Mechanics of Heterogeneous Materials

Preface I
Preface II
In Memory of Igor Sevostianov
Contents
1 Micromechanical Modeling of Non-linear Stress–Strain Behavior of Polycrystalline Microcracked Ceramics
1.1 Introduction
1.2 Materials and Experiments
1.2.1 β-Eucryptite Subjected to Cyclic Tensile Loading of Increasing Amplitude
1.2.2 Aluminum Titanate Subjected to Compressive Interrupted Loading
1.3 Micromechanical Explanation and Modeling
1.3.1 Uniaxial Compression
1.3.2 Uniaxial Tension
1.4 Concluding Remarks
References
2 Shamrovskii's Version of the Refined Dynamical Plate Theory
2.1 Introduction. Uflyand-Mindlin Theory: History of Question
2.2 Newton Polygon and Its Generalizations
2.3 The Idea of Shamrovskii's Algorithm
2.4 Shamrovskii’s Refined Plate Theory
2.5 Conclusion
2.6 Brief Biography of A. D. Shamrovskii
References
3 Time-Resolved Multifractal Analysis of Electron Beam Induced Piezoelectric Polymer Fiber Dynamics: Towards Multiscale Thread-Based Microfluidics or Acoustofludics
3.1 From Charging of the SEM Samples to the Formation of SAW Potential Contrasts and Micromechanical Local Movements in Piezoelectric Fiber Samples, Induced by the Acoustic Waves
3.2 The Possibility of Designing Electron Beam-Controlled Acoustofluidics, Including Electron Beam-Controlled Thread-Based Micro-Acoustofluidics
3.3 Methods for Studying the Dynamics of PVDF Fibers
3.4 Investigation of the Characteristic Dimensions of Piezoelectric Polymer Fibers
3.5 Results and Discussion
References
4 Simple Coarse-Grained Model of the Zebrafish Embryonic Aorta Suggesting the Mechanism Driving Shape Changes During Stem Cell Production
4.1 Introduction
4.2 The HSC Production Process in Zebrafish
4.3 Model of the Dorsal Aorta
4.4 Results and Discussion
4.5 Conclusion
References
5 Averaging-Based Approach to Toughness Homogenisation for Radial Hydraulic Fracture
5.1 Introduction
5.2 Problem Formulation
5.2.1 The Radial Model with Inhomogeneous Toughness
5.2.2 Form of the Material Toughness
5.2.3 Parameterising the Fracture Regime
5.2.4 Numerical Algorithm and Behaviour of the Key Parameters
5.3 Comparison of Homogenisation Strategies
5.3.1 The Maximum Toughness and Temporal-Averaging Approaches
5.3.2 Results for Balanced Toughness Distributions
5.3.3 Results for Unbalanced Layering
5.4 Conclusions
References
6 Towards Multi-Angle Multi-Channel Optical Porometry and Scanning Electron Microscopic Porometry of LDPE Composites Including Geotechnical Biodegradable Ones
6.1 Introduction
6.2 Materials and Methods
6.2.1 Materials and Sample Preparation
6.2.2 Dynamical Multi-Channel Multi-Angle Optical Porometry
6.2.3 Scanning Electron Microscopic Porometry
6.3 Results
6.3.1 Dynamic Multi-Channel Multi-Angle Optical Porometry
6.3.2 Scanning Electron Microscopic Porometry
6.4 Conclusions
References
7 Nonlinear Deformations of Anisotropic Elastic Bodies with Distributed Dislocations
7.1 Introduction
7.2 Input Relations
7.3 Cylindrical Tube with Distributed Dislocations
7.4 Numerical Results
7.4.1 Inflation
7.4.2 Hydrostatic Compression
7.5 Conclusion
References
8 Misfit Stress Relaxation at Boundaries of Finite-Length Tubular Inclusions Through the Generation of Prismatic Dislocation Loops
8.1 Introduction
8.2 Model
8.3 Results
8.4 Summary and Conclusions
References
9 A Numerical Determination of the Interactions Between Dislocations and Multiple Inhomogeneities
9.1 Introduction
9.2 Problem Formulation
9.3 Equivalent Inclusion Method for Inhomogeneity-Dislocation System
9.4 Interaction Energy and Force on Dislocation
9.5 Numerical Implementation of the EIM
9.6 Results and Discussions
9.6.1 The Interaction of a Screw Dislocation with a SiC/Ti–6Al–4V Inhomogeneity
9.6.2 Layered Inhomogeneities and Horizontally Distributed Dislocations
9.6.3 Layered Inhomogeneities and Vertically Distributed Dislocations
9.6.4 Multiple Circular Inhomogeneities Around a Dislocation
9.6.5 Multiple Elliptical Inhomogeneities Around a Dislocation
9.6.6 Multiple Rectangular Inhomogeneities Around a Dislocation
9.7 Conclusions
Appendix 1: The Solution of the Screw and Edge Dislocations
Edge Dislocation Solution in an Infinite Homogeneous Plane
Screw Dislocation Solution in an Anti-plane Shear Problem
Appendix 2: The Elementary Solution for a Rectangular Inclusion
A Notation for the Elementary Solution
The Elastic Field of a Rectangular Inclusion in an Infinite Plane
The Elastic Field of a Rectangular Inclusion in an Anti-plane Shear Problem
References
10 Numerical Simulations of Interface Propagation in Elastic Solids with Stress Concentrators
10.1 Introduction
10.2 Basic Relations for a Two-Phase Elastic Solid
10.3 Numerical Procedure and Its Verification
10.4 Numerical Results and Discussion
10.4.1 Evolution of the Interface Around a Circular Hole Under Tension
10.4.2 Phase Transformations Induced by a Stress Concentration at An Elliptical Hole
10.5 Conclusion
References
11 Effect of Gravity on the Dispersion and Wave Localisation in Gyroscopic Elastic Systems
11.1 Introduction
11.2 Passive Gyroscopic System under Gravity
11.2.1 Asymptotic Connection Between the Gyroscopic Pendulum and the Gyroscopic Flexural Beam
11.2.2 Dimensionless System of Equations: General Solution
11.2.3 Trajectories of the Gyropendulum
11.2.4 Gyropendulum Trajectories of Prescribed Shapes and Rotational Symmetry
11.2.5 Optimal Design of a Gyropendulum for Regular Polygonal Approximations
11.3 Active Gyroscopic Systems Subjected to Gravity
11.4 The Chain of Gyropendulums: Floquet-Bloch Waves
11.4.1 Floquet-Bloch Waves in a Chiral Chain Under Gravity
11.4.2 Illustrative Examples of Floquet-Bloch Waves
11.5 The Effect of Gravity on the Dynamic Green's Kernel
11.5.1 Construction of the Dynamic Green's Kernel
11.5.2 The Dynamic Response for Special Regimes Such as Stop Bands and Pass Bands
11.5.3 Illustration of the Effect of Gravity on the Elliptical Trajectories
11.6 Green's Matrix and Localised Defect Modes for the Case of No Pre-tension
11.6.1 Green's Matrix for a Chiral Lattice with No Pre-tension
11.6.2 Illustration of Exponentially Localised Defect Modes
11.7 Concluding Remarks
References
12 Controlling the Structure and Properties of Metal- and Polymer-Based Composites Fabricated by Combined 3D Methods
12.1 Introduction
12.2 The Ti–6Al–4V-Based Metal-Matrix Composites Built by Wire-Feed Electron Beam Additive Manufacturing
12.2.1 Problem Definition
12.2.2 Experimental
12.2.3 Results and Discussion
12.2.4 Conclusions to Sect. 12.2
12.3 The Structure and Properties of 3D Printed PEEK-Based Composites for Antifriction Applications
12.3.1 Problem Definition
12.3.2 Experimental
12.3.3 Results and Discussion
12.3.4 Comparison of the Characteristics of the “PEEK + 0.3%HA + 10%PTFE” Composites Fabricated by the HC and HDM Methods
12.3.5 Conclusions to Sect. 12.3
12.4 Evolution of the Functional Properties of Composites During the Formation of Intermediate Phases Between the Matrix and Inclusions
12.4.1 General Considerations
12.4.2 Research on Fe-Based Composites with Titanium Carbide Inclusions upon Their Laser-Beam Synthesis
12.4.3 The Behavior of the Ti–Al–C Composite Upon Its Synthesis
12.4.4 Mechanical Stresses Around the Diffusion Zone During the Synthesis of a Composite from Titanium and Carbon Powders
12.4.5 Conclusions to Sect. 12.4
References
13 Analysis of the Periodicity Cell Problems for the Fiber-Reinforced Plate and Applications
13.1 Homogenization Method as Applied to Fiber-Reinforced Plates. Linear Problems
13.2 Elastic Problem
13.2.1 Plates with Unidirectional Systems of Fibers
13.2.2 Plates with Unidirectional Systems of Channels
13.2.3 Plates with the Cross Reinforcements
13.3 Thermoelastic Problem
13.3.1 Plates with Unidirectional Systems of Fibers
13.3.2 Plates with the Cross Reinforcements
13.4 Non-Linear Problems
13.4.1 Fiber-Reinforced Plate
13.4.2 Plates with Unidirectional Systems of Channels
13.5 Applications of the Results of the Numerical Analysis
13.5.1 The Boundary Layers on the Top/bottom Surfaces of Inhomogeneous Plate
13.5.2 Wrinkling the Top/bottom Surfaces of Inhomogeneous Plates
13.5.3 The Representative Model of Multilayer Plate
13.5.4 The Strength of the Composite Plate
13.6 Conclusions
References
14 Boundary Layers at the Interface of Layers of Unidirectional Fibers in Fibrous Composites
14.1 Introduction
14.2 Contact and Connection
14.3 Boundary Layers
14.4 Calculation of Stress–strain State in a Fragment of a Composite Containing a Connection of Layers
14.5 Numerical Computations
14.6 Conclusions
References
15 Contact Problem for a Coating/Substrate Interface Crack Under Action of a Moving Punch. Statistical Model of Coating Delamination
15.1 Introduction
15.2 Formulation of a Contact Problem for Double Coated Half-Plane with an Interface Crack
15.3 Some Results for an Interface Crack
15.4 Statistical Model of Coating Delamination
15.5 Closure
References
16 Prediction of Dissipation in Electronic Components by Computing Electromagnetism
16.1 Introduction
16.2 Governing Equations
16.3 Weak Form for Computation
16.4 Computational Implementation
16.5 Conclusion
References
17 Integral Eshelby's Formulas for Generalized Continuum and Couple-Field Theories
17.1 Introduction
17.2 Second Gradient Theory of Continuum Media with Additional Internal Variables
17.3 Clapeyron's Theorem
17.4 Eshelby's Integral Formulas
17.5 Conclusions
References
18 Heterogeneous Contact Modelling and Analysis via Numerical Equivalent Inclusion Method
18.1 Introduction
18.2 Contact Theory for Heterogeneous Material
18.2.1 Equivalent Inclusion Method in Contact Problems
18.2.2 The Elementary Solution of the Elastic Field
18.2.3 Elementary Solution for Inclusion in Half-Space
18.3 Numerical Solutions for Contact of Heterogeneous Materials
18.3.1 Numerical EIM for Multiple Inhomogeneities
18.3.2 The Conjugate Gradient Method
18.3.3 Numerical Solutions for Distributed Inhomogeneities Under a Rough Surface
18.4 Numerical Studies on Heterogeneous Contact
18.4.1 Smooth Surface
18.4.2 Rough Contact
18.5 Extended Application for Heterogeneous Contact
18.5.1 Coated Material
18.5.2 Two Joined Quarter Spaces
18.6 Summary
Appendix 1: Response Primitive Functions of Half Space Contact Problem
Appendix 2: The Expression of the Primitive Functions in the Elementary Solution
The Explicit Expression of Tij
The Explicit Expression of Uij
References
19 Effective Engineering Constants for Micropolar Composites with Imperfect Contact Conditions
19.1 Introduction
19.2 Heterogeneous Problem Statement and Fundamental Equations
19.3 Asymptotic Homogenization Method and Effective Engineering Moduli for Periodic Laminated Micropolar Media
19.3.1 Effective Engineering Moduli
19.4 Numerical Results
19.4.1 Non-uniform Imperfect Interface
19.4.2 Uniform Imperfect Interface
19.5 Conclusions
References
20 The Mixed Problems of Poroelasticity for Rectangular Domains
20.1 Introduction
20.2 The Statement of the Poroelasticity Problems for Domains of Rectangular Shapes
20.3 Deriving the Exact Solution of the Stated Problem for the Poroelastic Finite Rectangular Domain
20.4 Deriving the Exact Solution of the Stated Problem for the Poroelastic Semi-infinite Rectangular Domain
20.5 The Behavior Features of Mechanical Characteristics and Pore Pressure in Rectangular Domains
20.5.1 The Behavior Features of Mechanical Characteristics and Pore Pressure in Finite Rectangular Domain
20.5.2 The Behavior Features of Mechanical Characteristics and Pore Pressure in Semi-infinite Rectangular Domain
20.6 Conclusions
References
21 Pore-Fluid Filtration by Squeezing a Fluid-Saturated Poroelastic Medium
21.1 Introduction
21.2 Statement of the Problem of Squeezing a Fluid-Saturated Poroelastic Material
21.3 Integral Equation of the Contact Problem
21.4 Analytical Solution of the Two-Dimensional Integral Equation
21.5 Dynamics of Fluid Extraction
21.6 Conclusion
References
22 2D Asymptotic Analysis of a Thin Elastic Beam with Density-Dependent Generalized Young's Modulus
22.1 Introduction
22.2 Statement of the Problem
22.3 Asymptotic Scaling
22.4 Two-Term Approximation
22.5 Refined 1D Equations
22.6 Concluding Remarks
References