When cooking at home, we often find that a perfectly good potato, once peeled, reveals brown and black spots inside. After removing these spots, there's hardly anything left of the potato. This kind of "internal damage" is also commonly seen in fruits like apples and pears. Common sense tells us that this must be due to the squeezing pressure between potatoes and apples during transportation. Damaged potatoes and apples can be easily identified, but how to explain the phenomenon that some potatoes and apples appear to be intact but actually have internal damage?
The "internal damage" problem is a typical contact problem in mechanics. For simplicity, we can regard potatoes as elastic balls subject to squeezing pressure between each other. Due to the deformation caused by squeezing, the contact area between two potatoes is no longer a point, but a contact circular surface. The squeezing pressure between objects causes shear stress inside the balls. Surprisingly, the maximum shear stress does not occur on the contact surface, but at a certain distance from it. Calculations show that the location of the maximum shear stress, which is also the place where "internal damage" occurs, is 47% of the radius away from the surface, which is almost at the center. Therefore, when potatoes are squeezed, they are almost completely damaged. It seems that improving packaging and transportation conditions during transportation is the fundamental way to "save" potatoes.
During the Ming Dynasty, there was a popular punishment called "court flogging": the emperor ordered that disobedient or wrongdoing ministers be publicly "spanked" in the courtroom. Although those who received court flogging didn't break bones or have obvious external injuries, they suffered internal injuries that were extremely painful. This also reflects the same principles of mechanics.