Mechanics of High-Contrast Elastic Solids: Contributions from Euromech Colloquium 626

Preface
Contents
1 Adjustment of Micro-structure Parameters of Aggregated Structures for Dynamic Modeling of Silica Aerogels
1.1 Introduction
1.2 Methodology
1.2.1 Diffusion-Limited Cluster–Cluster Aggregation (DLCA) Method
1.2.2 Derivation of the Dispersion Relation
1.3 Comparison of Analytical and Numerical Results
1.3.1 Testing of the Abaqus Code for a 3D Continuous Elastic Layer
1.3.2 Numerical Analysis of Cuboid DLCA Structure
1.4 Conclusions
References
2 3D Dynamic Problems for Three-Layered Shells with Delamination Between the Layers
2.1 Introduction
2.2 Forced Vibrations of a Three-Layered Shell When There is a Separation Between the Second and Third Layers
2.3 Numerical Calculation
2.4 Conclusion
References
3 On Some Methods Analysing Reinforced Materials and Structures
3.1 Preliminary Remarks
3.2 Simplest Models
3.3 Particle-Reinforced Composites
3.4 Spherical Inhomogeneity with Interphase
3.5 Summary and Outlook
References
4 High-Contrast Multi-layered Plates. Statics, Dynamics and Buckling
4.1 Introduction
4.2 The HCS Plate Model
4.2.1 Notations
4.2.2 In-Plane/Out-of-Plane Splitted Formulation
4.2.3 Scaling of Highly Contrasted Stratified Plates
4.2.4 Kinematics at the Leading Order
4.2.5 Strain and Stress State at the Leading Order
4.2.6 Balance Equations at the Leading Order
4.2.7 Synthesis
4.3 Features of High-Contrast Stratified Plates
4.3.1 Criteria of Relevant Model
4.3.2 Energy Balance and Boundary Conditions
4.3.3 Flexural Waves
4.3.4 Buckling
4.3.5 Plates with Soft Viscoelastic Layer
4.4 Generalization to Multi-layered Contrasted Plates
4.4.1 Plates with Three Stiff Layers
4.4.2 Plates with n Stiff Layers
4.5 Conclusion
References
5 Universal Representation of Dynamic Frequency Spectra for Canonical Generalised Quasicrystalline-Generated Waveguides
5.1 Introduction
5.2 Wave Propagation in Silver-Mean Quasicrystalline Waveguides
5.3 Universal Representation of the Frequency Spectrum
5.4 Canonical Configurations
5.5 Results
5.6 Conclusions
References
6 Overall Properties for Elastic Micropolar Heterogeneous Laminated Composites with Centro-symmetric Constituents
6.1 Introduction
6.2 Mathematical Formulation for Micropolar Media
6.3 Method of Solution: Local Problems and Effective Properties for Laminated Composites
6.4 Effective Coefficients of Centro-symmetric Multi-laminated Cosserat Media with Isotropic Constituents
6.5 Numerical Results
6.6 Conclusions
References
7 Free Localized Vibrations of a Thin Elastic Composite Panel
7.1 Introduction
7.2 Conclusions
References
8 Detection of a Hidden Sandy Layer in a Stratified Substrate by Dispersion Analysis
8.1 Introduction
8.2 Original Weiskopf Model for Sandy Material
8.3 Modified Weiskopf Model
8.3.1 Cubic Anisotropy
8.3.2 Relation Between Parameters
8.4 Dispersion Equation for Rayleigh–Lamb Waves
8.5 Dispersion Analyses
8.5.1 The Models
8.5.2 Dispersion Portraits
8.5.3 Sandiness Parameter Variation
8.6 Concluding Remarks
References
9 Tunable Static and Dynamic Responses of Soft Porous Phononic Crystals
9.1 Introduction
9.2 Two Designs
9.3 Simulations
9.3.1 Material Model and Basic Equations
9.3.2 Finite Deformation and Linear Wave Propagation Analysis
9.3.3 Numerical Results
9.4 Experimental Validation
9.4.1 Experiments on the First PnC
9.4.2 Experiments on the Second PnC
9.5 Conclusions
References
10 Blur Effect in a Multiple Particle Inverse Problem for Fiber-Reinforced Composites
10.1 Introduction
10.2 Boundary Value Problem for a Multiply Connected Domain
10.2.1 Constructive form of the Dirichlet-to-Neumann Operator
10.3 Discussion and Conclusion
References
11 Asymptotic Theory of Generalised Rayleigh Beams and the Dynamic Coupling
11.1 Introduction
11.2 A Generalised Rayleigh Beam
11.2.1 Model for a Generalised Rayleigh Beam
11.2.2 A Beam with a Resonant Microstructure: Derivation of the Generalised Rayleigh Beam
11.2.3 Solution for the Displacements
11.2.4 Dynamic Homogenisation versus Meso-scale Approximations: The Generalised Rayleigh Beam
11.3 Dispersive Properties of a Generalised Rayleigh Beam
11.3.1 Comparison of Dispersive Features of the Effective Continuum and the Periodic Medium
11.3.2 Wave Phenomena and Structure of Solutions to (11.22)
11.3.3 Dispersion Curves
11.4 Green's Matrix for the Generalised Rayleigh Beam
11.4.1 Closed form Representation of Γ
11.4.2 Flexural-Longitudinal Coupling of Waves
11.5 Conclusions
References
12 Higher-Order and Nonlocal One-Dimensional Thermal Lattices with Short- and Long-Range Interactions
12.1 Introduction
12.2 Analytical Solution to the Discrete Equation
12.3 Numerical Solution to the Discrete Equation
12.4 Analytical Solution to the Nonlocal Equation
12.5 Extension to p-Order Neighbor Equation
12.5.1 Analytical Solution
12.5.2 Numerical Solution
12.5.3 Nonlocal Length Scale Calibration
12.6 Results
12.7 Conclusion
References
13 Large Deformations and Stability of the Two-Bar Truss Under Vertical Loads
13.1 Introduction
13.2 Analytical Formulation
13.2.1 Material Models
13.3 Experimental Investigation
13.3.1 Uniaxial Tests for Rubber Characterization
13.3.2 Experimental Test on the von Mises Truss
13.4 Finite Element Simulation
13.5 Calibration of the Rubber Constitutive Model
13.6 Results and Discussion
13.6.1 Effect of Euler Buckling
13.7 Conclusions
References
14 Coupling Finite Element Method with Incremental Harmonic Balance Method for Analysis of Nonlinear Vibrations of Stepped Beams and Frames
14.1 Introduction
14.2 Equations of Motion of Beams
14.3 Spatial Discretization of the Beam Using Finite Elements
14.4 Incremental Harmonic Balance (IHB) Analysis of Periodic Vibrations of Beams
14.4.1 Fourier Series Describing the Periodic Response of the Beam
14.4.2 Application of the Newton-Raphson Iterative Procedure
14.4.3 Application of the Galerkin Procedure
14.5 Conclusion
References