remark A.705 The dangerous stress is below the surface

open in the book · appendices/A-long-proofs.tex:34170 · p. 3135

remark -- no derivation owed by its kind

Rests on

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 definition 7.126 Line and surface integrals ¶
      - depends_on definition 30.2 Representative volume element; continuum field ¶
    - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
      - depends_on definition 30.17 Traction ¶ ↺
      - depends_on definition 13.5 Tensor under orthogonal transformations ¶
      - proves proof ch:13-continuum-elasticity@proof-7 ¶
    - 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 ¶
depends_on theorem A.702 Hertz's solution ¶
- depends_on definition A.698 The Hertz contact problem ¶
  - depends_on phenomenon 30.70 Hertzian contact ¶
    - depends_on definition 30.31 The engineering moduli ¶
      - depends_on definition 30.20 Pressure and deviatoric stress ¶ ↺
      - depends_on equation 30.21 eq:elast-hooke-isotropic ¶
    - depends_on proposition 30.23 Virtual work; the weak form ¶
      - depends_on definition 30.22 Boundary conditions of elastostatics ¶
      - depends_on theorem 30.21 Cauchy's equation of motion ¶
      - proves proof ch:13-continuum-elasticity@proof-10 ¶
    - proves proof ch:13-continuum-elasticity@proof-34 ¶
    - proves proof ch:13-continuum-elasticity@prooflink-3 ¶
  - depends_on theorem A.695 Boussinesq's point-force solution, quoted ¶
    - depends_on definition 30.31 The engineering moduli ¶ ↺
    - depends_on equation 30.21 eq:elast-hooke-isotropic ¶ ↺
    - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶ ↺
- depends_on lemma A.700 The displacement produced by an elliptic pressure ¶
  - depends_on definition A.698 The Hertz contact problem ¶ ↺
  - depends_on lemma A.697 Surface displacement under a distributed pressure ¶
    - depends_on theorem A.695 Boussinesq's point-force solution, quoted ¶ ↺
    - proves proof app:A-long-proofs@proof-411 ¶
  - proves proof app:A-long-proofs@proof-412 ¶
- depends_on proposition A.701 The two-body compliance rule ¶
  - depends_on definition A.698 The Hertz contact problem ¶ ↺
  - depends_on lemma A.697 Surface displacement under a distributed pressure ¶ ↺
  - proves proof app:A-long-proofs@proof-413 ¶
- proves proof app:A-long-proofs@proof-414 ¶

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type	direction	node	provenance	where
`depends_on`	→	The maximum shear stress, and its indifference to pressure	declared	appendices/A-long-proofs.tex:34192
`depends_on`	→	Hertz's solution	declared	appendices/A-long-proofs.tex:34192