, as
well as methods for modeling structures and materials using numerical and
analyticalapproaches.Inaddition,theseriesshowshowthesematerialsengineering
and design processes are implemented and how new technologies can be used to
optimize materials and processes.
Advanced Structured Materials is indexed in Google Scholar and Scopus.
Holm Altenbach Arkadi Berezovski
(cid:129) (cid:129)
’
Francesco dell Isola Alexey Porubov
(cid:129)
Editors
Sixty Shades of Generalized
Continua
Dedicated to the 60th Birthday
of Prof. Victor A. Eremeyev
123
Editors
HolmAltenbach Arkadi Berezovski
Institut für Mechanik, Fakultät für Tallinn University of Technology
Maschinenbau Tallinn, Estonia
Otto-von-Guericke-UniversitätMagdeburg
Magdeburg, Sachsen-Anhalt, Germany Alexey Porubov
Institute of Problems of Mechanical
Francesco dell’Isola Engineering
Universitàdegli Studi dell’Aquila Saint Petersburg, Russia
L’Aquila, Italy
ISSN 1869-8433 ISSN 1869-8441 (electronic)
AdvancedStructured Materials
ISBN978-3-031-26185-5 ISBN978-3-031-26186-2 (eBook)
https://doi.org/10.1007/978-3-031-26186-2
©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature
SwitzerlandAG2023
Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether
thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseof
illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and
transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar
ordissimilarmethodologynowknownorhereafterdeveloped.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom
therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
The publisher, the authors, and the editorsare safeto assume that the adviceand informationin this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authors or the editors give a warranty, expressed or implied, with respect to the material contained
hereinorforanyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregard
tojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations.
ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
Preface
Victor Anatolyevich Eremeyev is a brilliant
scientistwithaninternationalreputationwho
has enrichedthe science withmany achieve-
mentsinthefieldofmechanicsofdeformable
solids with the main focus on Generalized
Continuaandthetheoriesofone-dimensional
andtwo-dimensionalstructuralelementslike
beams,rods,platesandshellsandcelebrates
his60thbirthdayinMarch2023.
This anniversary is reason that numerous
friends and colleagues from more than 10
countries have dedicated scientific works to
him,whichhavebeensummarizedinthisbook.
It is easy to see that some of the works are
directlyrelatedtothepublicationsofthejubi-
larian.Othersoriginatefromthescientificen-
vironmentorfromthecircleoffriends,which, VictorAnatolyevichEremeyev
however,donotalwayshaveadirectconnec-
tion to the publications of Victor Eremeyev.
Thisalsoexplainswhythebooktitlewaschosenbytheeditors-therearedifferent
aspectsofthegeneralizedcontinuummodels.
VictorEremeyevwasbornonMarch7th,1963inPiliponovka/Vinnytsiaregion
(Soviet Union, now Ukraine). He studied at the Department of Mechanics and
MathematicsoftheStateUniversityinRostov-on-Don(formerSovietUnion)from
1980to1985andsuccessfullygraduated(withdistinction).From1985until1989
he had a fellowship for Candidate of Science in Physics and Mathematics at the
Division of Elasticity of Rostov State University. In 1990, he was awarded PhD
(Candidate ofPhysics & Mathematics) atRostovState University. The thesis title
wasThestabilityoftwo-phasenonlinearthermo-elasticbodies.In2004,hefinished
his secondthesis Mechanics oftwo-phase bodies withmicrostructure underfinite
deformationsandwasawardedDoctorofscienceofPhysics&Mathematicsatthe
v
vi Preface
InstituteofProblemsofMechanicalEngineeringofRussianAcademyofSciences
(Saint-Petersburg,RussianFederation).
In1996,hewasappointedasAssociateProfessor(Docent)attheSouthernFederal
UniversityinRostov-on-Don.From2003hestartedhisinternationalcarrier.During
thefirstperiodhewasaresearchassociateattheInstituteofFluid-FlowMachinery
ofthePolishAcademyofSciencesinGdańsk(Poland).Hewasinclosecontactwith
Prof.WojciechPietraszkiewicz.Togethertheymakesomefundamentalpublications
highlycitedbythescientificcommunity,amongthemthepaperOnnaturalstrain
measures of the non-linear micropolar continuum published in the International
JournalofSolidsandStructures(46(3-4),pp.774-787)cited229times(20.11.2022).
Later he was a invited as a research associate to Germany. He spent several
yearattheChairofEngineeringMechanicsattheMartin-Luther-UniversitätHalle-
Wittenberg and Otto-von-Guericke-Universität Magdeburg. During this period he
organisedtogetherwithoneoftheeditors(H.A.)aEuromechColloquiumin2011
(EM527-Shell-likeStructures–NonclassicalTheoriesandApplications)andtwo
CoursesattheCISM(InternationalCentreforMechanicalSciences)inUdine,Italy
(2011-GeneralizedContinua-fromtheTheorytoEngineeringApplications,2014
- Shell-like Structures - Advanced Theories and Applications). The proceedings
of the Colloquium and the two Courses were published by Springer. Among his
activities was also the publication ofhis mostcitedpaper(304 times/20.11.2022)
On generalized Cosserat-type theories of plates and shells: A short review and
bibliographypreparedtogetherwithJ.&H.AltenbachandpublishedintheArchive
ofAppliedMechanics(80(1),pp.73-92).
LeavingGermany,in2015VictorEremeyevwasappointedasaprofessor(PRz)
atPolitechnikaRzeszowskaim.IgnacegoLukasiewiczainRzeszow(Poland),later
(2017)asaprofessor(PG)andfinallyasafullprofessoratPolitechnikaGdańskain
Gdańsk(Poland).DuringthisperiodhecollaboratedwithseveralPolishscientists,
amongthemV.Konopińska-Zmysłowska,T.Wiczenbach,J.ChróścielewskiandK.
Wiśniewski.Since2020hehasthepositionofProfessoreassociatoattheUniversità
degliStudidiCagliariinCagliari(Italy).
VictorEremeyev’sscientificinterestsareverydiverse.Theyincludebutnotlimited
to
• Nonlinear elasticity. Infinitesimal stability of solids undergoing stress-induced
phasetransitionswerestudied;
• Plates,shells and beams. Within six-parameter theory of shells phase transfor-
mationinthin-walledstructureswerestudied,thematerialsymmetrygroupwas
introduced. The five-parameter theory of shells was applied to thin structures
madeoffunctionallygradedmaterialsandfoams.Layer-wiseapproachwasused
formodellingofsolarpanels;
• Generalizedmediaincludingmicropolarandmicromorphicmedia,stressandstrain
gradient elasticity and strain gradient fluids. Infinitesimal stability of micropo-
larsolids was studied. Materialsymmetry group was discussedformicropolar,
micromorphic,and strain gradient continua. Acceleration waves and ellipticity
conditionswerestudied.ElasticnetworksweremodelledasaCosseratcontinuum;
Preface vii
• Surfaceelasticity.Theeffectivepropertiesforplatesandshellswithsurfacestresses
werediscussed.Surfacewavesinmediawithsurface/interfacemicrostructurewere
discussed.
• Electro-magnetic-mechanical coupling. The effects of piezo-, flexoelectricity,
piezo- and flexomagneticity were discussed for applications in mechanics of
compositesandthin-walledstructures;
• Applicationofmathematicalmethodsinmechanics.Usingthecalculusofvari-
ations and functional analysis the existence and uniqueness of weak solutions
of some boundary-value problems of six-parameter shells,media with surface
elasticity,andstraingradientcontinuawereproved. Forexample,aremarkable
application ofanisotropicSobolev’s spacetowell-posednessanalysisofpanto-
graphicmetamaterialswasgiven.
Hepublishedmorethan270scientificpapersindexedinScopusandthelistof
co-authorslookslikeWhoiswhoinMechanics:fromRussiaL.Zubov,A.Nasedkin,
S. Lurie, L. Igumnov, N. Morozov, A. Porubov, E. Ivanova, E. Vilchevskaya, A.
Freidin,fromGermanyW.H.Müller,E.Abali,K.Naumenko,M.Lazar,fromItaly
F.dell’Isola,I.Giorgio,L.Placidi,E.Reccia,G.Rosi,A.Cazzani,A.Luongoand
E.Turco,fromFranceJ.-F.Ganghoffer,C.Boutin,S.Naili,fromUKG.Mishuris,
fromColombiaL.LebedevandL.Rendón,fromUSAD.SteigmannandM.Cloud,
fromBelarusG.Mikhasev,fromGreeceE.AifantisandfromPolandT.Sadowski,
F. Stachowicz, A. Skrzat, and M. Malikan. In addition, he wrote and edited 21
books in Russian, English and Spanish. During the last years he was invited by
severaluniversitiesandresearchinstitutes:InstituteofFluid-FlowMachineryofthe
PolishAcademyofSciencesin2003,2005,2008,2009(Gdańsk,Poland),Martin-
Luther-UniversitätHalle-Wittenbergin2007,2008,2009(Halle,Germany),National
UniversityofColombiain2008,2012(Bogota,Colombia),PolitechnikaLubelska
in2011,2012(Lublin,Poland)andInternationalResearchCenterforMathematics
&MechanicsofComplexSystems(M&MoCS)in2014(CisternadiLatina,Italy).
Since2015heservedasavisitingprofessoratSapienzaUniversityofRome,Italy
(2015,2017),atUniversitéParis-EstCréteilValdeMarne,France(2015,2019),at
UniversitaDegliStudiadiGenova,Genoa,Italy(2016),atUniversitàdegliStudidi
Cagliari,Cagliari,Italy(2017)andatUniversitàdegliStudidiSassari,Alghero,Italy
(2017,2018).
VictorEremeyev’sscientificactivitieswereawardedin2000and2008withthe
prizefromElsevierScienceLtd.forthebestpaperpublishedinthejournalPrikladnaya
MatematikaiMekhanika(JournalofAppliedMathematicsandMechanics):
• YeremeyevVA,ZubovLM(1999)Thetheoryofelasticandviscoelasticmicropolar
liquids,JournalofAppliedMathematicsandMechanics63(5):755–767.
• EremeyevVA,FreidinAB,SharipovaLL(2007)Thestabilityoftheequilibriumof
two-phaseelasticsolids,JournalofAppliedMathematicsandMechanics(PMM)
71(1):61–84.
In 2018,he got the International Prize “Tullio Levi-Civita” for the Mathematical
and Mechanical Sciences and in 2021-2022 the Royal Society Wolfson Visiting
Fellowships.In2021,hewasawardedtheprofessorshipfromthePresidentofPoland,
viii Preface
heisincludedinthelistoftheWorld’sTop-citedScientists(World’sTop2%Scientists
List,2020-2022,https://elsevier.digitalcommonsdata.com/datasets/btchxktzyw).
Victor Eremeyev is an active member in the following scientific societies or
organizations: American Mathematical Society,International Research Center on
Mathematics&MechanicsofComplexSystems(M&MoCS)andthePolishSociety
ofTheoreticalandAppliedMechanics. In addition,he is a memberofthe follow-
ing editorial boards: Acta Mechanica, Archive of Applied Mechanics, Computer
Modeling in Engineering & Sciences, Mathematics and Mechanics of Complex
Systems, Mathematics and Mechanics of Solids, Mechanics of Composite Mate-
rials,Symmetry,Technische Mechanik,Nanomechanics Science and Technology:
An International Journal, Zeitschrift für Angewandte Mathematik und Mechanik,
Problems ofStrengthandPlasticity,WorldJournalofMechanics andMechanical
BulletinofPermNationalResearchPolytechnicUniversity.Hewasappointedasa
guesteditorofZeitschriftfürAngewandteMathematikundMechanik(2009,2010,
2011,2014),InternationalJournalofEngineeringandScience(2014),Continuum
MechanicsandThermodynamics(2015,2019,2020),MathematicsandMechanics
ofSolids(2015,2021),Symmetry(2020,2021),Mathematics(2020),Nanomaterials
(2020)andMechanicsResearchCommuncations(2021).Heactedasaco-editorand
member of the scientific committee of Gabrio Piola edition which was published
in2014(VolumeI)as“ThecompleteworksofGabrioPiola,commentedEnglish
translation(EdsFrancescodell’Isola,GiulioMaier,UmbertoPerego,UgoAndreaus,
RaffaeleEsposito,SamuelForest),AdvancedStructuredMaterials,Vol38,Springer”.
Last,butnotleast,itisessentialtohighlighthispersonalcharisma.Heeasilyfinds
acommongroundwithdifferentpeopleregardlessoftheirage,gender,nationality,
education,orkeyscientificfield.Hisdiscussionstyleisdistinguishedbyrespectfor
opposing viewpoints. He possesses the rare abilityto highlightthe main idea and
formulateaproblemwithcompletemathematicalrigor.Puresciencedoesnotcover
theentireareaofhisinterests.Likeanythinkingman,heisinterestedinart,literature,
music,andsocialissues.
Magdeburg, HolmAltenbach
Tallin, ArkadiBerezovski,
Rome, Francescodell’Isola,
St.Petersburg, AlexeyPorubov
January2023
Contents
1 Effectsof3-DPrintingInfillDensityParameterontheMechanical
PropertiesofPLAPolymer................................... 1
RezaAfshar,SimonJeanne,andBilenEmekAbali
1.1 Introduction.............................................. 2
1.2 AdditiveManufacturing .................................... 2
1.3 MaterialsandMethods..................................... 3
1.3.1 FusedDepositionModeling(FDM) .................. 4
1.3.2 UnidirectionalTensileTests ......................... 5
1.3.3 DigitalImageCorrelationMethod.................... 5
1.4 ResultsandDiscussions.................................... 6
1.5 Conclusions.............................................. 8
References ..................................................... 9
2 AdvanceApproximateAnalyticalSolutionsoftheContactProblem
foranInhomogeneousLayer ................................. 13
SergeiM.Aizikovich,PolinaA.Lapina,andSergeiS.Volkov
2.1 Introduction.............................................. 13
2.2 Statement of the Problem of a Shear of the Surface of an
InhomogeneousLayer ..................................... 14
2.3 IntegralEquationsofContactProblems....................... 15
2.4 NumericalAnalysis ....................................... 16
2.5 Closure.................................................. 18
References ..................................................... 19
3 TheDirectApproachforPlatesConsideringHygrothermalLoading
andResidualKinetics ....................................... 21
MarcusAßmus,ZiaJavanbakht,andHolmAltenbach
3.1 Introduction.............................................. 21
3.2 FrameofReference........................................ 23
3.3 ThermalEffectsandHygroscopicImpact ..................... 27
3.4 ResidualKinetics ......................................... 28
ix
