equation 30.21 eq:elast-hooke-isotropic

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Supports

• assumes experiment Coulomb: the torsion pendulum ¶
• depends_on definition 30.31 The engineering moduli ¶
  • depends_on phenomenon 30.70 Hertzian contact ¶
    • depends_on definition A.698 The Hertz contact problem ¶
      • depends_on lemma A.700 The displacement produced by an elliptic pressure ¶
        • depends_on theorem A.702 Hertz's solution ¶
      • depends_on proposition A.701 The two-body compliance rule ¶
        • depends_on theorem A.702 Hertz's solution ¶ ↺
      • depends_on remark A.699 The third condition is not decoration ¶
      • depends_on theorem A.702 Hertz's solution ¶ ↺
    • depends_on example A.703 The numbers of the chapter, recomputed ¶
    • depends_on example 30.71 Contact stresses are enormous ¶
  • depends_on phenomenon 30.60 Coulomb's law of torsion ¶
    • depends_on example 30.61 A torsion fibre as a force sensor ¶
    • depends_on phenomenon 34.3 The stiffness of a twisted wire is geometric ¶
    • depends_on remark 30.62 Saint-Venant's theory: non-circular sections warp ¶
    • tests experiment Coulomb: the torsion pendulum ¶ ↺
  • depends_on proposition 30.33 Conversion among the moduli ¶
    • depends_on definition 30.63 Flexural rigidity ¶
      • depends_on proposition A.684 The plate energy ¶
        • depends_on lemma A.685 The Gaussian-curvature term is a null Lagrangian ¶
        • depends_on theorem A.688 The Kirchhoff plate equation ¶
      • depends_on proposition A.682 The plane-stress law ¶
        • depends_on definition A.689 Edge resultants ¶
        • depends_on proposition A.684 The plate energy ¶ ↺
        • depends_on remark A.683 Where the factor $1-\nu^{2}$ comes from ¶
      • depends_on proposition 30.66 Chladni scaling ¶
        • depends_on phenomenon 30.65 Chladni figures ¶
      • depends_on remark A.704 $E^{*}$ in two roles, and one trap ¶
      • depends_on remark A.686 Why the operator comes out as $\nabla^{4}$ ¶
      • depends_on remark A.683 Where the factor $1-\nu^{2}$ comes from ¶ ↺
      • depends_on remark 30.68 Shells carry load in a different way ¶
      • depends_on theorem 30.64 The Kirchhoff plate equation ¶
        • depends_on phenomenon 30.65 Chladni figures ¶ ↺
        • depends_on proposition 30.66 Chladni scaling ¶ ↺
        • depends_on remark 30.67 Germain, Kirchhoff, and the edge conditions ¶
    • depends_on example 30.35 From single crystals to the isotropic aggregate ¶
    • depends_on proposition A.682 The plane-stress law ¶ ↺
    • depends_on proposition 30.44 The speed ratio is fixed by Poisson's ratio ¶
      • depends_on example 30.45 Elastic waves in steel, and the distance to a source ¶
    • depends_on remark 30.36 How the moduli are actually measured ¶
  • depends_on proposition 30.51 Moment and curvature ¶
    • depends_on definition A.680 Kirchhoff kinematics ¶
      • depends_on lemma A.687 Kinetic energy ¶
        • depends_on theorem A.688 The Kirchhoff plate equation ¶ ↺
      • depends_on lemma A.681 Strains under the Kirchhoff hypothesis ¶
        • depends_on proposition A.684 The plate energy ¶ ↺
    • depends_on definition 30.63 Flexural rigidity ¶ ↺
    • depends_on phenomenon 30.52 Euler buckling ¶
      • depends_on example 30.53 A steel rod buckles at a twentieth of its crushing load ¶
      • depends_on remark 30.54 Other end conditions, and what buckling is variationally ¶
      • depends_on remark 30.55 Beyond the critical load: the elastica ¶
      • depends_on remark 30.68 Shells carry load in a different way ¶ ↺
    • depends_on theorem 30.56 The beam equation ¶
      • depends_on example 30.58 A steel ruler ¶
      • depends_on proposition 30.57 Bending waves are dispersive ¶
        • depends_on example 30.58 A steel ruler ¶ ↺
        • depends_on remark 30.59 Where Euler–Bernoulli fails ¶
  • depends_on remark A.676 The third cubic constant is measured, and it is not small ¶
  • depends_on theorem A.695 Boussinesq's point-force solution, quoted ¶
    • depends_on definition A.698 The Hertz contact problem ¶ ↺
    • depends_on lemma A.697 Surface displacement under a distributed pressure ¶
      • depends_on lemma A.700 The displacement produced by an elliptic pressure ¶ ↺
      • depends_on proposition A.701 The two-body compliance rule ¶ ↺
• depends_on definition 30.79 Maxwell viscoelasticity ¶
  • depends_on proposition 30.80 A Maxwell material is a solid or a fluid depending on how long you watch ¶
• depends_on phenomenon 30.60 Coulomb's law of torsion ¶ ↺
• depends_on proposition A.682 The plane-stress law ¶ ↺
• depends_on proposition 30.51 Moment and curvature ¶ ↺
• depends_on remark 30.72 Stress concentration ¶
  • depends_on proposition 30.76 Griffith's criterion ¶
    • depends_on example 30.77 Why glass is weak, and thin glass is not ¶
    • depends_on phenomenon 30.73 Yield and brittle fracture ¶
• depends_on remark 30.29 The Lamé constants and the energy ¶
• depends_on theorem A.695 Boussinesq's point-force solution, quoted ¶ ↺
• depends_on theorem 30.40 Navier–Cauchy equations ¶
  • depends_on phenomenon 30.43 Two bulk wave speeds ¶
    • depends_on phenomenon 30.47 The three seismic phases ¶
    • depends_on remark 30.46 Why the plane-wave route, and not the potentials ¶
  • depends_on proposition 30.41 Energy balance and its flux ¶
    • depends_on theorem 30.42 Uniqueness in elastodynamics ¶
  • depends_on proposition 30.50 Love waves need a slow surface layer ¶
  • depends_on proposition 30.48 Rayleigh's secular equation ¶
    • depends_on proposition 30.49 The Rayleigh speed of a Poisson solid ¶
      • depends_on phenomenon 30.47 The three seismic phases ¶ ↺
  • depends_on remark 30.46 Why the plane-wave route, and not the potentials ¶ ↺