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8.31 Surfaces - Strains - Rankine

To control the graphical display of surface strains available with the equivalent stress hypothesis according to Rankine, select Surfaces → Strains in the Results navigator (see Figure 8.63). Table 4.31 shows these strains in numerical form.

Image 8.66 Table 4.31 *Surfaces - Strains - Rankine*

The Grid Point and Grid Point Coordinates table columns correspond to those of results table 4.29 Surfaces - Strains - von Mises.

In the approach according to Rankine, it is assumed that failure is caused by the maximum principal stress (see Chapter 8.24).

The strains according to Rankine are determined as follows:

Table 8.24 Strains according to Rankine
ε_+,Rankine	Equivalent strain on the positive side of the surface (i.e. side in direction of positive surface axis z) $ε_{+} = \frac{1}{2} (\frac{\|ε_{x, +} + ε_{y, +}\|}{1 - ν} + \frac{\sqrt{(ε_{x, +} - ε_{y, +})^{2} + γ_{x y, +}^{2}}}{1 + ν})$
ε_−,Rankine	Equivalent strain on the negative side of the surface $ε_{-} = \frac{1}{2} (\frac{\|ε_{x, -} + ε_{y, -}\|}{1 - ν} + \frac{\sqrt{(ε_{x, -} - ε_{y, -})^{2} + γ_{x y, -}^{2}}}{1 + ν})$
ε_Rankine	Maximum equivalent strain on the positive or negative side of the surface (columns E and F)

Parent Chapter

8 Results