After some cursory research online about memory foam and its applications, many explanations include descriptions on how memory foam is “visco-elastic”, which I suppose suggests that it is both viscous and elastic. How exactly is this characteristic achieved?
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Memory foam is, despite all the marketing, just regular polyurethane foam.
Polyurethane foam, like all foams, begins its life as a liquid. This liquid then polymerizes, the act by which its constituent molecules join together like a bunch of people in a room linking arms. Once everyone is linked, no one can move. What was once a free-flowing crowd is now a tangled web of people.
The liquid has solidified into a foam.
Since each person is linked to two others, no one can move very much relative to their neighbours. However, the crowd as a whole can still move. If half the crowd were to take a step, the other half would get squished, and would push back. This would result in the crowd expanding back to where it was before.
The same is true of the foam. Once its hardened, and all of the molecules are frozen in space, they cannot flow past each other anymore, like a liquid. But, the mass as a whole can squeeze and stretch, but will always return to the shape it assumed when it first solidified.