SolidMechanics

In the rigid body assumption, things always maintain their shape without deforming.

For example, imagine two cars running into each other at 30 miles per hour each and 1 car driving straight into a wall (that does not move or deform) at 60 miles per hour. With the rigid body assumption, both would be the exact same situation. But in practice, the cars would deform, absorbing some energy. So, the second situation would be worse than the first.

While the Rigid Body assumption is useful for understanding how forces act onto an object, Solid Mechanics is equally useful for understanding the forces inside an object. In this section, we will cover some basic ideas related to Solid Mechanics.

Elasticity: How much something bounces back from a change. Rubber bands have high elasticity. They can recover from relatively heavy stretching and bending. However, steel has low elasticity. Although it takes a lot of force, if you bend steel. It will likely stay in that form.

Deformation: How much something’s shape changes after a force is exerted upon it. There are two types.

Plastic Deformation: A temporary deformation. After a force is no longer exerted, it will return to its previous form.

Elastic Deformation: A permanent deformation. Even when a force is no longer exerted, it will not entirely return to its previous form.

To measure deformation, we use stress and strain. Stress is calculated by the equation and measured in psi. To summarize stress is the amount of force exerted at each point of contact.

Strain is calculated by the equation and measured in no units, but simply percentage. This means that strain is the increase in length that comes when something is squished.

As an example, imagine a hand gripping the handle of a fridge. The stress would be the grip force of the hand divided by the area of the hand contacting the handle. As another example, imagine you were playing with generic putty with no brand association at all and you squished it. The strain would be how much longer it gets after being squished divided by its original length.

Returning back to deformation, elastic deformation must become plastic deformation at some point. This amount of necessary stress to permanently deform a material is called yield strength. When stress exceeds the yield strength, elastic deformation becomes plastic deformation.

Also, at some point the material itself has to break. This happens when stress exceeds the UTS. UTS stands for Ultimate Tensile Strength and when stress exceeds the UTS, a break occurs. In Ultimate Tensile Strength, the Ultimate means maximum, and strength refers to how strong something is. But, what does the Tensile section even mean? Tensile, or tension is an outward pulling force, like pulling a string apart until it is taut.

On the other hand, compression is the opposite, or an inward pushing force. So, when strain is below 1, you are facing compression, and when it is above 1, there is tension.

When something is bending, there is compression on one side and tension on the other. Also, one key thing to remember is that everything breaks on the tension side first because tension is pulling it apart. That is why we measure the Ultimate Tensile Strength, not the Ultimate Compression Strength.

Finally, here are two other terms you will encounter in Solid Mechanics:

Ductility: How much tensile force something can withstand without causing fractures. This is the opposite of malleability which allows for hammering into sheets vs stretching into wires.

Nucleation: the idea that when something breaks, it will happen where the radius of curvature is the smallest. The radius of curvature is how sharp the tip of a crack is so those areas are the weakest. This is because the highest stress concentration will be there. To understand this better, imagine a crack in the material. The smaller the smallest marble that can fit at the part of the crack that is the smallest, the more likely a break is to occur.