remark 30.72 Stress concentration

open in the book · parts/03-classical-mechanics/13-continuum-elasticity.tex:2557 · p. 1035

remark -- no derivation owed by its kind

Rests on

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 7.20 Continuity at a point ¶
      - depends_on definition 7.97 Partial derivative; gradient ¶
    - depends_on definition 7.125 Multiple integral ¶
      - depends_on axiom 7.1 Completeness of $\R$ ¶
      - depends_on definition 7.39 Darboux sums and the definite 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 ¶

Supports

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 ¶

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`	→	Theory of Elasticity	derived	parts/03-classical-mechanics/13-continuum-elasticity.tex:2560
`depends_on`	→	eq:elast-hooke-isotropic	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2577
`depends_on`	→	Cauchy: the stress tensor exists	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2577
`depends_on`	←	Griffith's criterion	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2699