Implementation of the ‘smart’ rotor concept - Wind Power Generation and Wind Turbine Design - page 489

s

M d

s cr
f

A

M t,d ,A

s cr
s

M t,d

M M s A s A f T f

Figure 14: T , s -phase diagram for the Brinson model. The arrows indicate in
which direction of the T , s -path the phase change occurs.

Figure 15: e , s -space to x , p -space mapping in the van der Wijst model.

s -paths between transition points and shifting these points with the temperature.
van der Wijst does that by mapping the stress-strain envelope onto a x , p -plane, where
p is the elastic load parameter and x is again the martensite fraction (see Fig. 15).
It is then stipulated that changes in elastic stress and in martensite fraction cannot
occur simultaneously:

pt () () x t =∀ 0 t

( 36)

van der Wijst then uses the x , p -map in conjunction with a set of bilinear equations
for stress and strain to determine the state of the SMA material and calculate the
corresponding stress and strain state:

( 37)

ee e =+ + + p exex p

1 2 3 4

ss s =+ + + p sxsx p

( 38)

1 2 3 4

In these equations, the coeffi cients are linearly dependent on the temperature:

ee =+ T e

1 1 a 1 b

( 39 )

ss = T + s

4 4 a 4 b