Invariants

33 The principal stresses are physical quantities, whose values do not depend on the coordinate system in which the components of the stress were initially given. They are therefore invariants of the stress state.

34 When the determinant in the characteristic Eq. 2.32 is expanded, the cubic equation takes the form

where the symbols Ia, IIa and IIIa denote the following scalar expressions in the stress components:

35 In terms of the principal stresses, those invariants can be simplified into

Ia

= 0(1) + 0(2) + 0(3)

(2.41)

IIa

= -(0(1)0(2) + 0(2)0(3) + 0(3) 0(1))

(2.42)

IIIa

= 0(1)0(2)0(3)

(2.43)

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