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Analysis of Cartesian Stiffness And Compliance With ... - helix

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Orthonormal Basis <strong>of</strong> Isotropic Vectors<br />

U T AU =<br />

0 x x<br />

x 0 x<br />

x x 0<br />

...<br />

...<br />

...<br />

...<br />

...<br />

...<br />

A has a complete orthonormal set <strong>of</strong> isotropic vectors<br />

if and only if<br />

trace(A) = 0<br />

3D Example:<br />

c<br />

a<br />

a<br />

b b<br />

c<br />

shear stress<br />

σ 3<br />

σ 2<br />

σ 1<br />

normal<br />

stress<br />

Pure shear state for deviatoric stress case<br />

39

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