Controlling flexinol with an arduino board?
First thing's first, this just seems to be a wire that has special characteristics. If so, we just need to find out the resistance and use Ohm's law.

From the product page, I found this image:


  


I can tell from that that it has a resistance of 20 ohms and a recommended current of 1 amp. First, let's see how much current it would draw with a 5V supply. I prefer using a Ohm's law triangle, just because I'm a very visual person. So with this math:


  5 / 20 = 0.25


That's 250 mA, but an Arduino can only provide 40 mA! Furthermore, it is only 1/4 of the recommended current that the manufacturer specifies.

To get the full current the OEM specifies you'll need a 20 V power supply capable of at least 1A. Even then, you might want to put in a power resistor to limit the current.

Driving this with Arduino: So, we have a few problems here:


It is 20W, which is quite a bit in the Arduino world
We need to control the current/voltage dynamically
You need 16 of them, so we don't want something too costly
You probably can't find something to fit your needs that is one shield.


What comes to mind is a transistor. I'm not skilled with picking them out, but there are a lot of guides online. You'd then want to add a capacitor and a resistor to make some sort of filter and connect it to a PWM pin to send a varied voltage to the transistor, which will vary the amount of power going through it.

Alternatively, you could use a relay. However, that only does ON or OFF. A solid state relay (SSR) would allow you to use PWM on the relay and then you could add a capacitor/resistor combo on the other end of it, but you'd need a pretty large capacitor or a pretty large frequency for the PWM (which you can modify).