Shape to shape iteration morph

[Michael35079317szcq]

I'm trying to attempt a shape to shape, morph. So hard to even explain without a picture when trying to Google  I find nothing. Does anyone have any tutorial or tips on how to attempt and iteration line shape, morph outwards? The attached images all I have to explain what I am trying to accomplish. Please help!

[Bobby Henderson]

Have you tried using the blend tool?

[CarlosCanto]

straight blend is not getting it right, 

but we can draw the first inner copy with offset path, 

Smooth it, here about 80%

then blending the smoothed copy with the outer shape, yields better results

it needs some manual tweaking to get it better