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

Description

This book contains the most recent results in the area of strongly inhomogeneous composite structures, including layered materials as well as continua with microstructure. This collection of papers mainly arises from the Euromech Colloquium No. 626 on “Mechanics of High-Contrast Elastic Composites”. Focus is set on the peculiar mechanical behaviour caused by adjoining widely different structural elements (high contrast) in terms of material and/or geometrical properties. 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