Dynamics, Strength of Materials and Durability in Multiscale Mechanics

Contents
1 Modeling Fatigue Life of Structural Alloys Under Block Asymmetric Loading
1.1 Introduction
1.2 Constitutive Equations of MDM
1.2.1 Constitutive Equations in Plasticity
1.2.2 Evolutionary Equations Describing Fatigue Damage Accumulation
1.2.3 Strength Criterion of Damaged Material
1.3 Numerical Results
1.3.1 Block-Type Asymmetric Soft Cyclic Loading
1.3.2 Multi-axial Proportional and Non-proportional Regimes of Soft Block-Type Cyclic Loading
1.3.3 Hard Block-Type Asymmetric Low-Cycle Loading
1.4 Conclusion
References
2 Excitation of the Waves with a Focused Source, Moving Along the Border of Gradient-Elastic Half-Space
2.1 Introduction
2.2 The Basic Equations of Gradient Theory of Elasticity
2.3 The Statement and Solution to the General Problem of Waves Propagation in Gradient-Elastic Medium
2.4 The Statement and Solution to the Problem of a Gradient-Elastic Medium with a Moving Source Generating Surface Waves
2.4.1 The Subsonic Case
2.4.2 The Supersonic Case
2.5 Conclusion
References
3 On the Spectrum of Relaxation Times in Coupled Diffusion and Rheological Processes in Metal Alloys
3.1 Introduction
3.2 The Brassart’s Model Supplemented with Elastic Strains
3.2.1 Deformation and Volumetric Expansion
3.2.2 Free Energy
3.2.3 Thermodynamic Inequality
3.2.4 Elastic Relations and Functions of State
3.2.5 Kinetic Equations
3.2.6 Balance Equations
3.3 Analysis of Relaxation of Spatial Perturbations
3.3.1 Model Problem
3.3.2 Field Equations
3.3.3 Perturbed System and Its Analysis
3.3.4 The Relaxation Time of Perturbations and Their Asymptotics
3.4 Conclusion
References
4 Finite Element Method Study of the Protection Damping Elements Dynamic Deformation
4.1 Introduction
4.2 Constitutive System of Equations and Problem Solution Method
4.2.1 MHS Filler Modeling
4.2.2 Finite Element Analysis
4.3 Results of Computational Experiments
4.4 Conclusion
References
5 Analyzing the Problem of a Spherical Cavity Expansion in a Medium with Mohr-Coulomb-Tresca’s Plasticity Condition
5.1 Introduction
5.2 Formulation of an Initial Boundary-Value Problem for a System of Partial Differential Equations
5.3 Formulating a Boundary-Value Problem for a System of Two First-Order Ordinary Differential Equations in the Plastic Region
5.4 Formulation and Solution of the Boundary-Value Problem for Second-Order ODE’s in the Elastic Deformation Region
5.5 Determining the Critical Pressure
5.6 An Analytical Solution of the Cavity Expansion Problem in a Medium with a Linear Shock Adiabat
5.7 Determining Stresses in a Medium with the Mohr-Coulomb Yield Condition
5.8 Determining Stress in a Medium with Mohr-Coulomb-Tresca’s Yield Condition
5.9 Comparative Analysis of the Results of Analyzing the Cavity Problem in Media with Tresca’s, Mohr-Coulomb, and Mohr-Coulomb-Tresca’s Plasticity Conditions
5.10 Conclusion
References
6 Construction of the Solutions of Non-stationary Dynamic Problems for Linear Viscoelastic Bodies with a Constant Poisson’s Ratio
6.1 Introduction
6.2 Mathematical Statement of Problem
6.3 Representation of the Problem in Transform Domain
6.4 Example
6.5 Notes and Comments
References
7 Features of Subsonic Stage of Contact Interaction of Viscoelastic Half-Plane and Absolutely Rigid Striker
7.1 Introduction
7.2 Problem Statement
7.3 Green Function Construction
7.4 Contact Problem Solution Algorithm
7.5 Example
References
8 Interaction of Harmonic Waves of Different Types with the Three-Layer Plate Placed in the Soil
8.1 Introduction
8.2 Problem Statement of Interaction of Harmonic Spherical Wave Propagating in Continuum and a Three-Layered Plate
8.3 Motion Equation of Soil
8.4 Incoming Wave
8.5 The Plate Geometry
8.6 Conditions on the Contact Surface
8.7 Fourier Decomposition of Unknown Functions
8.8 Computing of the Fourier Coefficients for the Potentials in Ambient Media
8.9 Example
8.10 Notes and Comments
References
9 Computer Simulation of the Process of Loss of Stability of Composite Cylindrical Shells Under Combined Quasi-static and Dynamic Loads
9.1 Introduction
9.2 Problem Formulation and Solution Method
9.3 Results of Research
9.3.1 Internal Pressure
9.3.2 External Pressure
9.4 Conclusion
References
10 The Effect of Preheating on the Thermoelastic Structurally Inhomogeneous Medium Spectral Properties in the Presence of an Initial Strain
10.1 Introduction
10.2 Formulation of the Problem
10.3 The 3D Linear Thermoelasticity Equations
10.4 The Plane Surface Waves
10.5 Results Discussion
References
11 Numerical Evaluation of Integrals in Laplace Domain Anisotropic Elastic Fundamental Solutions for High Frequencies
11.1 Introduction
11.2 Fundamental Solutions
11.3 Evaluation of Integrals I1 [,τ] and I2 [,τ]
11.4 Numerical Example and Discussions
11.4.1 Numerical Example Explanation
11.4.2 Computations
11.4.3 Discussion
References
12 The Dynamics of Eccentric Vibration Mechanism (Part 2)
12.1 Introduction
12.2 Problem Setting
12.3 The Phase Space
12.4 Investigation of Nonlinear Dynamics of the Mechanism Using the Method of Point Transformations.
12.5 The Numerical Study of the Dynamics of the Mechanism
12.5.1 The Region of Existence and Stability of Periodic Motions
12.5.2 Coordinate Dependencies of Fixed Points on Frequency Parameter
12.5.3 Bifurcation Diagrams
12.5.4 The Analysis of the Diagrams and Stability Regions
12.6 Conclusion
References
13 High Strain Rate Tension Experiments Features for Visco-Plastic Materials
13.1 Introduction
13.2 Split Hopkinson bar Technique
13.3 High Strain Rate Tension Based on Measuring Bars Techniques
13.3.1 Schemes for Dynamic Tension Experiments
13.3.2 Experimental Setups
13.3.3 True Stresses and Strains in the Tension Experiments
13.4 True Stress–Strain Determination from the Tension Experiments Data
13.4.1 The Models for Estimation of Stress and Strains in Neck
13.4.2 Numerical Analysis
13.4.3 Experimental and Numerical Procedure of Construction a True Strain Curve According to Experiment on High-Speed Tension
13.4.4 Testing the Procedure on Experiments
13.5 Conclusion
References
14 Flocking Rules Governing Swarm Robot as Tool to Describe Continuum Deformation
14.1 Introduction
14.2 Tool Description
14.3 Results from Previous Works
14.4 Results for a Bending Beam
14.5 Future Work and Conclusion
References
15 Homogenization-Based Mechanical Behavior Modeling of Composites Using Mean Green Operators for Infinite Inclusion Patterns or Networks Possibly Co-continuous with a Matrix
15.1 Introduction
15.2 Effective (Piece-Wise) Linear Elastic-like Properties of Composites of the Matrix-Reinforced Type
15.3 Elementary Axial and Planar Alignments of Axially Symmetric or Fiber-like Elements
15.4 From Elementary Alignments to Bundles or Networks
15.5 Other Potential Application Extension Directions
15.5.1 From Linear to Nonlinear Behavior
15.5.2 From Elasticity-Type to Coupled Piezo-Type Properties
15.5.3 From Static to Dynamical Problems
15.6 Conclusion
Appendix
References
16 Strain Gradient Models for Growing Solid Bodies
16.1 Introduction
16.2 Evolution Laws for Growing Solid Bodies with Strain Gradient Effects
16.3 Micromechanical Second Gradient Models for Bone Growth in the Framework of Thermodynamics of Irreversible Processes
16.4 Formulation of Different Classes of Enhanced Growth Models: Standard Strain Gradient Growth, Strain Gradient Materials with Growth, Gradient of Internal Variable Approach of Growth
16.4.1 Standard Strain Gradient Growth Model
16.4.2 Strain Gradient Growth Model with Growth Strain as an Additional DOF
16.4.3 Gradient of Growth Model
16.5 Conclusion
References
17 Microplane Modeling for Inelastic Responses of Shape Memory Alloys
17.1 An Introduction to the Basics of Microplane Modeling
17.2 Microplane Modeling of Shape Memory Alloys
17.2.1 Introduction of Tension–Compression Asymmetry
17.2.2 Modeling Plasticity and Cyclic Responses
17.3 Conclusions
References
18 A Plausible Description of Continuum Material Behavior Derived by Swarm Robot Flocking Rules
18.1 Introduction
18.2 The Origin of the Problem
18.3 The Algorithm
18.4 Some Examples
18.5 Future Work
18.6 Conclusion
References
19 Mud Shrinkage and Cracking Phenomenon Experimental Identification Using Digital Image Correlation
19.1 Introduction
19.2 Basic Notions—Hypotheses and Soil–Water Characteristic Curve
19.3 Characterization of Free Shrinkage Development
19.3.1 Material and Methods
19.3.2 DIC Experimental Method and Principle of Measurement
19.3.3 Shrinkage Development in a Square Form Sample of Kaolin K13
19.4 Restrained Shrinkage and Stress Concentration
19.5 Cracks Initiation and Propagation in Opening Mode (Mode I)
19.6 Conclusions
References