EXPERIMENTAL MECHANICS OF SOLIDS -- About the Authors -- Preface -- Foreword -- 1 Continuum Mechanics - Historical Background -- 1.1 Definition of the Concept of Stress -- 1.2 Transformation of Coordinates -- 1.3 Stress Tensor Representation -- 1.3.1 Two Dimensional Case -- 1.4 Principal Stresses -- 1.4.1 How to Calculate Principal Stresses after Making the Transformation -- 1.4.2 Maximum and Minimum Shear Stresses -- 1.5 Principal Stresses in Two Dimensions -- 1.6 The Equations of Equilibrium -- 1.7 Strain Tensor -- 1.8 Stress - Strain Relations -- 1.8.1 Homogeneous or Not? -- 1.8.2 Material Coordinate System -- 1.8.3 Linear, Elastic, Isotropic Materials. Lamé Constants -- 1.9 Equations of Compatibility -- References -- 2 Theoretical Stress Analysis - Basic Formulation of Continuum Mechanics. Theory of Elasticity -- 2.1 Introduction -- 2.2 Fundamental Assumptions -- 2.3 General Problem -- 2.3.1 Boundary Conditions -- 2.4 St. Venant's Principle -- 2.5 Plane Stress, Plane Strain -- 2.5.1 Solutions of Problems of 2D Using the Airy's Stress Function -- 2.6 Plane Stress Solution of a Simply Supported Beam with a Uniform Load -- 2.7 Solutions in Plane Strain and in Plane Stress -- 2.8 The Plane Problem in Polar Coordinates -- 2.9 Thick Wall Cylinders -- References -- 3 Strain Gages - Introduction to Electrical Strain Gages -- 3.1 Strain Measurements - Point Methods -- 3.2 Electrical Strain Gages -- 3.3 Basics of Electrical Strain Gages -- 3.3.1 Backing Material -- 3.3.2 Cements -- 3.3.3 Application of Gages onto Surfaces -- 3.4 Gage Factor -- 3.4.1 Derivation of Gage Factor -- 3.4.2 Alloys for Strain Gages -- 3.4.3 Semiconductor Strain Gages -- 3.5 Basic Characteristics of Electrical Strain Gages -- 3.5.1 Electrical Resistance -- 3.5.2 Temperature Effect -- 3.5.3 Corrections for Thermal Output -- 3.5.4 Adjusting Thermal Output for Gage Factor.

3.6 Errors Due to the Transverse Sensitivity -- 3.6.1 Corrections Due to the Transversal Sensitivity -- 3.7 Errors Due to Misalignment of Strain Gages -- 3.8 Reinforcing Effect of the Gage -- 3.9 Effect of the Resistance to Ground -- 3.10 Linearity of the Gages. Hysteresis -- 3.11 Maximum Deformations -- 3.12 Stability in Time -- 3.13 Heat Generation and Dissipation -- 3.14 Effect of External Ambient Pressure -- 3.14.1 Additional Consideration Concerning the Effect of Pressure on Strain Gages -- 3.14.2 Additional Environment Effects to Consider -- 3.14.3 Electromagnetic Fields -- 3.15 Dynamic Effects -- 3.15.1 Transient Effects -- 3.15.2 Steady State Response. Fatigue Characteristics of Strain Gauges -- References -- 4 Strain Gages Instrumentation - The Wheatstone Bridge -- 4.1 Introduction -- 4.1.1 Derivation of the Wheatstone Equilibrium Condition -- 4.1.2 Full Bridge Arrangements in Some Simple Cases of Loadings -- 4.1.3 Linearity Errors of the Wheatstone Bridge with Constant Voltage -- 4.1.4 Temperature Compensation in the Bridge Circuit -- 4.1.5 Leadwire Resistance/Temperature Compensation -- 4.1.6 Shunt Calibration of Strain Gage Instrumentation -- 4.1.7 Series Resistance Null Balance -- 4.1.8 Available Commercial Instrumentation -- 4.1.9 Dynamic Measurements -- 4.1.10 Potentiometer Circuit -- 4.1.11 Operational Amplifiers -- References -- 5 Strain Gage Rosettes: Selection, Application and Data Reduction -- 5.1 Introduction -- 5.1.1 Strain Gages Rosettes -- 5.1.2 Data Analysis of the Strain Gage Rosettes -- 5.2 Errors, Corrections, and Limitations for Rosettes -- 5.3 Applications of Gages to Load Cells -- References -- 6 Optical Methods - Introduction -- 6.1 Historical Perspective and Overview -- 6.1.1 Greek and Hellenistic Theories -- 6.1.2 Middle Eastern Theories -- 6.1.3 Western Theories (1600s-1800s).

6.1.4 Western Theories (1900s-Present) -- 6.2 Fundamental Basic Definitions of Optics -- 6.2.1 Wave-Particle Duality -- 6.3 The Electromagnetic Theory of Light -- 6.3.1 Cartesian Coordinates System Solutions of Maxwell Equations -- 6.4 Properties of Polarized Light -- 6.5 The Jones Vector Representation -- 6.6 Light Intensity -- 6.7 Refraction of the Light -- 6.7.1 Fresnel Equations -- 6.7.2 Total Internal Reflection -- 6.7.3 Evanescent Field -- 6.8 Geometrical Optics. Lenses and Mirrors -- 6.8.1 Lens Aberrations -- 6.8.2 Compound Thin Lenses -- 6.8.3 Curved Mirrors, Basic Relationships -- References -- 7 Optical Methods - Interference and Diffraction of Light -- 7.1 Connecting Light Interference with Basic Optical Concepts -- 7.2 Light Sources -- 7.2.1 Phase Velocity and Group Velocity -- 7.3 Interference -- 7.3.1 Derivation of the Equations of Interference -- 7.4 Interferometers -- 7.4.1 Wave Front-Splitting Interferometers -- 7.4.2 Michelson Interferometer -- 7.4.3 The Mach-Zehnder Interferometer -- 7.4.4 The Fabry-Pérot Interferometer -- 7.4.5 Polariscopes -- 7.4.6 Concept of Phasor -- 7.5 Diffraction of the Light -- 7.5.1 Solutions of the Problem of an Aperture in the Field of Propagation of Light Wave Fronts -- 7.5.2 Fourier Transforming Property of Lenses -- References -- 8 Optical Methods - Fourier Transform -- 8.1 Introduction -- 8.2 Simple Properties -- 8.2.1 Linearity -- 8.2.2 Frequency Shifting -- 8.2.3 Space Shifting -- 8.2.4 Space Differentiation -- 8.2.5 Correlation and Convolution -- 8.2.6 Autocorrelation Function -- 8.2.7 The Parseval's Theorem -- 8.3 Transition to Two Dimensions -- 8.4 Special Functions -- 8.4.1 Dirac Delta -- 8.4.2 Comb Function -- 8.4.3 Rectangle Function -- 8.4.4 The Signum Function -- 8.4.5 Circle Function -- 8.5 Applications to Diffraction Problems -- 8.5.1 Rectangular Aperture -- 8.5.2 Circular Aperture.

8.6 Diffraction Patterns of Gratings -- 8.7 Angular Spectrum -- 8.8 Utilization of the FT in the Analysis of Diffraction Gratings -- 8.8.1 An Approximated Method to Describe the Diffraction Pattern of Gratings -- References -- 9 Optical Methods - Computer Vision -- 9.1 Introduction -- 9.2 Study of Lens Systems -- 9.3 Lens System, Coordinate Axis and Basic Layout -- 9.4 Diffraction Effect on Images -- 9.4.1 Examples of Pupils -- 9.5 Analysis of the Derived Pupil Equations for Coherent Illumination -- 9.6 Imaging with Incoherent Illumination -- 9.6.1 Coherent and Non Coherent Illumination. Effect on the Image -- 9.6.2 Criteria for the Selection of Lenses -- 9.6.3 Standard Nomenclatures -- 9.7 Digital Cameras -- 9.7.1 CCDs and CMOSs -- 9.7.2 Monochrome vs. Color Cameras -- 9.7.3 Basic Notions in the Image Acquisition Process -- 9.7.4 Exposure Time of a Sensor. Relationship to the Object Intensity -- 9.7.5 Sensor Size -- 9.8 Illumination Systems -- 9.8.1 Radiometry -- 9.8.2 Interaction of Light with Matter and Directional Properties -- 9.8.3 Illumination Techniques -- 9.9 Imaging Processing Systems -- 9.9.1 Frame Grabbers -- 9.10 Getting High Quality Images -- 9.10.1 Resolution -- 9.10.2 Perspective Errors -- References -- 10 Optical Methods - Discrete Fourier Transform -- 10.1 Extension to Two Dimensions -- 10.1.1 Windowing -- 10.2 The Whittaker-Shannon Theorem -- 10.3 General Representation of the Signals Subjected to Analysis -- 10.3.1 Signal Structure -- 10.3.2 Signal Information and Noise Presence in the Signal -- 10.3.3 Linear Filters -- 10.4 Computation of the Phase of the Fringes -- 10.4.1 Computation of the Phase. Signals in Quadrature -- 10.4.2 Phase Stepping Technique -- 10.4.3 Comparison between in-Quadrature and Phase Stepping Techniques of Phase Retrieval -- 10.4.4 Two Dimensional Phase Unwrapping -- 10.5 Fringe Patterns Singularities.

10.5.1 Fringe Dislocations -- 10.6 Extension of the Fringes beyond Boundaries -- References -- 11 Photoelasticity - Introduction -- 11.1 Introduction -- 11.2 Derivation of the Fundamental Equations -- 11.3 Wave Plates -- 11.3.1 Utilization of the Jones Notation to Characterize Wave Plates -- 11.4 Polarizers -- 11.5 Instrument Matrices -- 11.6 Polariscopes -- 11.6.1 Plane Polariscope -- 11.6.2 Circular Polariscope -- 11.7 Artificial Birefringence -- 11.7.1 Constitutive Equations -- 11.8 Polariscopes -- 11.8.1 Lens Polariscopes -- 11.8.2 Diffuse Light Polariscopes -- 11.9 Equations of the Intensities of the Plane Polariscope and the Circular Polariscope for a Stressed Plate -- References -- 12 Photoelasticity Applications -- 12.1 Calibration Procedures of a Photoelastic Material -- 12.1.1 Different Notations and Meaning for the Photoelastic Constant -- 12.2 Interpretation of the Fringe Patterns -- 12.3 Determination of the Fringe Order -- 12.3.1 Determination of Fractional Orders -- 12.3.2 Tardy Compensation Method -- 12.3.3 Séanarmont Compensation -- 12.3.4 Babinet and Babinet-Soleil Compensators -- 12.4 Relationship between Retardation Changes of Path and Sign of the Stress Differences -- 12.5 Isoclinics and Lines of Principal Stress Trajectories -- 12.6 Utilization of White Light in Photoelasticity -- 12.7 Determination of the Sign of the Boundary Stresses -- 12.7.1 Calibration of the Polariscope -- 12.7.2 Utilization of the FT Algorithms -- 12.7.3 Errors in the Application of the Full Field Method Utilizing the FT -- 12.8 Phase Stepping Techniques -- 12.9 RGB Photoelasticity -- 12.9.1 The RGB Method as a Multi-Channel Method for Phase Stepping -- 12.9.2 Observations on the Recorded Patterns -- 12.9.3 Effect of Dispersion on the Measured Values -- 12.9.4 Phase Stepping Utilizing Monochromatic Light -- 12.9.5 Phase Stepping Utilizing White Light.

12.10 Reflection Photoelasticity.