Sumbatyan Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials

Theoretical and Experimental Methods
1. Auflage 2019
ISBN: 978-3-030-17470-5
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 109, 261 Seiten

Reihe: Advanced Structured Materials

This book addresses theoretical and experimental methods for exploring microstructured metamaterials, with a special focus on wave dynamics, mechanics, and related physical properties. The authors use various mathematical and physical approaches to examine the mechanical properties inherent to particular types of metamaterials. These include: •Boundary value problems in reduced strain gradient elasticity for composite fiber-reinforced metamaterials •Self-organization of molecules in ferroelectric thin films •Combined models for surface layers of nanostructures •Computer simulation at the micro- and nanoscale •Surface effects with anisotropic properties and imperfect temperature contacts •Inhomogeneous anisotropic metamaterials with uncoupled and coupled surfaces or interfaces •Special interface finite elements and other numerical and analytical methods for composite structures 


Prof. Mezhlum Sumbatyan is a principal researcher and a Head of Ultrasonic Laboratory in the Institute for Mathematics, Mechanics and Computer Science, Southern Federal University, Russia. He is the Member of the Editorial Board in 2 International journals, Member of the Russian Acoustical Society, Member of Technical Committee, European Acoustical Association (EAA), Foreign Member of the National Academy of Sciences, Republic of Armenia, Member of Russian National Committee on Theoretical and Applied Mechanics. He has more than 120 papers published in SCOPUS journals. 12 PhD students passed with their thesis under his leaderships.
Research topics:Ultrasonic NDT, Integral Equations, Inverse problems in mechanics and acoustics, Asymptotic methods in short-wave diffraction, Propagation of ultrasonic waves, Computational Hydrodynamics, Aeroacoustics, Turbulence, Boundary Elements Method. 

Autoren/Hrsg.

Sumbatyan, Mezhlum A.

Inhaltsverzeichnis

1;Foreword;6
2;Contents;9
3;Contributors;11
4;On Anti-Plane Surface Waves Considering Highly Anisotropic Surface Elasticity Constitutive Relations;14
4.1;1 Introduction;14
4.2;2 Constitutive Relations;15
4.3;3 Anti-plane Motions of an Elastic Half-Space;17
4.4;4 Conclusions;20
4.5;References;21
5;Periodic Problem for a Plane Composed of Two-Layer Strips with a System of Longitudinal Internal Inclusions and Cracks;23
5.1;1 Introduction;23
5.2;2 Problem Statement and Derivation of the Governing Equations;24
5.3;3 Solution of the System of Governing Equations;28
5.3.1;3.1 Numerical Analysis;31
5.4;4 Conclusion;33
5.5;References;33
6;An Experimental Model of the Acoustic Wave Propagation Through a Cascading Triple-Periodic Array of Cylindrical Holes;35
6.1;1 Introduction;35
6.2;2 Applied Instrumentation;36
6.3;3 Results of the Measurements;40
6.4;4 Conclusion;41
6.5;References;43
7;Simulation of the Surface Structure of Ferroelectric Thin Films;45
7.1;1 Introduction;45
7.2;2 Simulation Method Using the Wang-Landau Algorithm;47
7.3;3 Investigation of the Influence of Bulk Properties on the Surface Ones of Ferroelectric Systems;52
7.4;4 Effect of Thickness on the Magnitude of Spontaneous Polarization in Thin Ferroelectric Films;58
7.5;5 Modeling of Geometric and Optical Properties of Textured Coatings of Steel Sheet with Anisotropic Defects;63
7.6;6 Conclusion;67
7.7;References;69
8;Diffraction of the High-Frequency Waves by Arrays of Obstacles in the Two-Dimensional Elastic Medium, with Multiple Reflections and Transformations;71
8.1;1 Introduction;71
8.2;2 Problem Formulation;72
8.3;3 Method of Solution;72
8.4;4 The Study of the Problem in the Local Formulation;72
8.5;5 Two-Fold Reflection of Elastic Waves on the Plane Contours of Obstacles Taking into Account Possible Transformations;74
8.6;6 Multiple Reflections with All Possible Transformations of Elastic Waves;81
8.7;7 Conclusion;82
8.8;References;83
9;The Mixed Boundary Conditions Problem of Layered Composites with Meta-Surfaces in Electro Elasticity;85
9.1;1 Introduction;86
9.2;2 Basic Linear Relations of Electro Elasticity for Piezoelectric Materials;88
9.3;3 Mathematical Modeling of the Metasurfaces by the Introduction of Magneto Elastic Layered Systems Hypotheses (Hypothesis MELS);90
9.3.1;3.1 The Connection of Two Piezoelectric Layers with Rough Surfaces with the Other Piezoelectric Thin Layer (Model–1);90
9.3.2;3.2 Smoothing the Roughness of the Surfaces of the Piezoelectric Layer by Pouring Different Materials (Model–2);94
9.3.3;3.3 The Propagation of High-Frequency Shear Elastic Waves on Interface of Isotropic Elastic Half-Spaces with Canonical Surface Protrusions (Model–3);100
9.4;4 Conclusion;106
9.5;References;107
10;A Comparative Analysis of Wave Properties of Finite and Infinite Cascading Arrays of Cracks;109
10.1;1 Introduction;109
10.2;2 Problem Formulation;110
10.3;3 Infinite Periodic System. Anti-plane Problem;111
10.4;4 Infinite Periodic System. Plane Problem;114
10.5;5 Finite Periodic System. Scalar Formulation;116
10.6;6 Numerical Analysis;119
10.7;7 Conclusions;122
10.8;References;123
11;Homogenization of Piezoelectric Composites with Internal Structure and Inhomogeneous Polarization in ACELAN-COMPOS Finite Element Package;125
11.1;1 Introduction;126
11.2;2 Homogenization of Piezoelectric Composites;127
11.3;3 Some Models of Inhomogeneous Polarization for Piezoelectric Composites;129
11.4;4 ACELAN-COMPOSE Package Structure;133
11.4.1;4.1 Software Package Concept;133
11.4.2;4.2 Material Editor;134
11.4.3;4.3 Representative Volume Element Models;135
11.4.4;4.4 Finite Elements, Solvers, and Postprocessing;137
11.5;5 Numerical Examples;138
11.6;6 Conclusion;141
11.7;References;141
12;Three-Dimensional Problems of Harmonic Wave Propagation in an Elastic Layer;144
12.1;1 Introduction;144
12.2;2 Problem Statement;144
12.3;3 Harmonic Waves Representation;145
12.4;4 Navier Conditions at the Second Surface;147
12.5;5 Boundary Conditions of Sliding Contact and Clamped Edge at the Second Surface;149
12.6;6 Conclusion;151
12.7;References;152
13;The Experimental Study of a Metamaterial with a Triple-Periodic Microstructure on the Epoxy Base;153
13.1;1 Introduction;153
13.2;2 Materials and Samples;154
13.3;3 Results of the Experiments;157
13.4;4 Conclusion;160
13.5;References;162
14;On the Equations of the Surface Elasticity Model Based on the Theory of Polymeric Brushes;163
14.1;1 Introduction;164
14.2;2 Polymeric Brush and Its Mechanical Interpretation;164
14.3;3 Surface Energy of a Beam-Lattice-Type Coating;166
14.4;4 Equilibrium Conditions;168
14.5;5 Conclusions;169
14.6;References;169
15;Finite Element Study of Ceramic Matrix Piezocomposites with Mechanical Interface Properties by the Effective Moduli Method with Different Types of Boundary Conditions;172
15.1;1 Introduction;173
15.2;2 Formulation of Homogenization Problems;174
15.3;3 Representative Volumes and Finite Element Models;180
15.4;4 Numerical Results;182
15.5;5 Concluding Remarks;185
15.6;References;186
16;A Far-Field Asymptotic Analysis in the High-Frequency Diffraction by Cracks;189
16.1;1 Introduction;189
16.2;2 Anti-plane Diffraction Problem;190
16.3;3 Anti-plane Diffraction Problem for Interface Crack;191
16.4;4 In-Plane Diffraction Problem;197
16.5;5 Results and Conclusions;199
16.5.1;5.1 Anti-plane Problem in Homogeneous Medium;199
16.5.2;5.2 Anti-plane Problem for Interface Crack;199
16.5.3;5.3 In-Plane Problem;200
16.5.4;5.4 General Conclusions;205
16.6;References;205
17;3d Propagation of Ultrasonic Waves Through a System of Defects in an Elastic Material, with Arbitrary Reflections and Transformations;207
17.1;1 Introduction;207
17.2;2 Formulation of the Three-Dimensional Local Problem;208
17.3;3 Method of Solution;208
17.4;4 Multiple Re-reflections of the Longitudinal Wave;211
17.5;5 Multiple Reflections with Periodic Transformation of Elastic Waves;216
17.6;6 Multiple Reflections with All Possible Transformations of Elastic Waves;219
17.7;7 Conclusion;222
17.8;References;222
18;Numerical Investigation of Effective Moduli of Porous Elastic Material with Surface Stresses for Various Structures of Porous Cells;224
18.1;1 Introduction;224
18.2;2 Mathematical Problem Statement;225
18.3;3 Finite Element Results and Discussion;228
18.4;References;233
19;Electro-Magneto-Elastic Coupled Waves in Piezoactive Periodic Structures;236
19.1;1 Introduction;236
19.2;2 General Relations and Equations of MEE Media;237
19.3;3 Magneto-Electro–Elastic Polariton Coupling in a Periodic Structure;241
19.4;4 Numerical Analysis and Results;244
19.5;5 Conclusion;246
19.6;References;246
20;Non-linear Dynamics of Pantographic Fabrics: Modelling and Numerical Study;248
20.1;1 Introduction;248
20.2;2 2-Dimensional Finite Deformations Strain Gradient Elasticity;249
20.3;3 Weak Form Problem and Numerical Simulations;252
20.4;4 Conclusions;257
20.5;References;257