Whats the name of this Effect?
I don't think there is a name to the effect. If I were to describe it, it would just be "the effect of a shell of an object cracking up and falling / peeling away in fractured pieces".

I am sure you already know the compositing side of things, where you do the colour grading, atmospheric effects and such in After Effects. 

For the 3D software I work primarily with Maya and 3D Studio Max. I am very certain any 3D software that can simulate dynamic objects (rigid bodies / soft bodies / cloth) will be able to achieve an effect like this. These include Blender, Maya, Max, C4D, Houdini, Softimage XSI and a host of many others.

In motion graphics C4D is definitely a good choice for procedural effects like breaking, cracking, fracturing. In some software (like Maya and 3D Studio Max), creating the fractured pieces procedurally could be a challenge. The artist might need to use a fracturing plug. 

After the objects are properly fractured, the dynamics portion of any the software listed aboev would definitely be able to achieve the physically believable simulation of the pieces falling away.

Thereafter you would need shading/lighting/rendering skills to render out the full image, or portions of it in passes, in order to achieve the final image.