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Mechanics of Solid Materials

Book Description

Elasticity, plasticity, damage mechanics and cracking are all phenomena which determine the resistance of solids to deformation and fracture. The authors of this book discuss a modern method of mathematically modelling the behaviour of macroscopic volume elements. The book is self-contained and the first three chapters review physical mechanisms at the microstructural level, thermodynamics of irreversible processes, mechanics of continuous media, and the classification of the behaviour of solids. The rest of the book is devoted to the modelling of different types of material behaviour. In each case the authors present characteristic data for numerous materials, and discuss the physics underlying the phenomena together with methods for the numerical analysis of the resulting equations.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Contents
  6. Foreword to French edition
  7. Foreword to English edition
  8. Introduction
  9. Notation
  10. 1. Elements of the physical mechanisms of deformation and fracture
    1. 1.1 Metals and alloys
      1. 1.1.1 Structure
      2. 1.1.2 Physical mechanisms of deformation
      3. 1.1.3 Physical mechanisms of fracture
    2. 1.2 Other materials
      1. 1.2.1 Polymers
      2. 1.2.2 Granular material: concrete
      3. 1.2.3 Wood
      4. Bibliography
  11. 2. Elements of continuum mechanics and thermodynamics
    1. 2.1 Statement of the principle of virtual power
      1. 2.1.1 Motion and virtual power
      2. 2.1.2 Frames of reference and material derivatives
      3. 2.1.3 Principle of virtual power
    2. 2.2 Method of virtual power
      1. 2.2.1 Rates of strain and stress
      2. 2.2.2 Equations of equilibrium
      3. 2.2.3 Strains and displacements
      4. 2.2.4 Tensorial representation: invariants
    3. 2.3 Fundamental statements of thermodynamics
      1. 2.3.1 Conservation laws; first principle
      2. 2.3.2 Entropy; second principle
    4. 2.4 Method of local state
      1. 2.4.1 State variables
      2. 2.4.2 Thermodynamic potential, state laws
      3. 2.4.3 Dissipation, complementary laws
    5. 2.5 Elements of heat
      1. 2.5.1 Fourier’s law
      2. 2.5.2 Heat equation
      3. Bibliography
  12. 3. Identification and rheological classification of real solids
    1. 3.1 The global phenomenological method
    2. 3.2 Elements of experimental techniques and identification process
      1. 3.2.1 Characteristic tests
      2. 3.2.2 Experimental techniques
      3. 3.2.3 Identification methods
    3. 3.3 Schematic representation of real behaviour
      1. 3.3.1 Analogical models
      2. 3.3.2 Rigid solid and perfect fluid
      3. 3.3.3 Viscous fluid
      4. 3.3.4 Elastic solids
      5. 3.3.5 Plastic solids
      6. 3.3.6 Viscoplastic solids
      7. 3.3.7 Characterization of work-hardening
      8. 3.3.8 Ageing
    4. 3.4 Schematic representation of fracture
      1. 3.4.1 Fracture by damage of a volume element
      2. 3.4.2 Fracture by crack propagation in a structure
    5. 3.5 Schematic representation of friction
      1. 3.5.1 Coulomb model
      2. 3.5.2 Boundary layer model
      3. Bibliography
  13. 4. Linear elasticity, thermoelasticity and viscoelasticity
    1. 4.1 Elasticity
      1. 4.1.1 Domain of validity and use
      2. 4.1.2 Formulation
      3. 4.1.3 Identification
      4. 4.1.4 Table of elastic properties of common materials
      5. 4.1.5 Concepts of the finite element method
    2. 4.2 Thermoelasticity
      1. 4.2.1 Formulation
      2. 4.2.2 Identification
      3. 4.2.3 Thermoelastic properties of common materials
    3. 4.3 Viscoelasticity
      1. 4.3.1 Domain of validity and use
      2. 4.3.2 Thermodynamic formulation
      3. 4.3.3 Functional formulation
      4. 4.3.4 Viscoelastic properties of common materials
      5. 4.3.5 Elements of viscoelastic analysis of structures
      6. Bibliography
  14. 5. Plasticity
    1. 5.1 Domain of validity and use
    2. 5.2 Phenomenological aspects
      1. 5.2.1 Uniaxial behaviour
      2. 5.2.2 Multiaxial plasticity criteria
    3. 5.3 Formulation of general constitutive laws
      1. 5.3.1 Partition hypothesis
      2. 5.3.2 Choice of thermodynamic variables
      3. 5.3.3 Loading surface and dissipation potential
    4. 5.4 Particular flow laws
      1. 5.4.1 Different types of criteria and flow laws
      2. 5.4.2 Isotropic hardening rules
      3. 5.4.3 Linear kinematic hardening rules
      4. 5.4.4 Flow rules under cyclic or arbitrary loadings
      5. 5.4.5 Classification of different models
    5. 5.5 Proportional loading
      1. 5.5.1 Definition
      2. 5.5.2 Integrated Hencky–Mises law. Equivalent stress and strain
      3. 5.5.3 Existence theorem for proportional loading
    6. 5.6 Elements of computational methods in plasticity
      1. 5.6.1 Structural analysis
      2. 5.6.2 Limit analysis
      3. 5.6.3 Approximate global method of uniform energy
      4. Bibliography
  15. 6. Viscoplasticity
    1. 6.1 Domain of validity and use
    2. 6.2 Phenomenological aspects
      1. 6.2.1 Results derived from hardening tests
      2. 6.2.2 Results derived from creep tests
      3. 6.2.3 Results derived from relaxation tests
      4. 6.2.4 Viscosity-hardening law
      5. 6.2.5 Influence of temperature
      6. 6.2.6 Results derived from cyclic tests
      7. 6.2.7 Results derived from multiaxial tests
    3. 6.3 General formulation of the constitutive equations
      1. 6.3.1 Partition of strains
      2. 6.3.2 Choice of thermodynamic variables
      3. 6.3.3 Dissipation potential
    4. 6.4 Particular constitutive equations
      1. 6.4.1 Laws of perfect viscoplasticity
      2. 6.4.2 Viscoplasticity laws with isotropic hardening
      3. 6.4.3 Viscoplasticity law with kinematic hardening
      4. 6.4.4 Modelling of particular effects
    5. 6.5 Elements of the methods of viscoplastic structural analysis
      1. 6.5.1 General scheme of viscoplastic analysis
      2. 6.5.2 Methods of step by step linearization
      3. Bibliography
  16. 7. Damage mechanics
    1. 7.1 Domain of validity and use
    2. 7.2 Phenomenological aspects
      1. 7.2.1 Damage variable
      2. 7.2.2 Effective stress
      3. 7.2.3 Measurement of damage
      4. 7.2.4 Elementary damage laws
      5. 7.2.5 Multiaxial damage criteria
    3. 7.3 Thermodynamic formulation
      1. 7.3.1 Multiaxial representation of damage
      2. 7.3.2 Theory of isotropic damage
      3. 7.3.3 A nonisotropic damage theory
    4. 7.4 Particular models
      1. 7.4.1 Ductile plastic damage
      2. 7.4.2 Creep damage
      3. 7.4.3 Fatigue damage
      4. 7.4.4 Interaction effects of fatigue and creep damage
    5. 7.5 Deformation and damage coupling
      1. 7.5.1 Elasticity coupled with damage
      2. 7.5.2 Plasticity coupled with damage
      3. 7.5.3 Viscoplasticity coupled with damage
    6. 7.6 Prediction of crack initiation in structures
      1. 7.6.1 Initial damage
      2. 7.6.2 Calculation of damage at critical points
      3. Bibliography
  17. 8. Crack mechanics
    1. 8.1 Domain of validity and use
    2. 8.2 Elements of analysis of cracked media
      1. 8.2.1 Initial cracks
      2. 8.2.2 Elastic analysis
      3. 8.2.3 Elastoplastic analyses
    3. 8.3 Phenomenological aspects
      1. 8.3.1 Variables governing crack behaviour
      2. 8.3.2 Elementary experimental results
    4. 8.4 Thermodynamic formulation
      1. 8.4.1 Choice of variables. Thermodynamic potential
      2. 8.4.2 Elastic strain energy release rate
      3. 8.4.3 The crack growth threshold variable
      4. 8.4.4 Dissipation analysis
      5. 8.4.5 Bifurcation criteria for crack propagation in plane media
      6. 8.4.6 Three-dimensional cracked structures
    5. 8.5 Particular crack propagation models
      1. 8.5.1 Cracking by brittle fracture
      2. 8.5.2 Cracking by ductile fracture
      3. 8.5.3 Creep crack growth
      4. 8.5.4 Fatigue crack growth
    6. 8.6 Elements of the crack analysis of structures by the global approach
      1. 8.6.1 Elastic analysis by finite elements (two-dimensional media)
      2. 8.6.2 Three-dimensional cracked structures
      3. 8.6.3 Integration of the models
    7. 8.7 Crack analysis by the local approach
      1. 8.7.1 Limits and inadequacies of the global fracture mechanics
      2. 8.7.2 Principles of the local approaches
      3. 8.7.3 Examples
      4. Bibliography
  18. Index