Multiscale Solid Mechanics: Strength, Durability, and Dynamics

509 Pages·2021·17.74 MB·English

by  Holm Altenbach, Victor A. Eremeyev, Leonid A. Igumnov

Advanced Structured Materials
Holm Altenbach
Victor A. Eremeyev
Leonid A. Igumnov   Editors
Multiscale
Solid
Mechanics
Strength, Durability, and Dynamics
Advanced Structured Materials
Volume 141
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.)andapplications.
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
Holm Altenbach Victor A. Eremeyev
(cid:129) (cid:129)
Leonid A. Igumnov
Editors
Multiscale Solid Mechanics
Strength, Durability, and Dynamics
123
Editors
HolmAltenbach Victor A.Eremeyev
Faculty of MechanicalEngineering Faculty of Civil andEnvironmental
Otto vonGuericke University Magdeburg Engineering
Magdeburg, Sachsen-Anhalt, Germany Gdańsk University of Technology
Gdańsk,Poland
LeonidA.Igumnov
Research Institute for Mechanics
State University of Nizhny Novgorod
Nizhny Novgorod,Russia
ISSN 1869-8433 ISSN 1869-8441 (electronic)
AdvancedStructured Materials
ISBN978-3-030-54927-5 ISBN978-3-030-54928-2 (eBook)
https://doi.org/10.1007/978-3-030-54928-2
©SpringerNatureSwitzerlandAG2021
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Preface
The present book is a collection of papers of leading Russian scientists devoted to
thedescriptionandsimulationofdynamicsandstrengthofmaterialsanddurability
ofsystems.Theproblemsarisingfromtheoperationofmachinesandsystemsunder
multifactorial influences are considered. The design and experimental assessment
of the processes of deformation, the development of damage, the destruction of
materials and structures are studied. For given loading history, the appearance of
macroscopicmaterialdiscontinuitiesaredetermined.Thefundamentaldependences
on the strain rates of the ultimate characteristics of strength, dynamics, etc., are
formulated.
When modeling, the significant influence on the rate of the processes of
deformation, accumulation of damage, fracture, and such factors as the type of
deformation trajectory should be taken into account. In addition, the temperature
change, the stress state, thehistory ofthe stress state changes, etc., areconsidered.
In the framework of damage mechanics, the mechanisms of degradation of the
initial strength properties of structural materials under various conditions of
thermo-force loading are studied. The kinetics of the stress–strain state in the
corresponding places of structural elements is introduced in the theoretical models
andsimulations.Thenumericalexperimentsarebasedonvariational-differenceand
finite element technologies. The correctness of the simulations are proofed by
experiments.
Theresultsofnumerical modelingoftheprocesses ofvisco-plastic deformation
of structural elements are presented for several applied problems. Together with
elements of the analysis of the current state of the experimental, theoretical, and
numerical studies of the behavior of materials under quasi-static, cyclic, and
dynamicloading,thedevelopmentandimplementationofnewsimulationmethods
are presented. The identification and verification of mathematical models of
deformation, damage and fracture of structural materials is carried out including
experimental methods of high-speed deformation based on the Kolsky method.
The problems of basic experiments related to identification of the material
parameters and functions used material models are discussed. The study of the
processesofdeformationandfractureofstructuralmaterialsiscarriedoutfromthe
v
vi Preface
perspective of an experimental-theoretical approach. Finally, applications are pre-
sented including not only mechanical loading, but also the influence of the tem-
perature regimes, etc. Considering the scale factor multiscale approaches are
applied.
The editors hope that the readers of this book can get an excellent insight into
actualtheoretical,numericalandexperimentalresearchresultsofRussianscientists
working in the field of mechanics.
Magdeburg, Germany Holm Altenbach
Gdańsk, Poland Victor A. Eremeyev
Nizhny Novgorod, Russia Leonid A. Igumnov
June 2020
Contents
1 Practical Methods for Fatigue Characteristics Assessing
Based on the Monotonic Diffusion Distribution Under Random
Censorship Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
LevonV.Agamirov,VladimirL.Agamirov,andVladimirA.Vestyak
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Statistical Estimation Methods of a Randomly Censored
Sample Parameters Based on the Monotonic Diffusion
Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Bootstrap Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Quantile Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 Monte Carlo Model Testing . . . . . . . . . . . . . . . . . . . . 6
1.2.4 Statistical Processing of Test Results. . . . . . . . . . . . . . 6
1.3 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Earthquakes and Cracks of New Type Complementing
the Griffith–Irwin’s Crack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
VladimirA.Babeshko,OlgaV.Evdokimova,andOlgaM.Babeshko
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Rigid Contact of the Lithosphere Plates with the Base . . . . . . . 14
2.3 External Analysis of the Boundary Value Problem . . . . . . . . . . 17
2.4 On the Properties of Wedge-Shaped Cavities
and Griffith’ Cracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Optimal Attenuation of Transverse Vibrations for a Cantilever
Beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Dmitry V. Balandin and Egor V. Petrakov
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
vii
viii Contents
3.2 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Two-Criterion Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 Solution of Two-Criterion Problem . . . . . . . . . . . . . . . . . . . . . 31
3.5 Numerical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.6 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4 Numerical Study of the Mutual Influence of Nearby Buried
Structures Under Seismic Influences. . . . . . . . . . . . . . . . . . . . . . . . 37
Valentin G. Bazhenov and Nadezhda S. Dyukina
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Mathematical Model and Numerical Technique . . . . . . . . . . . . 38
4.3 AnalysisoftheMutualInfluenceofSeismicVibrationsofTwo
Nearby Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.4 Influence of Seismic Isolation Between Structures
on Their Mutual Influence During Seismic Impact . . . . . . . . . . 40
4.5 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5 DynamicDeformationandFailureCriterionofCylindricalShells
Subjected to Explosive Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Valentin G. Bazhenov, Alexander A. Ryabov, Vladimir I. Romanov,
and Evgeny E. Maslov
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2 Statement of Problem and Defining Relations. . . . . . . . . . . . . . 49
5.3 Experimental and Numerical Results and Analysis . . . . . . . . . . 50
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6 Plasticity of Materials with Additional Hardening Exposed
to Cyclic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Valentin S. Bondar and Dmitry R. Abashev
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.2 Mathematical Modeling of Elastoplastic Strain . . . . . . . . . . . . . 58
6.3 Additional Isotropic Hardening in Case of Disproportionate
Cyclic Loading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
7 Dynamic Compressibility of Birch Under Various Types
of Stress-Strain State. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Anatoly M. Bragov, Andrey K. Lomunov, and Tatiana N. Yuzhina
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
7.2 Material and Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.3 Method of Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Contents ix
7.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
8 On Description of Fast Diffusion in a Coupled Multicomponent
System with Microstructure Within the Framework
of the Thermodynamics of Irreversible Processes . . . . . . . . . . . . . . 81
Dmitry Dudin and Ilya Keller
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
8.2 Extended Brassart Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
8.2.1 Strain Tensor and Its Components. . . . . . . . . . . . . . . . 83
8.2.2 Helmholtz Free Energy. . . . . . . . . . . . . . . . . . . . . . . . 84
8.2.3 Thermodynamic Inequality . . . . . . . . . . . . . . . . . . . . . 84
8.2.4 Partial Energies and Elastic Equations . . . . . . . . . . . . . 86
8.2.5 Dissipative Equations . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.2.6 Balance Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
8.3 Analysis of the Relaxation of Spatial Perturbations. . . . . . . . . . 89
8.3.1 Model Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
8.3.2 Field Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
8.3.3 Perturbation Method. . . . . . . . . . . . . . . . . . . . . . . . . . 90
8.3.4 Relaxation Times of Perturbations
and Their Asymptotes. . . . . . . . . . . . . . . . . . . . . . . . . 91
8.4 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
9 Linear and Nonlinear Problems of Wave Resistance
to the Movement of Objects Along Elastic Guides . . . . . . . . . . . . . 97
Vladimir I. Erofeev, Sergey I. Gerasimov, Elena E. Lisenkova,
Alexey O. Malkhanov, and Vladimir M. Sandalov
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
9.2 Resistance to the Movement Along an Elastic Load Guide
with Its Own Degrees of Freedom . . . . . . . . . . . . . . . . . . . . . . 99
9.3 Some General Relations for Waves Propagating
in One-Dimensional Elastic Systems . . . . . . . . . . . . . . . . . . . . 105
9.4 ResistancetotheMovementoftheLoadAlongaGuideLying
on a Nonlinear Elastic Basement . . . . . . . . . . . . . . . . . . . . . . . 112
9.5 Stabilization of Transverse Vibrations of a Mass Moving
Along a String . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
9.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
10 Dispersion, Attenuation and Spatial Localization
of Thermoelastic Waves in a Medium with Point Defects . . . . . . . . 123
Vladimir I. Erofeev, Anna V. Leonteva, and Ashot V. Shekoyan
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124