phenomenon 30.73 Yield and brittle fracture

Rests on

• depends_on proposition 30.76 Griffith's criterion ¶
  • depends_on equation 30.23 eq:elast-energy-density ¶
  • depends_on remark 30.72 Stress concentration ¶
    • depends_on equation 30.21 eq:elast-hooke-isotropic ¶
    • depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
      • depends_on definition 30.17 Traction ¶
        • depends_on definition 7.126 Line and surface integrals ¶
        • depends_on definition 30.2 Representative volume element; continuum field ¶
      • depends_on definition 13.5 Tensor under orthogonal transformations ¶
        • depends_on definition 13.4 Orthogonal coordinate transformation ¶
      • proves proof ch:13-continuum-elasticity@proof-7 ¶
  • proves proof ch:13-continuum-elasticity@proof-37 ¶
• depends_on proposition 30.74 The maximum shear stress, and its indifference to pressure ¶
  • depends_on definition 30.20 Pressure and deviatoric stress ¶
    • depends_on proposition 30.19 The stress tensor is symmetric ¶
      • depends_on definition 30.17 Traction ¶ ↺
      • depends_on theorem 30.18 Cauchy: the stress tensor exists ¶ ↺
      • proves proof ch:13-continuum-elasticity@proof-8 ¶
    • depends_on theorem 5.79 Spectral theorem for a self-adjoint operator ¶
      • depends_on corollary 5.72 Existence of an eigenvalue over $\C$ ¶
        • depends_on theorem 8.19 Fundamental theorem of algebra ¶
        • depends_on theorem 5.71 The eigenvalues are the roots of the characteristic polynomial ¶
        • proves proof ch:03-linear-algebra-representations@proof-27 ¶
      • depends_on definition 5.41 Adjoint ¶
        • depends_on definition 5.18 Inner product ¶
        • depends_on definition 5.37 Linear transformation ¶
      • depends_on theorem 5.40 Rank–nullity ¶
        • depends_on definition 5.15 Basis ¶
        • depends_on definition 5.39 Kernel, image, nullity, rank ¶
        • depends_on lemma 5.38 Exchange and completion ¶
        • proves proof ch:03-linear-algebra-representations@proof-13 ¶
      • proves proof ch:03-linear-algebra-representations@proof-31 ¶
  • depends_on theorem 30.18 Cauchy: the stress tensor exists ¶ ↺
  • proves proof ch:13-continuum-elasticity@proof-36 ¶
• proves proof ch:13-continuum-elasticity@proof-35 ¶

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