# Elasticity

Elastic Moduli are how engineers quantify the strength of a material. Intuivitely, the stiffer the object, the less shape change that will result in response to an applied stress. Stress is Pressure, so you can think of it as “Stressure”.

This is the same elasticity used to describe a rubber (elastic) ball.

## Elastance vs Compliance

As usual, physicists have great names for things. Imagine two friends of yours with different personalities:

- The Elastic Personality bounces back from anything. They don’t get bent out of shape no matter how much stress they are under.
- The Compliant Friend doesn’t resist much. They will leave the library to go see the newest blockbuster movie when you apply even the least bit of peer pressure.

In Physiology, we talk about the “Stiffness” of a material as its Elastance. The inverse of that quantity is the “Floppiness,” or Compliance.

## Elastic Moduli

### Shear Modulus

Amount of strength to resist "shear" (deformation of solid while keeping equal volume). Force applied tangentially to a surface of a solid will cause a rectangular solid to become a parallelogramatic prism. The equation is simply:

Shear Modulus (S) = Tangential Stress / slope created = (F/A) / (∆x/l)

or:

Shear Modulus (S) = Tangential Stress / Tan θ = Tangential Stress/Tangential Strain

### Young Modulus

A measure of the strength of solids when they are compressed in a single direction (think car crash).

Young Modulus (Y) = Stress/Strain = (F/A) / (∆L/L)

===============================

### Bulk Modulus

(Not directly on MCAT): Basically, another measure of stiffness, like Young’s modulus, but when the solid is being compressed from all sides at once. Think of this like a 3-dimensional Young’s Modulus:

Bulk Modulus

Note: This differential equation is beyond the scope of the MCAT. You just need to know that a stiffer solid has a higher bulk modulus, and has a faster speed of sound.

If desired: Equation analysis still makes it understandable: You multiply the current volume by opposite of the derivative of Pressure with respect to Volume. As the Volume goes down, you expect to need more pressure to keep shrinking the solid, so the derivative increases with respect to decreasing volume. Since the change in volume is negative, the derivative must be negative, which is why the negative sign exists in the equation. So, in the end, stiffer solid → higher bulk modulus.