Equations for bending steel in a car crash?

[jetsfan83]

I wanted to know what formula's do I need to figure how much force is required to make a dent in a car. I am then placing a bumper guard made up of carbon fiber, and wanted to know what equation do I need to use to figure out how much force is required to make a dent with the carbon fiber bumper guard.

 

[Simon Bridge]

1. you want the body panels, especially the bumper, to crumple ... that is what saves you in a crash: an undentable car would be a death trap.
2. it's very complicated ... there are no standards.
3. even quite gentle collisions or crushes can easily produce many times the minimum force needed to dent the metal.
https://plastics-car.com/Todays-Automobiles/Automotive-Safety/Physics-in-the-Crumple-Zone-2.html

You can get an idea by looking up "sheet metal bending force" ... force to bend sheet metal.
Extrapolate for the panel geometry of the bits you want to protect.

 

[Chestermiller]

Consult the literature on bending beams and plates, and also the literature on quantitative yield criteria of metals. Look up von mises and Tresca yield criteria.

 

[marcusl]

The process of crumpling is incompletely understood. Energy is dissipated in plastic deformations, especially in ridges and creases,.
BTW, carbon fiber doesn't behave like steel. It can shatter instead of denting or bending. Energy is still dissipated, but it may not be comparable to a standard bumper.