proposition 30.76 Griffith's criterion

open in the book · parts/03-classical-mechanics/13-continuum-elasticity.tex:2687 · p. 1037

Rests on

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 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 ¶
proves proof ch:13-continuum-elasticity@proof-37 ¶

Supports

depends_on example 30.77 Why glass is weak, and thin glass is not ¶
depends_on phenomenon 30.73 Yield and brittle fracture ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`cites`	→	The phenomena of rupture and flow in solids	derived	parts/03-classical-mechanics/13-continuum-elasticity.tex:2698
`depends_on`	→	eq:elast-energy-density	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2699
`depends_on`	→	Stress concentration	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2699
`depends_on`	←	Why glass is weak, and thin glass is not	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2755
`depends_on`	←	Yield and brittle fracture	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2599
`proves`	←	ch:13-continuum-elasticity@proof-37	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2702