You guys are oversimplifying it - simply animating a global transparency won't achieve the correct results. You need to sharpen or blur the texture based on the amount of stretch that is present on each edge in the direction of the stretch/compression. You could use a tension map to give you the amount of stretch/compression. SOuP has one: https://www.soup-dev.com/ However, in order to replicate the paper, you need to blur/sharpen in the correct direction as well.

This video has more information on the technique: https://www.youtube.com/watch?v=tuZMMZ8vbNk