remark 30.78 Anharmonicity: what the quadratic energy also suppresses

open in the book · parts/03-classical-mechanics/13-continuum-elasticity.tex:2758 · p. 1038

remark -- no derivation owed by its kind

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depends_on definition 30.24 The elasticity tensor ¶
- depends_on definition 30.6 Linear strain and infinitesimal rotation ¶
  - depends_on definition 13.91 Symmetric and antisymmetric parts ¶
  - depends_on equation 30.2 eq:elast-displacement ¶
- 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 7.98 Functions of class $C^{1}$ ¶
      - depends_on definition 7.125 Multiple integral ¶
    - depends_on definition 30.2 Representative volume element; continuum field ¶
      - depends_on definition 7.97 Partial derivative; gradient ¶
  - depends_on definition 13.5 Tensor under orthogonal transformations ¶
    - depends_on definition 13.4 Orthogonal coordinate transformation ¶
      - depends_on definition 13.3 Orthogonal coordinate system ¶
  - proves proof ch:13-continuum-elasticity@proof-7 ¶
depends_on phenomenon 30.28 Hooke's law ¶
- depends_on definition 30.24 The elasticity tensor ¶ ↺
- depends_on lemma 30.26 Isotropic Cartesian tensors of rank four ¶
  - depends_on definition 13.5 Tensor under orthogonal transformations ¶ ↺
  - depends_on theorem 5.133 Isotropic Cartesian tensors of rank at most four ¶
    - depends_on lemma 5.33 Determinant through the Levi–Civita symbol ¶
      - depends_on definition 5.32 Levi–Civita symbol; cross product ¶
      - depends_on equation 5.19 eq:lin-leibniz-det ¶
      - proves proof ch:03-linear-algebra-representations@proof-8 ¶
    - depends_on lemma 5.132 Parity constraint ¶
      - depends_on definition 5.131 Isotropic Cartesian tensor ¶
      - depends_on equation 5.162 eq:rep-special-orthogonal ¶
      - proves proof ch:03-linear-algebra-representations@proof-57 ¶
    - depends_on proposition 5.130 An orthogonal transformation is an isometry ¶
      - depends_on definition 5.18 Inner product ¶
      - depends_on equation 5.44 eq:lin-norm-assoc ¶
      - depends_on proposition 5.49 Injective, surjective, invertible ¶
      - proves proof ch:03-linear-algebra-representations@proof-56 ¶
    - proves proof ch:03-linear-algebra-representations@proof-58 ¶
  - proves proof ch:13-continuum-elasticity@prooflink-1 ¶
- proves proof ch:13-continuum-elasticity@proof-12 ¶

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type	direction	node	provenance	where
`depends_on`	→	The elasticity tensor	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2776
`depends_on`	→	Hooke's law	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2776