Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials (eBook)

Foreword 6
Contents 9
Contributors 11
On Anti-Plane Surface Waves Considering Highly Anisotropic Surface Elasticity Constitutive Relations 14
1 Introduction 14
2 Constitutive Relations 15
3 Anti-plane Motions of an Elastic Half-Space 17
4 Conclusions 20
References 21
Periodic Problem for a Plane Composed of Two-Layer Strips with a System of Longitudinal Internal Inclusions and Cracks 23
1 Introduction 23
2 Problem Statement and Derivation of the Governing Equations 24
3 Solution of the System of Governing Equations 28
3.1 Numerical Analysis 31
4 Conclusion 33
References 33
An Experimental Model of the Acoustic Wave Propagation Through a Cascading Triple-Periodic Array of Cylindrical Holes 35
1 Introduction 35
2 Applied Instrumentation 36
3 Results of the Measurements 40
4 Conclusion 41
References 43
Simulation of the Surface Structure of Ferroelectric Thin Films 45
1 Introduction 45
2 Simulation Method Using the Wang-Landau Algorithm 47
3 Investigation of the Influence of Bulk Properties on the Surface Ones of Ferroelectric Systems 52
4 Effect of Thickness on the Magnitude of Spontaneous Polarization in Thin Ferroelectric Films 58
5 Modeling of Geometric and Optical Properties of Textured Coatings of Steel Sheet with Anisotropic Defects 63
6 Conclusion 67
References 69
Diffraction of the High-Frequency Waves by Arrays of Obstacles in the Two-Dimensional Elastic Medium, with Multiple Reflections and Transformations 71
1 Introduction 71
2 Problem Formulation 72
3 Method of Solution 72
4 The Study of the Problem in the Local Formulation 72
5 Two-Fold Reflection of Elastic Waves on the Plane Contours of Obstacles Taking into Account Possible Transformations 74
6 Multiple Reflections with All Possible Transformations of Elastic Waves 81
7 Conclusion 82
References 83
The Mixed Boundary Conditions Problem of Layered Composites with Meta-Surfaces in Electro Elasticity 85
1 Introduction 86
2 Basic Linear Relations of Electro Elasticity for Piezoelectric Materials 88
3 Mathematical Modeling of the Metasurfaces by the Introduction of Magneto Elastic Layered Systems Hypotheses (Hypothesis MELS) 90
3.1 The Connection of Two Piezoelectric Layers with Rough Surfaces with the Other Piezoelectric Thin Layer (Model–1) 90
3.2 Smoothing the Roughness of the Surfaces of the Piezoelectric Layer by Pouring Different Materials (Model–2) 94
3.3 The Propagation of High-Frequency Shear Elastic Waves on Interface of Isotropic Elastic Half-Spaces with Canonical Surface Protrusions (Model–3) 100
4 Conclusion 106
References 107
A Comparative Analysis of Wave Properties of Finite and Infinite Cascading Arrays of Cracks 109
1 Introduction 109
2 Problem Formulation 110
3 Infinite Periodic System. Anti-plane Problem 111
4 Infinite Periodic System. Plane Problem 114
5 Finite Periodic System. Scalar Formulation 116
6 Numerical Analysis 119
7 Conclusions 122
References 123
Homogenization of Piezoelectric Composites with Internal Structure and Inhomogeneous Polarization in ACELAN-COMPOS Finite Element Package 125
1 Introduction 126
2 Homogenization of Piezoelectric Composites 127
3 Some Models of Inhomogeneous Polarization for Piezoelectric Composites 129
4 ACELAN-COMPOSE Package Structure 133
4.1 Software Package Concept 133
4.2 Material Editor 134
4.3 Representative Volume Element Models 135
4.4 Finite Elements, Solvers, and Postprocessing 137
5 Numerical Examples 138
6 Conclusion 141
References 141
Three-Dimensional Problems of Harmonic Wave Propagation in an Elastic Layer 144
1 Introduction 144
2 Problem Statement 144
3 Harmonic Waves Representation 145
4 Navier Conditions at the Second Surface 147
5 Boundary Conditions of Sliding Contact and Clamped Edge at the Second Surface 149
6 Conclusion 151
References 152
The Experimental Study of a Metamaterial with a Triple-Periodic Microstructure on the Epoxy Base 153
1 Introduction 153
2 Materials and Samples 154
3 Results of the Experiments 157
4 Conclusion 160
References 162
On the Equations of the Surface Elasticity Model Based on the Theory of Polymeric Brushes 163
1 Introduction 164
2 Polymeric Brush and Its Mechanical Interpretation 164
3 Surface Energy of a Beam-Lattice-Type Coating 166
4 Equilibrium Conditions 168
5 Conclusions 169
References 169
Finite Element Study of Ceramic Matrix Piezocomposites with Mechanical Interface Properties by the Effective Moduli Method with Different Types of Boundary Conditions 172
1 Introduction 173
2 Formulation of Homogenization Problems 174
3 Representative Volumes and Finite Element Models 180
4 Numerical Results 182
5 Concluding Remarks 185
References 186
A Far-Field Asymptotic Analysis in the High-Frequency Diffraction by Cracks 189
1 Introduction 189
2 Anti-plane Diffraction Problem 190
3 Anti-plane Diffraction Problem for Interface Crack 191
4 In-Plane Diffraction Problem 197
5 Results and Conclusions 199
5.1 Anti-plane Problem in Homogeneous Medium 199
5.2 Anti-plane Problem for Interface Crack 199
5.3 In-Plane Problem 200
5.4 General Conclusions 205
References 205
3d Propagation of Ultrasonic Waves Through a System of Defects in an Elastic Material, with Arbitrary Reflections and Transformations 207
1 Introduction 207
2 Formulation of the Three-Dimensional Local Problem 208
3 Method of Solution 208
4 Multiple Re-reflections of the Longitudinal Wave 211
5 Multiple Reflections with Periodic Transformation of Elastic Waves 216
6 Multiple Reflections with All Possible Transformations of Elastic Waves 219
7 Conclusion 222
References 222
Numerical Investigation of Effective Moduli of Porous Elastic Material with Surface Stresses for Various Structures of Porous Cells 224
1 Introduction 224
2 Mathematical Problem Statement 225
3 Finite Element Results and Discussion 228
References 233
Electro-Magneto-Elastic Coupled Waves in Piezoactive Periodic Structures 236
1 Introduction 236
2 General Relations and Equations of MEE Media 237
3 Magneto-Electro–Elastic Polariton Coupling in a Periodic Structure 241
4 Numerical Analysis and Results 244
5 Conclusion 246
References 246
Non-linear Dynamics of Pantographic Fabrics: Modelling and Numerical Study 248
1 Introduction 248
2 2-Dimensional Finite Deformations Strain Gradient Elasticity 249
3 Weak Form Problem and Numerical Simulations 252
4 Conclusions 257
References 257