Recent Advances in Mechanics - Selected Papers from the Symposium on Recent Advances in Mechanics, Academy of Athens, Athens, Greece, 17-19 September, 2009, organised by the Pericles S. Theocaris Foundation in Honour of P. S. Theocaris, on the Tenth

Title

Preface

Biography

Contents

Contributors

Part I Mathematical Methods in Applied Mechanics

Application of Reciprocity Relations to Laser-Based Ultrasonics

Introduction

Thermo-anisotropic Elasticity

Reciprocity Theorem

Transverse Isotropy with Depth Dependent Properties

Heating of the Boundary

Surface Waves due to Laser Irradiation

References

An Asymptotic Method of Boundary-Value Problems Solution of Elasticity Theory for Thin Bodies

Introduction

The Asymptotic Solution of the First Boundary Value Problem of Elasticity Theory for the Orthotropic Thermoelastic Strip: The Connection with the Classical Theories of Beams and Bars

Conjugation of the Inner Problem and the Boundary Layer Solutions: Proof of Validity of Saint-Venant Principle

The Solution of the Second and Mixed Space Boundary-Value Problem for Thin Bodies

Solutions of Plane and Space Dynamic Problems

Conclusions

References

Reliable Optimal Design in Contact Mechanics

Introduction

Formulation of the Problem

Finding of the Optimal Pressure Distribution

Determination of the Optimal Punch Shape

Conclusions

References

Scaling of Strength and Lifetime Distributions of Quasibrittle Structures

Introduction

Failure Statistics of Nano-structure

Multi-scale Transition of Strength Statistics

Lifetime Distribution of One RVE

FiniteWeakest Link Model and Optimum Fits of Histograms

Size Effect on Mean Structural Strength and Lifetime

Conclusion

References

Directional Distortional Hardening in Plasticity within Thermodynamics

Introduction

Mathematical Formulation of Models

Model Performance

Ratchetting

Conclusion

References

Forced Vibrations of the System: Structure – Viscoelastic Layer

Introduction

Investigation and Analysis of the FFM Vibrations

Conclusion

References

Extreme Instability Phenomena in Autonomous Weakly Damped Systems: Hopf Bifurcations, Double Pure Imaginary Eigenvalues, Load Discontinuity

Introduction

Basic Equations

Conservative Systems

Conditions for Dynamic Bifurcation

Approximate Technique: |C|<-e^{2} for e.0

.on-conservative Systems

Li\'{e}nard-Chipart Stability Criterion

Symmetrization of Asymmetric Matrices

Numerical Results

Conservative System (.=1)

Non Conservative Systems (..1)

Conclusions

References

Variational Approach to Static and Dynamic Elasticity Problems

Introduction

Statement of the Problems

Dynamical Formulation

Formulation for the Static Problem

The Method of Integrodifferential Relations

MIDR for Static Problems

MIDR for Dynamical Problems

Relations of the Dynamical Variational Principles

Dynamical Variational Principle in Displacements and Stresses

Numerical Algorithm and Error Analysis

3D Beam Lateral Motions

Numerical Results

Conclusions

References

An Accelerated Newmark Scheme for Integrating the Equation of Motion of Nonlinear Systems Comprising Restoring Elements Governed by Fractional Derivatives

Introduction

Fractional Derivative Estimation

Dual Mesh of the Time Domain

Accelerated Algorithm

Numerical Example

Numerical Results for Earthquake Excitation

Concluding Remarks

References

Part II Experimental Mechanics

Photoelastic Tomography as Hybrid Mechanics

Classical Tomography

Photoelastic Tomography

Linear Approximation in Integrated Photoelasticity

The Method of Decomposition

Algorithms of Hybrid Mechanics

Stresses due to External Loads

The Case of Residual Stresses in Glass

Conclusions

References

Using an Electronic Speckle Interferometry for Measurement of a Stress-Deformation State of Elastic Bodies and Structures

Introduction

Combined Methods of the ESPI and Blind-Hole Drilling

Calculating Models in the Blind-Hole Method

Experimental Studies of the Residual Stresses

Other Applications of Use ESPI

References

Structural Integrity and Residual Strength of Composites Exposed to Fire

Introduction

Temperature, Char Distribution and Thermal Buckling Analysis

Numerical Results

Experiments

References

Theory and Application of Sampling Moir\'{e} Method

Introduction

Theory of Moiré Method

Phase Analysis of Grating or Fringe Pattern

Measurement Method of Displacement and Strain by Phase Analysis of Moir\'{e} Fringe

Sampling Moire Method (Scanning Moire Method)

Background of Sampling Moir\'{e} Method

Process of Sampling Moiré Method Using 1-D Grating

Process of 2-D Displacement Analysis by Sampling Moiré Method Using 2-D Cross Grating

Deflection Measurement by Sampling Moiré Method

Experimental Setup and Grating Tape

Experimental Results of Deflection Measurement

Shape and Displacement Measurement by Sampling Moir\'{e} Method

Process of Measurement

Calibration with Two Reference Planes

Shape and Strain Distribution Measurement

Experimental Results of Shape and Strain Distributions of Rotating Object

Conclusions

References

Recent Advances in Microelectromechanical Systems and Their Applications for Future Challenges

Introduction

Representative MEMS Samples

ACES Methodology

Analytical Solution

Computational Solution

Optoelectronic Methodology

Representative Results

Motions of HRS Microengine

Deformations of a Microgyroscope

Deformations of a Pressure Sensor

Deformations of a Cantilever Microcontact

Conclusions and Future Work

References

Experimental Mechanics in Nano-engineering

Introduction and Theoretical Background

Properties of Evanescent Waves

Super-Resolution

Applications to Nanometrology

Observation of Nano-crystals and Nano-spheres

Generation of Multi-k Vector Fields

Formation of Holograms at the Nano-scale

Analysis of the Polystyrene Nano-spheres

Application of Surface Plasmon Resonance to Surface Roughness Topography

Generation of a Wide Spectrum of Frequencies due to Interaction between Evanescent Waves and Rough Surfaces

Application of the Model to the Analysis of Surface Topography

High Accuracy Measurements of Surface Topography

Determination of Contact Strains

Determination of the Contact Strains of a Small Cylinder

Summary and Conclusions

References

Advanced Cement Based Nanocomposites

Introduction

Applications of Nanotechnology in Cement Based Materials

Dispersion

Effect of CNTs/CNFs Type and Concentration

Nanomechanical Properties

Autogenous Shrinkage

A New Generation of Cement Based Materials-Conclusions

References

Application of Digital Speckle Pattern Interferometry (DSPI) in Determination of Elastic Modulus Using Plate Vibration

Introduction

Principle

Determination of Elastic Modulus Using the Concept of Plate Vibration

Theoretical Background of Time-Averaged Specklegrams

Interferogram Formation

Subtraction Fringe Formation

Experiments and Results

Conclusion

References

The Development and Applications of Amplitude Fluctuation Electronic Speckle Pattern Interferometry Method

Introduction

Principle of Time-Averaged ESPI Method

The Traditional TA ESPI Method

The AF ESPI Method

Experiments and Discussions

Engineering Applications of the AF ESPI Method

Conclusions

References

Part III Fracture Mechanics

Piezonuclear Transmutations in Brittle Rocks under Mechanical Loading: Microchemical Analysis and Geological Confirmations

Introduction

Neutron Emission Detection Techniques

\^{3}He Proportional Counter

Neutron Bubble Detectors

Preliminary Tests on Prismatic Specimens in Carrara Marble and Green Luserna Granite

Experimental Set-Up

Compression Tests under Monotonic Displacement Control

Compression Test under Cyclic Loading

Ultrasonic Test

Experimental Results

Compression Tests under Monotonic Displacement Control

Compression Test under Cyclic Loading

Ultrasonic Test

Compositional and Microchemical Evidence of Piezonuclear Fission Reactions in the Rock Specimens

EDS Results for Phengite

EDS Results for Biotite

Piezonuclear Reactions: From the Laboratory to the Earth Scale

Heterogeneity in the Composition of the Earth’s Crust: Fe and Al Reservoir Locations

Geochemical Evidence of Piezonuclear Reactions in the Evolution of the Earth’s Crust

Conclusions

References

Stress Triaxiality at Crack Tips Studied by Caustics

Introduction

Stress-Optical Equations

Plane Stress

Plane Strain

The Optical Method of Caustics

Experimental

Limits of Applicability of the Method of Caustics

Conclusions

References

Reinforcement of a Cracked Infinite Elastic Plate with Defects

Introduction

Reinforcement of a Cracked Plate with Stringers

Reinforcement of a Plate with a Patch

Linear Crack of Finite Size, the Lips of Which Are Connected with Elastic Springs

Linear Crack of Finite Size, with Transverse Loading, the Lips of Which Are Connected with Thin Inclusions

Reinforcement of the Crack Lips with Stringers and Elastic Springs

Conclusions

References

Some Actual Problems of Fracture Mechanics of Materials and Structures

Introduction

Classical and Non-classical Approaches

Griffith–Irwin Concept

Linear Fracture Mechanics

Non-linear Fracture Mechanics

Fatigue Crack Nucleation and Growth (Fatigue of Materials)

Interaction between Environments and Deformed Metal

References

Cyclic Plasticity with an Application to Extremly Low Cycle Fatigue of Structural Steel

Introduction

The Preisach Model of Hysteresis

The Preisach Model for Cyclic Behaviour of Ductile Materials

A Three-Element Unit

Ilustrative Example

Extremly Low Cycle Fatigue

Application and Testing of DC90 Dampers

Conclusions

References

The Fracture Toughness of a Highly Filled Polymer Composite

Introduction

Materials and Experiments

Experimental Results

Toughness Model

Analysis of Results

Discussion

Conclusions

References

Author Index