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I've noticed two trends in rugged cell-phone cases:

  1. Lots of soft material
  2. An inner layer of soft material coupled with an outer layer of hard material.

Considering an equal thickness for both designs, which approach should protect a phone better? I'm mostly interested in the corners, which are often where a phone will sustain damages when dropped.

I do realize there are many variable and tons of different materials on the market, and I'm not looking for a specific case recommendation, just the theory behind it.

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  • $\begingroup$ A rounded corner might spread the load, but for the size of a smartphone, there can't be much difference in having a square corner. It's far more important what you drop it onto, (or into if you are unfortunate in the bathroom : ) I am sorry, but no real physics is jumping out at me here, so apologies but I VTC as engineering. $\endgroup$
    – user108787
    Nov 3, 2016 at 23:18
  • $\begingroup$ @CountTo10 I was not so much asking about the shape, but more about layering different density of material VS going with a thicker layer of soft silicon. $\endgroup$
    – FMaz008
    Nov 4, 2016 at 2:45
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    $\begingroup$ This is essentially an egg-drop challenge replacing eggs with smartphones. Since the only constraint you specified was protecting the phone the best, the obvious answer would be that a smartphone is best protected by being encased in a gigantic blob of soft foam with no hard outer shell. I'd say 4 or 5 meters thick would be enough to protect it from virtually any physical damage you can think of. It's not very practical for daily usage, but you didn't say it had to be practical. You just asked which is better for the same thickness. $\endgroup$
    – Jim
    Nov 4, 2016 at 12:48
  • $\begingroup$ @Jim True I asked which is better for the same thickness, but one of the constraints is that it has to be a cellphone case, which is only a few mm thick at most. Also, the shape of a phone is different and has corners. But yes, this is a similar question to the egg challenge, but with a few more constraints. $\endgroup$
    – FMaz008
    Nov 4, 2016 at 13:16

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There are not really any structural reasons for several layers of different softness/hardness. I believe that a hard surface as the outer layer is only added for a better user-feel.

If you only seek good protection, then you have two parameters to aim for:

  • Make it soft and
  • make it thick.

The softer and thicker the better. To prevent collision damage, you are looking at Newton's 2nd law:

$$\sum F= \frac{\Delta p}{\Delta t}$$

Your phone hits the floor and there will be a momentum-change $\Delta p$ from it's impact speed to zero. You can't reduce that. But you can change the duration $\Delta t$ of this impact. Larger collision duration means smaller forces $\sum F$ on the phone.

Increasing $\Delta t$ means that you must cover it in a material that absorbs the kinetic energy; materials that deform at collision. Therefore soft. Not too soft, because it should be able to absorb the entire amount of kinetic energy. By making a thicker layer of this soft material, you again acheive more energy absorbed. A pillow is perfect.

(Just remember that you don't want to add too much mass by adding this cover, since mass raises $\Delta p$. But luckily, lightweigth and softness usually follow along.)

So, there's not really any argument for more layers. The softest material able to absorb the whole amount of kinetic energy with the given thickness that you will allow for, is the prefered solution. Any other materials are merely for design or user-feel purposes.

As the PO points out in the comments, there may very well be an advantage in having a hard outer shell, because the energy then can be dispersed by a large area. Maybe we shouldn't rule out such outer shell completely then. We are entering the engineering field then, since the design of the shell and evenly distribution of soft material under evenly spaced outer material is important here.

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  • $\begingroup$ So it is a myth that a thin hard outer layer would disperse energy across more surface of an inner soft layer ? $\endgroup$
    – FMaz008
    Nov 4, 2016 at 13:18
  • $\begingroup$ @FMaz008 Aha, that's a good point. I have not considered design influence on the shape here. A hard outer surface would of course be able to disperse the energy. We are moving more into the engineering field now, though, than the pure physics $\endgroup$
    – Steeven
    Nov 4, 2016 at 15:49
  • $\begingroup$ Yeah I tried to find a design/engineering stack but failed miserably. :-\ $\endgroup$
    – FMaz008
    Nov 6, 2016 at 0:05
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    $\begingroup$ @FMaz008 This is the one: engineering.stackexchange.com $\endgroup$
    – Steeven
    Nov 6, 2016 at 23:06

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