Mechanics and Physics of Structured Media: Asymptotic and Integral Equations Methods of Leonid Filshtinsky. PDF
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Mechanics and Physics of Structured Media This page intentionally left blank Mechanics and Physics of Structured Media Asymptotic and Integral Equations Methods of Leonid Filshtinsky Edited by Igor Andrianov RWTHAachenUniversity Aachen,Germany Simon Gluzman Toronto,ON,Canada Vladimir Mityushev ResearchGroupMaterialica+ FacultyofComputerScienceandTelecommunications CracowUniversityofTechnology Kraków,Poland AcademicPressisanimprintofElsevier 125LondonWall,LondonEC2Y5AS,UnitedKingdom 525BStreet,Suite1650,SanDiego,CA92101,UnitedStates 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom Copyright©2022ElsevierInc.Allrightsreserved. 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Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgein evaluatingandusinganyinformation,methods,compounds,orexperimentsdescribedherein.In usingsuchinformationormethodstheyshouldbemindfuloftheirownsafetyandthesafetyof others,includingpartiesforwhomtheyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors, assumeanyliabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterofproducts liability,negligenceorotherwise,orfromanyuseoroperationofanymethods,products, instructions,orideascontainedinthematerialherein. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN:978-0-323-90543-5 ForinformationonallAcademicPresspublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:MatthewDeans AcquisitionsEditor:DennisMcGonagle EditorialProjectManager:MarianaL.Kuhl ProductionProjectManager:PrasannaKalyanaraman Designer:MarkRogers TypesetbyVTeX LeonidAnshelovichFilshtinsky This page intentionally left blank Contents Listofcontributors xvii Acknowledgements xxi 1. L.A.Filshtinsky’scontributiontoAppliedMathematics andMechanicsofSolids VladimirMityushev,IgorAndrianov,andSimonGluzman 1.1 Introduction 1 1.1.1 Personalityandcareer 1 1.1.2 Lessonsofcollaboration(V.Mityushev) 3 1.1.3 Filshtinsky’scontributiontothetheoryofintegral equations 5 1.2 Doubleperiodicarrayofcircularinclusions.Founders 7 1.2.1 Preliminaries 7 1.2.2 ContributionbyEisenstein 10 1.2.3 ContributionbyRayleigh 12 1.2.4 ContributionbyNatanzon 14 1.2.5 ContributionbyFilshtinsky 18 1.3 Synthesis.Retrospectiveviewfromtheyear2021 22 1.4 Filshtinsky’scontributiontothetheoryof magneto-electro-elasticity 27 1.5 Filshtinsky’scontributiontothehomogenizationtheory 30 1.6 Filshtinsky’scontributiontothetheoryofshells 32 1.7 Decentandcreativeendeavor 33 Acknowledgment 34 References 34 2. Cracksintwo-dimensionalmagneto-electro-elastic medium DmytroNosov,LeonidFilshtinsky,andVladimirMityushev 2.1 Introduction 41 2.2 Boundary-valueproblemsforanunboundeddomain 42 2.3 Integralequationsforanunboundeddomain 45 2.4 Asymptoticsolutionattheendsofcracks 50 vii viii Contents 2.5 Stressintensityfactors 52 AcrackinMMEplane 55 2.6 Numericalexample 56 2.7 Conclusion 60 References 60 3. Two-dimensionalequationsof magneto-electro-elasticity VladimirMityushev,DmytroNosov,andRyszardWojnar 3.1 Introduction 63 3.2 2Dequationsofmagneto-electro-elasticity 65 3.2.1 Linearequationsofmagneto-electro-elasticityand potentials 66 3.2.2 Complexrepresentationoffieldvalues 67 3.3 Boundaryvalueproblem 70 3.4 Dielectrics 72 3.5 Circularhole 77 Numericalexample 80 3.6 MEEequationsandhomogenization 82 3.7 Homogenizationof2Dcompositesbydecompositionof coupledfields 89 3.7.1 Straley-Milgromdecomposition 90 3.7.2 Rylkodecomposition 91 3.7.3 Example 94 3.8 Conclusion 95 References 96 4. Hashin-Shtrikmanassemblageofinhomogeneous spheres AndrejCherkaevandVladimirMityushev 4.1 Introduction 99 4.2 TheclassicHashin-Shtrikmanassemblage 100 4.3 HSA-typestructure 102 4.4 Conclusion 107 Acknowledgments 107 References 107 5. Inverseconductivityproblemforsphericalparticles VladimirMityushev,NataliaRylko,ZhanatZhunussova,and YeskendyrAshimov 5.1 Introduction 109 5.2 ModifiedDirichletproblem 110 5.2.1 Reductiontofunctionalequations 110 Contents ix 5.2.2 Explicitasymptoticformulas 114 5.3 Inverseboundaryvalueproblem 116 5.4 Discussionandconclusion 119 Acknowledgments 120 References 120 6. Compatibilityconditions:numberofindependent equationsandboundaryconditions IgorAndrianovandHeikoTopol 6.1 Introduction 123 6.2 GoverningrelationsandSouthwell’sparadox 126 6.3 Systemofninthorder 128 6.4 CounterexamplesproposedbyPobedryaandGeorgievskii 129 6.5 Variousformulationsofthelineartheoryofelasticityproblems instresses 130 6.6 Otherapproximations 131 6.7 Generalization 132 6.8 Concludingremarks 133 Conflictofinterest 134 Acknowledgments 134 References 134 7. Criticalindexforconductivity,elasticity, superconductivity.Resultsandmethods SimonGluzman 7.1 Introduction 141 7.2 Criticalindexin2Dpercolation.Rootapproximants 144 7.2.1 Minimaldifferenceconditionaccordingtooriginal 145 7.2.2 Iteratedroots.Conditionsimposedonthresholds 145 7.2.3 Conditionsimposedonthecriticalindex 146 7.2.4 Conditionsimposedonamplitudes 147 7.2.5 Minimalderivative(sensitivity)condition 148 7.3 3DConductivityandelasticity 149 7.3.1 3Delasticity,orhigh-frequencyviscosity 150 7.4 Compressibilityfactorofhard-disksfluids 151 7.5 Sedimentationcoefficientofrigidspheres 152 7.6 Susceptibilityof2DIsingmodel 153 7.7 Susceptibilityofthree-dimensionalIsingmodel.Root approximantsofhigherorders 155 7.7.1 Commentonunbiasedestimates.Iteratedroots 155 7.8 3DSuperconductivitycriticalindexofrandomcomposite 157 7.9 Effectiveconductivityofgraphene-typecomposites 159 7.10 Expansionfactorofthree-dimensionalpolymerchain 165 7.11 Concludingremarks 167
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