Advanced Structured Materials Holm Altenbach · Svetlana M. Bauer · Alexander K. Belyaev · Dmitri A. Indeitsev · Valery P. Matveenko · Yuri V. Petrov   Editors Advances in Solid and Fracture Mechanics A Liber Amicorum to Celebrate the Birthday of Nikita Morozov Advanced Structured Materials Volume 180 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 Svetlana M. Bauer (cid:129) (cid:129) Alexander K. Belyaev Dmitri A. Indeitsev (cid:129) (cid:129) Valery P. Matveenko Yuri V. Petrov (cid:129) Editors Advances in Solid and Fracture Mechanics A Liber Amicorum to Celebrate the Birthday of Nikita Morozov 123 Editors HolmAltenbach SvetlanaM. Bauer Lehrstuhl für Technische Mechanik Faculty of Mathematics &Mechanics Institut für Mechanik St.Petersburg State University Fakultät für Maschinebau St.Petersburg, Russia Otto-von-Guericke-Universität Magdeburg, Germany Dmitri A.Indeitsev IPME RAS Alexander K.Belyaev St.Petersburg, Russia IPME RAS St.Petersburg, Russia YuriV.Petrov IPME RAS Valery P.Matveenko St.Petersburg, Russia UralBranch RAS Institute of Continuous Media Mechanics Perm, Russia ISSN 1869-8433 ISSN 1869-8441 (electronic) AdvancedStructured Materials ISBN978-3-031-18392-8 ISBN978-3-031-18393-5 (eBook) https://doi.org/10.1007/978-3-031-18393-5 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2022 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. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Nikita Fedorovich Morozov, a full member oftheRussianAcademyofSciences,anout- standing Russian scientist who has enriched the science with many achievements in the fieldofmechanicsofdeformablesolids,are- markable teacher, who created the country’s authoritative scientific school of mechanics, celebratedhis90thbirthday. NikitaMorozovwasbornonJuly28,1932 in Leningrad. His childhood coincided with the hard times for the country. During the Second World War, he remained in besieged Leningrad. At the age of 11 he received his first government award: the medal ”For De- fenseofLeningrad”-foractiveparticipation NikitaFedorovichMorozov intheworkoffirebrigades. In1949,heenteredtheFacultyofMathe- maticsandMechanicsoftheLeningradStateUniversity(nowSt.PetersburgState University-theoldestRussianuniversityestablishedin1724),wherehewastaught bytheworld-wideknownscientistslikeY.V.Linnik,S.G.Mikhlin,V.V.Novozhilov, D.K.Faddeevandothers.Aftergettinghisdiploma,hecontinuedhispostgraduate course at the Leningrad University. In 1958, he defended his PhD thesis and was awarded “Candidate of physico-mathematical sciences”. After successful comple- tionofthepostgraduatecoursein1958,hestartedworkingasaseniorengineeratthe KrylovCentralResearchInstitute,andayearlaterbeganteachingattheLeningrad TechnologyInstituteofPulpandPaperIndustry,wherehewasappointedasanas- sistantprofessorandbecameheadofthedepartmentfor13years. Duringthoseyears,N.F.Morozovsuccessfullycombinesteachingwithscientific work.Themaindirectionofhisscientificinterestswasthestudyofnonlinearprob- lemsinthetheoryofthinplates.Heprovedtheexistence,uniquenessandsolvability oftheboundaryandinitialboundaryproblemsofthetheoryofplatesandshellsus- v vi Preface ingtherigorousmathematicalapproach.Hesolvedtheproblemoftheexistenceof asymmetricsolutionsinthesymmetricallyloadedcircularplateandformulatedthe sufficientconditionsofinstabilityofsymmetricsolutions[1,2,3].Theresultsob- tainedbyN.F.Morozovonthequalitativeresearchofnonlinearproblemsofthethin platetheoryareclassicalandformedabasisofhisdoctoral(DSc)thesis”Nonlinear problemsofthetheoryofthinplatesandshells”defendedin1967attheLeningrad StateUniversity. In 1971, N.F. Morozov was invited to Leningrad State University to head the laboratory of mathematical physics at the Leningrad State Research Institute of MathematicsandMechanicsnamedafteracademicianV.I.Smirnov.In1973hewas electedprofessorofthedepartmentofmathematicalphysicsoftheFacultyofMath- ematicsandMechanics,andin1976hebecameheadofthedepartmentoftheoryof elasticityofLeningradStateUniversity,oneoftheoldestdepartmentsoftheuniver- sity,whichheheadstodate.Atdifferenttimes,thestudents,postgraduatestudents and employees of the department were well-known scientists. Among them there are,forexample,thelaterPresidentoftheAcademyofSciencesofUSSRacademi- cianG.I.Marchuk,academiciansA.S.Alekseev,E.I.Shemyakin,S.L.Sobolevand N.I. Muskhelishvili, professors V.M. Babich, K.F. Chernikh, V.A. Likhachev, and others. TheorganizationalworkofN.F.Morozovastheheadofthefamousdepartment andthecombinationofhisbrightscientificandteachingactivityledtothedevelop- mentandgrowthofthescientificschoolofmechanicsofSt.PetersburgStateUni- versity(SPbSU),whichnowrightfullyoccupiesoneoftheleadingpositionsamong theRussianschoolsinthisfield.AmongthegraduatesofthedepartmentandN.F. Morozov’sstudentstherearemanywell-knownscientistswhohavemadeasignif- icantcontributiontomechanicsandmathematicalphysics:CorrespondingMember of the Russian Academy od Sciences Y.V. Petrov, Prof. S.A. Nazarov, Prof. M.V. Paukshto,Prof.A.E.Volkov,Prof.A.I.Razov,Prof.A.A.Utkin,andalsomanyspe- cialistsworkinginthefieldofhightechnologies.Eveninthemostdifficulttimes,the departmentundertheleadershipofN.F.Morozovcontinueditsresearchactivities, andexploitednewopportunitiesforgrowth.So,thankstohisenergyandorganiza- tionaltalent,indifficulttransitionalperiodof1990sthedepartmentcouldsuccess- fullybegincarryingoutofboththeoreticalandexperimentalresearchesinanumber ofnewessentiallyimportantdirections,inparticular,inthefieldofoptimizationof elasticmechanicalsystems,dynamicproblemsandproblemsofbiomechanics. NikitaMorozovwasoneoftheinitiatorsoftheapplicationofstrictmathemati- calmethodsinthetheoryofelasticityandnonlinearmechanics.Thenewresultshe obtainedinanumberofscientificbranchesofthemathematicaltheoryofelasticity and nonlinear problems of mechanics put N.F. Morozov among the most famous specialists in the country and abroad. N.F. Morozov and his pupils and colleagues madesignificantprogressinthestrictmathematicalformulationandinvestigationof thestrengthandfractureproblems,suggestedbyacademicianV.V.Novozhilov.N.F. Morozov made a significant contribution to the development of crack theory. He madeasignificantcontributiontothedevelopmentofcracktheory.Theapplication ofrigorousmathematicalanalysistoolsallowedhimandhisstudentstodevelopef- Preface vii fectivemethodsforanalyzingthesingularfieldsofelasticitytheoryarisinginstatic problemswithsharpstressconcentratorssuchascracksandsharpnotches.This,in turn, led to the necessity of constructing new criteria of brittle fracture that could correctlypredicttheultimateloadsincaseswheretraditionalapproachesbasedon the classical Griffith-Irwin model do not work. One of the main achievements of N.F. Morozov and his collaborators in this field was the development of nonlocal strength criteria. In particular, it was proved that the integral fracture criterion - mean stress fracture criterion - offered earlier for special problems by H. Neuber andV.V.Novozhilovcanbemodifiedfortheproblemsofcontinuummechanicsso thataverywideclassofproblemscouldbeconsidered-fromtheproblemsforre- gionswithcracksandsharpnotches(jointlywithB.N.SemenovandS.A.Nazarov) to the problems with small crack-like defects (jointly with Yu.V. Petrov). The key notion that was introduced in these studies was the notion of linear fracture size. Thephysicaltreatmentandthemethodofdeterminationofthisparameterproposed intheseworksopenedupthepossibilityforfurthergeneralizationsofthetheoryto other fields of mechanics. This led to the formation of the SPbSU school of frac- ture mechanics, which is still the leading school in this field. The monograph [4] becameasignificantcontributiontothescienceoffracture,whichwasintensively developinginmanyscientificcentersworld-wideduringthoseyears. Attheendof1980s,N.F.MorozovtogetherwithYu.V.Petrovturnedtodynamic problemsofmechanics.Thethenprevailingconceptionsoffracturecameintocon- flictwiththelatestexperimentalresearchonextremehigh-speedeffectsinmaterials, whichrevealedanumberoffundamentaleffectsthatdidnotfitintothetraditional models. To resolve these contradictions, new ideas were required, which were de- velopedinanumberofworksoftheSt.PetersburgSchoolofMechanics.Thejoint works[5,6]withYu.PetrovandA.Utkingeneratedasetofideasthatlaterserved asabasisforformulatingageneralstructural-timeapproachtosolvingdynamical problems and studying the critical extreme states of continuous media under dy- namic actions. Using this approach, it was possible to formulate a number of new criteria or limit conditions for transient processes in the theory of fracture, plas- ticdeformation,electro-physics(pulsebreakdown),cavitation,thetheoryofphase transformations.Basedonthisapproachandnewfracturecriteria,newmaterialtest- ingmethodswereproposedtomeettheneedsofmodernindustry. Problems of free vibrations and stability of compressed transverse isotropic space,half-spaceandtransverseisotropiccompressedplateweresolvedjointlywith P.E.Tovstik.Specialattentionispaidtotheanalysisoftheformsofstabilitylossof both the elastic foundation itself and the plate resting on it. Using the equations of geometrically nonlinear elasticity theory, the surface stability of a transverse anisotropic elastic half-space under the action of compressive stresses is studied [7,8].Ananalysisofthelossofstabilityinthesupercriticalstageshowedthatthe dentsnearthefreesurfaceofthehalf-spacearearrangedina“staggered”manner, whichcorrespondstotheexperimentalresults. N.F. Morozov is distinguished by his constant interest in new topical problems ofdeformablesolidmechanics,intheapplicationofsolidmechanicsmethodstore- lateddisciplines,andinthesolutionofpracticalproblems.Since1994,hehasbeen viii Preface active in the field of applying the methods of deformable solid mechanics to the problems of nanomechanics and theoretical material science and the relationship between deformation, stability, and fracture, and the diffusion processes of phase transformations. Together with E.A. Ivanova and A.M. Krivtsov, the dependence ofelasticmodulionnanocrystalsizeistheoreticallyinvestigated.Thescaleeffects that arise when the continuum theory of elasticity is applied to nanoobjects were estimatedandalsotheinfluenceofscaleeffectswhenthemethodofmoleculardy- namicsisusedformodelingmacroscopicobjects[9,10].TogetherwithI.A.Ovidko, theprocessesofdeformationandfractureofgraphenesheetswithdifferenttypesof structuraldefectsarestudied[11,12]. N.F.Morozovandhisco-authorsmodifiedtheequilibriumequationsandconsti- tutiverelationsoflineartheoryofplatesandshellswithconsiderationoftransverse shear deformations by reducing the relations of spatial elasticity theory with sur- facestressestotwo-dimensionalequationsgivenonthemiddlesurfaceoftheshell andanalyzingtheeffectofsurfaceelasticmoduliontheeffectivestiffnessofplates andshells[13,18,14,15,16,17].N.F.Morozovandco-authorsI.A.Ovidko,A.G. Sheynerman, and S.V. Bobylev studied the mechanisms of deformation and frac- tureofnanocrystallinebodies.Atheoreticalmodeldescribingtheeffectofspecial rotational deformation on crack growth in deformed nanocrystalline ceramics and metals was proposed and its effect on the growth of pre-existing relatively large cracksinnanocrystallinemetalsandceramicswasevaluated[19]. A special physical mode of plastic deformation in nanocrystalline, ultrafine- grained and polycrystalline bodies caused by grain boundary slip and nucleation of nanosized grains (resulting from grain boundary splitting and migration under stress)wasproposedandtheoreticallydescribed.Itwasshownthatthespecialdefor- mationmodeenhancedtheplasticityofnanocrystallineandultrafine-grainedsolids and this enhancement effect was more pronounced compared to the effect of co- operative grain boundary slip and migration [20]. The micromechanics of plastic deformation by grain boundary migration in metal-graphene nanocomposites was alsostudied[21]. N.F. Morozov together with L.V. Shtukin, I.E. Berinskii, D.A. Indeitsev and D.Yu.Skubovstudiedtheeffectofnanoscaleontheperformanceofelectromechan- icalstructures.Inparticular,theelectromechanicalmodelofthegraphenenanores- onator was considered, taking into account the capacitor’s capacity change due to thedeformationofthegraphenelayer(oneoftheplates)andtakingintoaccountthe nonlinear-elasticpropertiesofthegraphenesheetatasmallinitialstretching.Two newschemesofthegraphenenanoresonatorswereproposed,namelythedifferential andparametricones[22]. Thewell-knownKirschproblemanditsvariousmodificationsinnanomechani- cal formulation was considered: a plate stretched by diametrically opposite forces withacircularorellipticalholeorinclusionmadeofanothermaterial,aplateweak- ened by various combinations of parallel cracks. The features of deformation and destructionofbothdefect-freeanddefect-containinggraphenesheetswereconsid- ered[23,24,25]. Preface ix TogetherwithA.K.BelyaevandP.E.Tovstik,N.F.Morozovconductedaseries ofstudiesonthedynamicstabilityofrodsunderlongitudinalloading,knowninme- chanicsastheLavrent’ev-Ishlinskyproblem[26,27].Amongothers,aninteresting result was obtained about the loss of stability of a rod under a stepwise applica- tion of a longitudinal load smaller than the Eulerian load. In 2016, N.F. Morozov, A.K. Belyaev, and P.E. Tovstik were awarded the M.A. Lavrentyev Prize of the RussianAcademyofSciencesfortheirseriesofpapers”TheDynamicsofaRodin LongitudinalCompression.DevelopmentoftheIdeaofM.A.Lavrent’evandA.Yu. Ishlinsky”. N.F. Morozov left his mark not only as an author. He had also acted as editor intheSpringerbookseries“AdvancedStructuredMaterials”[28,29],thelastbook was devoted to his friend and colleague Prof. P.E. Tovstik, who passed away in December2020. UndertheleadershipofN.F.MorozovattheInstituteforProblemsofMechan- ical Engineering of the Russian Academy of Sciences (RAS) a creative team was formedthatworksfruitfullyonthesolutionofurgentproblemsofdeformablesolid mechanicsandincludesmanytalentedyoungpeople.Continuingthebesttraditions ofA.I.LurieandV.V.Novozhilov,N.F.Morozovorganizedapermanentcitysemi- narattheInstituteforProblemsofMechanicalEngineeringRAS,wherescientists fromleadingRussianandforeignscientificcentersdiscusstopicalproblemsofme- chanics and physics and present their achievements. Thanks to the efforts of N.F. Morozov at the Institute for Problems of Mechanical Engineering of the Russian Academy of Sciences, the following directions were created and are actively de- veloped: micromechanics of materials, creation and application of carbon nanos- tructures,methodsofmoleculardynamics,mechanicsofnanomaterialsanddefect theory,anddynamicsofextremestatesandstructuraltransformations. For more than 50 years, the outstanding scientist and talented teacher has been teachingatSt.PetersburgStateUniversity.Thescientificschoolofstrengthmechan- icsthathecreatedenjoysgreatauthorityinRussiaandabroad.Bythedecisionsof theGrantsCouncilunderthePresidentoftheRussianFederation,theAcademician N.F.Morozov’sScientificSchoolhasbeenrepeatedlyrecognizedasaleadingsci- entificschoolofRussia.ThepupilsofN.F.Morozovdefended8doctoralthesesand morethan50PhDtheses. N.F.Morozovistheauthorofmorethan450scientificworks,including8mono- graphsand3textbooks.Since1994hewasacorrespondingmemberoftheRussian Academy of Sciences and in 2000 he was elected as full member (academician) oftheRussianAcademyofSciences.HeisthechairmanoftheScientificCouncil on mechanics of deformable solids of the Russian Academy of Sciences. In 2000, N.F.MorozovwasawardedtheStatePrizeoftheRussianFederationinthefieldof science and technology for a cycle of papers on nonlinear problems of mechanics ofdeformablesolids.In2006,N.F.Morozovwasawardedthe“A.F.IoffePrize”of the Government of St. Petersburg in Physics and Mathematics for his outstanding contributiontothedynamictheoryoffractureofmaterials.In2017N.F.Morozov wasawardedthe“BlaisePascalMedal”,establishedbytheEuropeanAcademyof Sciencesin2003,inrecognitionofhisoutstandingpersonalcontributiontoscience