Advances in Solid and Fracture Mechanics: A Liber Amicorum to Celebrate the Birthday of Nikita Morozov

302 Pages·2022·14.333 MB·English

by  Holm Altenbach, Svetlana M. Bauer, Alexander K. Belyaev, Dmitri A. Indeitsev, Valery P. Matveenko, Yuri V. Petrov

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.
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
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