The stress vector is a frame-indifferent vector ( see Euler-Cauchy's stress principle ).
2.
Where \ lambda is a constant of proportionality, and in this particular case corresponds to the magnitudes \ sigma _ \ mathrm { n } of the normal stress vectors or principal stresses.
3.
Only for the case where the stress vector lies along one of the principal directions it is possible to know the direction of the plane, as the principal stresses act perpendicular to their planes.
4.
It seems to be normal to the stress vector, and the piezoelectric vector, I imagine this has to do with symmetry . ( TALK ) 18 : 10, 19 December 2005 ( UTC)
5.
If the stress vector itself is opposite to x, the material is said to be under "'normal compression "'or "'pure compressive stress "'along x.
6.
Stress tensor can be considered as a matrix with nine components being the nine stress vectors acting on a point, in which the three vectors along the diagonal ( highlighted in brown ) represent the principal axes.
7.
If the stress vector is purely compressive and has the same magnitude for all directions, the material is said to be under "'isotropic "'or "'hydrostatic compression "'at that point.
8.
Cauchy s stress principle asserts that as \ Delta S becomes very small and tends to zero the ratio \ Delta \ mathbf F / \ Delta S becomes d \ mathbf F / dS and the couple stress vector \ Delta \ mathbf M vanishes.
9.
The nine components " & sigma; ij " of the stress vectors are the components of a second-order Cartesian tensor called the " Cauchy stress tensor ", which completely defines the state of stress at a point and is given by
10.
Depending on the orientation of the plane under consideration, the stress vector may not necessarily be perpendicular to that plane, " i . e . " parallel to \ mathbf n, and can be resolved into two components ( Figure 2.1c ):
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