Is this possible to model?

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Hi. I have a hobby that has made me interested in modeling something. I'm not an artist or a physicist, and I've never used any modeling software before, so I wasn't even sure if what I'm thinking is possible to model, and if it is, how to approach it.  I was wondering if you might be able to either provide some advice or point me to someone whom I could ask?  My hobby is metaphysics and physics-related and I'd like to model a system with the following characteristics:

1. 3D, soft-body modeling of flexible spheres of equal diameters and in contact with one another.  The spheres are just a surface with no internal content or subunits. The spheres should be flexible and can change shape, but should not be able to stretch or shrink to a larger or smaller, respectively, surface length than that of the circumference of the sphere.
 
2. There's an initial sphere (layer 0) whose surface is entirely covered by non-overlapping, tangentially touching (“kissing”) spheres of the same size.  This is layer 1. From what I've read about sphere packing, there will be room for 12 spheres in layer 1 but not quite enough  room on the surface of the layer 0 sphere to allow in a 13th sphere. But, in order to completely cover the surface of the layer 0 sphere, there will be a 13th sphere.  Because of this, the 13th sphere and the immediately adjacent layer 1 spheres will be trying to occupy the same location. Because they're separate, flexible spheres trying to occupy overlapping positions, they will be compress each other and will meet the spheres with which they're “competing” at an interface.
 
3. Any of the outer surfaces of the layer 1 spheres that are not already covered by other spheres, will also be covered by non-overlapping, tangentially touching spheres of the same size (layer 2). Some of these layer 2 spheres will also be trying to occupy overlapping positions if there's not enough space to fit in an integral number of them. They will thus overlap and be compressed as in layer 1. This process of sphere creation next to surfaces not yet covered by other spheres will continue ad infinitum so that layers of spheres (0, 1, 2, etc.) are created sequentially (e.g. layer 0 sphere first, then the layer 1 spheres, then the layer 2 spheres, etc.).
 
4. The overlapping-in-position spheres are all trying to achieve their natural spherical shape and thus will exert pressure on each other. This is where the flexibility part comes in. As the overlapping entities push against each other, they will change shape (e.g. “bulge out”) and push into the adjacent spheres.  In one version of the model, these adjacent spheres will therefore be pushed and move away from the bulging out spheres. As this happens, new spheres will be created next to the surfaces of the bulging out and moving spheres that are no longer in contact.  In another version of the model, the adjacent spheres can't physically move away from the bulging out sphere but will just change shape/deform as they are bulged into.

Is it possible to make a 3D simulation of what happens when you start the above system running starting with sphere 0 and adding layers sequentially  to see how the pressure waves and forces move through the bulging out spheres?  Ideally, at the end, I'd like a map or some analysis  showing the net flows of the pressure waves, where they are and in what directions they're moving.   

  People I know have recommended various software programs including Houdini, Blender, 3ds Max, etc..  I'm not sure what would be best? Also, starting from no knowledge, very roughly how long might it take me to become proficient enough to make the model I described?
 
    I would be grateful for any advice you could provide.  Thank you!
 
                                                                                Sincerely,
                                                                                Roger Granet
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