Advanced Materials Modelling for Mechanical, Medical and Biological Applications

Description

The book is devoted to the 70th birthday of Prof. Sergey M. Aizikovich, which will celebrated on August 2nd 2021. His scientific interests are related to the following topics: Mechanics of contact interactions, Functionally graded materials, Mechanics of fracture, Integral equations of mathematical physics, Inverse problems of the theory of elasticity, and Applications of elasticity to biological and medical problems of mechanics of materials. The papers, collected in the book, are contributions of authors from 10 countries. Preface Contents Contributors 1 Estimate of Elastic Properties of Biological Tissues Using a Finite Element Methodology 1.1 Introduction 1.2 The Direct and Inverse Problems 1.2.1 Problem Formulation 1.2.2 Uniqueness 1.2.3 Weak Formulation of the Direct Problem 1.2.4 Weak Formulation of the Inverse Problem 1.3 Discrete Formulation 1.3.1 Discrete Direct Problem 1.3.2 Discrete Inverse Problem 1.4 Numerical Results 1.5 Discussion and Conclusion References 2 An Efficient Method for Describing Plane Strain Bending of Viscoplastic Sheets at Large Strains 2.1 Introduction 2.2 Statement of the Problem 2.3 General Solution 2.4 Method of Solution 2.5 Illustrative Example 2.6 Conclusions References 3 Using a Radio Interferometer for Measurement of the Dynamic Poisson’s Ratio of Wood 3.1 Introduction 3.2 Research Method 3.3 Test Results 3.4 Conclusions References 4 An Application of Thermal Analogy in Active Control Problems 4.1 Introduction 4.2 Thermal Analogy 4.3 Methodology Validation 4.4 Vibrations Control 4.5 Active Twist Analysis 4.6 Summary References 5 Pneumo-dynamic Experimental Setup for Studying the Behaviour of Structural Materials at Strain Rates of the Order of 100 1/s 5.1 Introduction 5.2 Experimental Setup Description 5.3 Numerical Analysis 5.4 Experimental Results 5.5 Conclusions References 6 Modeling Approaches for an Eyeball Deformation After Intravitreal Injection 6.1 Introduction 6.2 Problem Statement 6.3 Results and Discussion 6.4 Conclusion References 7 Numerical Simulation of the Dynamics of Three-Dimensional Anisotropic Bodies Based on Non-classical Boundary Integral Equations Under the Impact of a Shock Load 7.1 Introduction 7.2 Problem Statement and Solution Method 7.3 Boundary Element Discretization 7.4 Numerical Laplace Transform Inversion 7.5 Numerical Investigations 7.6 Conclusions References 8 Fracture Phenomena in Swarms 8.1 Introduction 8.2 Review and Development of the Model Used 8.2.1 A Brief Review of the Previous Model 8.2.2 The Model Developments Here Introduced 8.3 Numerical Simulations 8.3.1 Notations and Fracture Thresholds 8.3.2 Fractures with First Neighbors' Interaction 8.3.3 Fractures with Second Neighbors' Interaction 8.4 Conclusions References 9 Integral Equations in Semi-inverse Boundary Value Problems for an Elastic Strip 9.1 Introduction 9.2 Preliminaries 9.2.1 Kolosov–Muskhelishvili Formulas 9.2.2 Fourier Transforms 9.3 Problem Formulation 9.4 Fourier Solutions for the Semi-Inverse Boundary Value Problems for an Elastic Strip 9.5 Integral Equations 9.6 Conclusions References 10 Surface Wave Propagation in Elastic Half-Spaces with Periodic Coatings 10.1 Introduction 10.2 Mathematical Framework 10.3 Numerical Examples 10.4 Concluding Remarks References 11 Features of High-Speed Deformation and Fracture of Fine-Grained Concrete Under Tensile Stress 11.1 Introduction 11.2 Experimental Methods 11.3 Experimental Results Under Dynamic Direct Tension 11.4 Experimental Results for Dynamic Splitting 11.5 Conclusions References 12 Singularities in the Classical Elasticity Theory as Hidden Characteristics of a Non-Euclidean Model of a Continuous Medium 12.1 Introduction 12.2 Singularities of the Classical Elasticity Theory and the General Idea of Their Elimination 12.3 Nonsingular Solutions and Hidden Parameters for a System with Cylindrical Symmetry 12.4 Nonsingular Solutions and Hidden Parameters for a System with Spherical Symmetry 12.5 Conclusions References 13 Stress State of a Compound Plane with Interface Absolutely Rigid Inclusion and Crack Having Common Tip 13.1 Introduction 13.2 The Statement of the Problem and the Derivation of Governing Equations 13.3 Algorithm for Solving the Governing System of Equations 13.4 Numerical Analysis 13.5 Conclusions References 14 Finite Inflation of an Inhomogeneous Hyperelastic Cylindrical Membrane 14.1 Introduction 14.2 Non-linear Theory of Elastic Membranes 14.3 Pure Bending of Inhomogeneous Tube 14.4 Inflation 14.5 Conclusions References 15 Finite Element Analysis of Foam Models Based on Regular and Irregular Arrays of Cubic Open Cells Having Uniform or Normal Distributions 15.1 Introduction 15.2 Theoretical Aspects of the Homogenization Method 15.3 Description of the Algorithm for Constructing a Representative Volume 15.4 Numerical Results 15.5 Conclusions References 16 Effect of Atmosphere During Deposition on the Morphology, Mechanical Properties and Microfriction of Zr-Based Coatings 16.1 Introdution 16.2 Coatings Formation and Characterization 16.2.1 Coatings Formation 16.2.2 Coatings Characterization 16.3 Results 16.3.1 ZrN Coatings 16.3.2 ZrCN Coatings 16.4 Conclusion References 17 Flexomagneticity in Functionally Graded Nanostructures 17.1 Introduction 17.2 Mathematical Modeling 17.3 Solving Procedure 17.4 Results and Discussions 17.5 Conclusions References 18 An Iterative Technique for Rational Approximation of Laplace Domain Vector-Valued Functions 18.1 Introduction 18.2 Vector Fitting Technique 18.3 Iterative Algorithm for Vector Functions Approximation 18.4 Numerical Examples 18.5 Conclusions References 19 Advances in Modeling and Identification of Prestresses in Modern Materials 19.1 Introduction 19.2 Direct Problem on Vibrations of a Prestressed Plane Region 19.3 First-Type Inverse Problems on Prestress Reconstruction 19.3.1 On the Uniqueness of the Prestress Field Reconstruction for the First Inverse Problem Statement 19.3.2 Approach to Reconstruction of an Inhomogeneous Prestress State in a Plane Region Using the Cauchy Problems 19.3.3 Level Restoration of the Inhomogeneous Prestress State 19.4 Second-Type Inverse Problems on Prestress Reconstruction 19.4.1 Restoration of Small Prestress Components 19.4.2 Iterative-Regularization Scheme 19.5 Conclusions References 20 Three-Dimensional Dynamic Response of a Cylindrical Cavity in a Half-Space of Partially Saturated Soil Under Internal Step-Loading 20.1 Introduction 20.2 Poroelastic Model 20.3 Boundary Element Method Framework 20.4 Laplace Transform Inversion 20.5 Numerical Results and Analysis 20.6 Concluding Remarks References 21 Correlating the Mechanical Properties to the Mineral Density of Brown Spot Lesion in Dentine Using Nanoindentation and X-ray Micro-tomography 21.1 Introduction 21.2 Materials and Methods 21.3 Results and Discussion 21.4 Conclusion References 22 Characterization of Physical Properties of a Porous Material in Terms of Tortuosity of the Porous Space: A Review 22.1 Introduction: The Concept of Tortuosity 22.2 Micromechanical Meaning of Tortuosity 22.2.1 Electrical Resistivity Contribution Tensors 22.2.2 Non-interaction Approximation 22.2.3 Differential Scheme 22.2.4 Effective Field Method 22.3 Variational Bounds in Terms of Tortuosity 22.4 Cross-Property Connections Between Overall Electric Conductivity and Fluid Permeability of a Random Porous Media with Conducting Skeleton 22.4.1 Cross-Property Bounds 22.4.2 Explicit Cross-Property Connections 22.5 Connection Between Electrical Conductivity and Mass Transport Coefficient of a Conductive Porous Material Filled with Electrolyte 22.5.1 Two-Phase Material with Conductive Constituents: Replacement Relations for Electrical Conductivity 22.5.2 Connection Between Electric Conductivity and Diffusion Coefficient 22.5.3 Computer Simulation 22.6 Concluding Remark References 23 Effective Viscoelastic Properties of Chiral Structures with Hierarchy 23.1 Introduction 23.2 Theoretical Considerations 23.3 Numerical Considerations 23.4 Results and Discussion 23.5 Conclusions References 24 Method for Determining the Parameters of the Exponential Shear Modulus of a Functional-Gradient Half-Space 24.1 Introduction 24.2 Statement and General Plan for Solving the Main Task of the Research 24.3 Statement of the Pure Shear Problem for a Functional-Gradient Half-Space 24.4 Integral Equation of the Problem 24.5 Analytical Solution of the Contact Problem 24.6 Determination of d and 0 by Shear Contact Stresses 24.7 Area of Uniqueness of Determination of the Parameter d from Contact Stresses 24.8 Determination of d and 0 from Surface Displacements Outside the Contact Area 24.9 Areas of Uniqueness of d for Determining the Displacements of the Free Surface 24.10 Formula for Calculation d 24.11 Discussion of Some Generalizations 24.12 Conclusions Appendix 1: Asymptotic Solution of the Integral Equation (24.4.7) in the Range 0