Treatise of Physics

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proposition 30.7 Strain is a Cartesian tensor of rank two

open in the book · parts/03-classical-mechanics/13-continuum-elasticity.tex:208 · p. 1009

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proposition 30.7: Strain is a Cartesian tensor of rank two30.7definition 30.6: Linear strain and infinitesimal rotation30.6definition 13.5: Tensor under orthogonal transformations13.5proof : ch:13-continuum-elasticity@proof-1proofdefinition 13.91: Symmetric and antisymmetric parts13.91equation 30.2: eq:elast-displacement30.2definition A.680: Kirchhoff kinematicsA.680definition 30.24: The elasticity tensor30.24definition 30.11: Green strain30.11example 30.13: A rigid rotation forges a strain of -θ^2/230.13example 30.10: Simple shear and pure shear are the same strain30.10lemma A.681: Strains under the Kirchhoff hypothesisA.681proposition 30.14: Saint-Venant compatibility is necessary30.14proposition 30.8: The trace is the fractional volume change30.8proposition 30.9: Principal strains30.9definition 13.4: Orthogonal coordinate transformation13.4definition 19.42: Inertia tensor19.42definition 29.13: Inertia tensor, continuum form29.13lemma 30.26: Isotropic Cartesian tensors of rank four30.26notation 30.1: Strain and displacement share a letter30.1proposition 13.96: The cross product is an axial vector13.96proposition 13.6: Levi-Civita identities in three dimensions13.6proposition 19.43: The moment of inertia is a quadratic form in the axis19.43remark 13.7: What the classification is used for13.7theorem 30.18: Cauchy: the stress tensor exists30.18

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depends_on → Linear strain and infinitesimal rotation declared parts/03-classical-mechanics/13-continuum-elasticity.tex:215
depends_on → Tensor under orthogonal transformations declared parts/03-classical-mechanics/13-continuum-elasticity.tex:215
proves ← ch:13-continuum-elasticity@proof-1 declared parts/03-classical-mechanics/13-continuum-elasticity.tex:218