Developments and Novel Approaches in Nonlinear Solid Body Mechanics

491 Pages·2020·24.592 MB·English

by  Bilen Emek Abali, Ivan Giorgio

Advanced Structured Materials
Bilen Emek Abali
Ivan Giorgio   Editors
Developments
and Novel
Approaches in
Nonlinear Solid
Body Mechanics
Advanced Structured Materials
Volume 130
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 reach in many applications their limits and new
developments are required to fulfil increasing demands on engineering materials.
The performance ofmaterials can beincreasedby combiningdifferent materials to
achieve better properties than a single constituent or by shaping the material or
constituents in a specific structure. The interaction between material and structure
mayariseondifferentlengthscales,suchasmicro-,meso-ormacroscale,andoffers
possible applications in quite diverse fields.
Thisbookseriesaddressesthefundamentalrelationshipbetweenmaterialsandtheir
structure on the overall properties (e.g. mechanical, thermal, chemical or magnetic
etc.) and applications.
The topics of Advanced Structured Materials include but are not limited to
(cid:129) classical fibre-reinforced composites (e.g. glass, carbon or Aramid reinforced
plastics)
(cid:129) metal matrix composites (MMCs)
(cid:129) micro porous composites
(cid:129) micro channel materials
(cid:129) multilayered materials
(cid:129) cellular materials (e.g., metallic or polymer foams, sponges, hollow sphere
structures)
(cid:129) porous materials
(cid:129) truss structures
(cid:129) nanocomposite materials
(cid:129) biomaterials
(cid:129) nanoporous metals
(cid:129) concrete
(cid:129) coated materials
(cid:129) smart materials
Advanced Structured Materials is indexed in Google Scholar and Scopus.
More information about this series at http://www.springer.com/series/8611
Bilen Emek Abali Ivan Giorgio
(cid:129)
Editors
Developments and Novel
Approaches in Nonlinear
Solid Body Mechanics
123
Editors
Bilen EmekAbali IvanGiorgio
Institute of Mechanics Department ofMechanical
Technische UniversitätBerlin andAerospace Engineering
Berlin, Germany University of RomeLa Sapienza
Latina, Italy
ISSN 1869-8433 ISSN 1869-8441 (electronic)
AdvancedStructured Materials
ISBN978-3-030-50459-5 ISBN978-3-030-50460-1 (eBook)
https://doi.org/10.1007/978-3-030-50460-1
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Preface
TheICoNSOM2019,InternationalConferenceonNonlinearSolidMechanics,took
placeatPalazzoArgiletum,Rome,Italy,fromJune16toJune19,2019.Over200
participationfromthewholeglobe,theurgeofthisproceedingsbecameclear.With
theaidoftheorganizers,MarcoAmabili,Francescodell’Isola,IvanGiorgio,Nicola
Rizzi,andLucaPlacidi,thescientificcommunitydidshowagreatinterestallowing
ustobringtogetherthisproceedingscollectedintwovolumes:
• DevelopmentsandNovelApproachesinNonlinearSolidBodyMechanics
• DevelopmentsandNovelApproachesinBiomechanicsandMetamaterials
ICoNSoM 2019 Conference has been intended to provide an international oppor-
tunity for communicating recent developments in various areas of nonlinear solid
mechanics. This monograph consists theory, experiments, and applications in me-
chanics,thermodynamics,andmultiphysicssimulationinmanylengthscales.
Aseditors,weintendtothankallauthorsfortheircrucialcontributionsaswell
asallreviewersfortheirinvaluabletimeandeffort.WedelightedlyacknowledgeDr.
ChristophBaumann(SpringerPublisher)forinitiatingthebookproject.Inaddition,
wehavetothankDr.MayraCastro(SeniorEditorAppliedSciences;MaterialsSci-
ence; Materials Engineering; Nanotechnology and Nanomedicine) and Mr. Ashok
Arumairaj(ProductionAdministrator)givingtheirsupportintheprocessofpubli-
cation.
Brussels,Rome BilenEmekAbali
May2020 IvanGiorgio
v
Contents
1 International Conference on Nonlinear Solid Mechanics 2019:
GeneralTopicsandReviewofPlenaryLectures .................. 1
MarcoLaudato,DariaScerrato,Chuong AnthonyTran,andEmilio
Barchiesi
1.1 Why Nonlinear Solid Mechanics Deserves an International
Conference?.............................................. 1
1.2 PlenaryLectures.......................................... 4
1.2.1 NonlinearMechanicsofDrilling–B.Balachandran..... 4
1.2.2 Surface Elasticity with Applications to Material
ModelingattheNano-andMicro-Scales–V.A.Eremeyev 5
1.2.3 TenYearsofGlobalDigitalVolumeCorrelation:What
HasBeenAchieved?–F.Hild ....................... 6
1.2.4 GranularMicromechanics:BridgingGrainInteractions
andContinuumDescriptions–A.Misra .............. 6
1.2.5 OnSeven-andTwelve-ParameterShellFiniteElements
andNon-LocalTheoriesforCompositeStructures–J.
N.Reddy ........................................ 7
1.2.6 ExploitingGlobalDynamicstoUnveiltheNonlinear
ResponseandActualSafetyofSystemsandStructures
–G.Rega ........................................ 8
1.2.7 VibrationsofNonlinearContinuaSubjecttoCombined
Harmonic and Stochastic Forces: Linearization
ApproximationsandMonteCarloSimulations–P.D.
Spanos .......................................... 9
1.3 Conclusions.............................................. 9
References ..................................................... 10
PartI MathematicalToolsforMechanics
vii
viii Contents
2 Asymptotic Construction of Solutions of Ordinary Differential
EquationswithHolomorphicCoefficientsintheNeighborhoodof
anIrregularSingularPoint ................................... 17
MariaV.Korovina&VladimirYu.Smirnov
References ..................................................... 21
3 PoincareProblemandClassificationofIrregularSingularPoints
forLinearDifferentialEquationswithHolomorphicCoefficients.... 23
MariaV.Korovina&VladimirYu.Smirnov
References ..................................................... 26
4 Behavior of Solutions of the Cauchy Problem and the Mixed
InitialBoundaryValueProblemforanInhomogeneousHyperbolic
EquationwithPeriodicCoefficients ............................ 29
HovikA.Matevossian,GiorgioNordo,andAnatolyV.Vestyak
4.1 Introduction.............................................. 29
4.2 NotationandPreliminaries ................................. 31
4.3 MainResults ............................................. 33
References ..................................................... 34
5 ASoftEmbeddingTheoremforSoftTopologicalSpaces ........... 37
GiorgioNordo
5.1 Introduction.............................................. 37
5.2 Preliminaries............................................. 39
5.3 SoftEmbeddingTheorem .................................. 48
5.4 Conclusion............................................... 54
References ..................................................... 54
6 TheDiffusion–VortexProblemsinTermsofStressesforBingham
Materials .................................................. 59
DimitriGeorgievskii
6.1 TheGeneralizedDiffusionofVortex ......................... 59
6.2 DiffusionofPlaneVortexLayer.ExtractionofaPlaneoutof
Visco-PlasticSpace ....................................... 62
6.3 DiffusionofAxiallySymmetricVortexLayer.Extractionofa
ThreadoutofVisco-PlasticSpace ........................... 63
6.4 DiffusionofVortexThread ................................. 64
References ..................................................... 65
7 OntheBehaviorofSolutionsofQuasilinearEllipticInequalities
NearaBoundaryPoint....................................... 67
AndrejA.Kon’kov
7.1 Introduction.............................................. 67
7.2 EstimatesofSolutionsnearaBoundaryPoint.................. 70
References ..................................................... 76
Contents ix
8 IntegrableDissipativeDynamicalSystemswithThreeandFour
DegreesofFreedom ......................................... 77
MaximV.Shamolin
8.1 Introduction.............................................. 77
8.2 EquationsofGeodesicLines................................ 78
8.3 AFairlyGeneralCase ..................................... 79
8.4 PotentialFieldofForce .................................... 81
8.5 ForceFieldwithDissipation ................................ 82
8.6 StructureofTranscendentalFirstIntegrals..................... 84
8.7 Conclusions.............................................. 84
8.8 ImportantExample:CaseofFour-DimensionalManifold ........ 85
8.8.1 EquationsofMotioninaPotentialForceFieldandFirst
Integrals ......................................... 88
8.8.2 EquationsofMotioninaForceFieldwithDissipation
andFirstIntegrals ................................. 89
References ..................................................... 91
PartII Modeling,Design,andComputationofNonlinearStructures
9 AVariationalFormulationofClassicalNonlinearBeamTheories ... 95
SimonR.Eugster&JonasHarsch
9.1 Introduction.............................................. 95
9.2 NotationandKinematics ................................... 97
9.3 StrainEnergyFunctional ...................................101
9.4 VirtualWorkContributions.................................103
9.5 PrincipleofVirtualWorkandEquationsofMotion.............107
9.6 ConstrainedBeamTheories.................................109
9.6.1 NonlinearEuler–BernoulliBeam ....................109
9.6.2 NonlinearInextensibleEuler–BernoulliBeam..........110
9.7 ConstrainedandUnconstrainedPlanarBeamTheories ..........110
9.7.1 TimoshenkoBeam.................................111
9.7.2 Euler–BernoulliBeam .............................115
9.7.3 InextensibleEuler–BernoulliBeam...................117
9.8 Conclusion...............................................118
References .....................................................119
10 Finite Element Analysis of Planar Nonlinear Classical Beam
Theories ................................................... 123
JonasHarsch&SimonR.Eugster
10.1 Introduction..............................................123
10.2 Notation.................................................125
10.3 VirtualWorkContributionsinParameterSpace ................125
10.3.1 TimoshenkoBeam.................................127
10.3.2 Euler–BernoulliBeam .............................128
10.3.3 ConstraintVirtualWorkContributions................129
10.4 B-SplineShapeFunctions ..................................130
x Contents
10.5 DiscreteKinematics,SemidiscreteVirtualWork,andEquations
ofMotion................................................133
10.5.1 TimoshenkoBeam.................................134
10.5.2 Euler–BernoulliBeam .............................136
10.5.3 ConstraintForces..................................138
10.5.4 EquationsofMotionandBilateralConstraints .........140
10.6 NumericalExamples ......................................142
10.6.1 PureBendingofaCantileverBeam ..................142
10.6.2 CantileverBeamSubjectedtoConstantEndLoad ......143
10.6.3 CantileverBeamSubjecttoFollowerEndLoad ........145
10.6.4 Clamped-HingedCircularArchSubjecttoPointLoad...147
10.6.5 Buckling of a Hinged Right-Angle Frame under
FollowerPointLoad ...............................150
10.6.6 Natural Frequencies of a Two Sided Pinned
Euler–BernoulliBeam .............................152
10.7 Conclusion...............................................155
References .....................................................156
11 Modelling of Two-dimensional Timoshenko Beams in Hencky
Fashion.................................................... 159
EmilioTurco
11.1 Introduction..............................................159
11.2 ModellingofTwo-DimensionalTimoshenkoBeams ............160
11.3 NumericallyDrivenDrawingoftheEquilibriumPath ...........164
11.4 Quantitative Analysis of the Influence of the Shear Stiffness
Parameter................................................166
11.4.1 TipDeflectionofaCantileverBeam..................167
11.4.2 BucklingofaSimplySupportedBeam................169
11.5 ConcludingRemarksandFutureChallenges...................172
References .....................................................173
12 Nonlinear Phenomena in Granular Solids: Modeling and
Experiments................................................ 179
MarcoLaudato
12.1 Introduction..............................................179
12.2 Nonlinear Phenomena in Granular Solids: Modeling and
Experiments .............................................180
12.2.1 DeformationandDestructionatDeformationRateof
Order103s−1WoodofHardwoodTrees-TatianaYuzhina181
12.2.2 Experimental Study of the Dynamic Properties of
ConcreteunderCompressiveLoad-MikhailGonov ....181
12.2.3 DamageProbinginCementedGranularMaterialswith
Ultrasound-IoanIonescu ..........................182
12.2.4 TheRoleofFabricintheBehaviorofGranularMaterial
-NielsKruyt .....................................182