[Physics] Best cell-phone case design for impact energy absorption

designeveryday-life

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.

Best Answer

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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