Treatise of Physics

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proposition 30.8 The trace is the fractional volume change

open in the book · parts/03-classical-mechanics/13-continuum-elasticity.tex:241 · p. 1010

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proposition 30.8: The trace is the fractional volume change30.8definition 30.6: Linear strain and infinitesimal rotation30.6equation 30.2: eq:elast-displacement30.2proof : ch:13-continuum-elasticity@proof-2proofdefinition 13.91: Symmetric and antisymmetric parts13.91definition 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 30.9: Principal strains30.9proposition 30.7: Strain is a Cartesian tensor of rank two30.7

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typedirectionnode provenancewhere
depends_on → Linear strain and infinitesimal rotation declared parts/03-classical-mechanics/13-continuum-elasticity.tex:250
depends_on → eq:elast-displacement declared parts/03-classical-mechanics/13-continuum-elasticity.tex:250
proves ← ch:13-continuum-elasticity@proof-2 declared parts/03-classical-mechanics/13-continuum-elasticity.tex:253