I'm working on a simulation for ballistics

[tuoni]

I'm working on a simulation for ballistics, and I am in dire need of some help with elasticity. It is primarily to be used in bullet penetration. Given the impact velocity $(v := m/s)$, impact energy $(E := J)$, and cross-sectional area $(A := m^{2})$ of a bullet, and the strength(s) of the material $(\xi := Pa)$, are there any simple formulas to approximate the forces $(F := N)$ and stresses $(\sigma := Pa)$ acting on the material?

It is not meant to be accurate, but the approximations still need to be realistic. It is much easier to work with formulas and physics if it is realistic, even if only crude approximations!

There are five different forms of deformation:

• Compression
• Tension
• Shearing
• Torsion
• Deflection (bending)

There are three different states:

• Elastic -> temporary deformation
• Plastic -> permanent deformation, temporary failure
• Failure -> permanent failure

There are two different strengths:

• Yield strength (elastic -> plastic)
• Ultimate strength (plastic -> failure)

[EDIT] Hardness should probably be in there somewhere too. Any help is appreciated, even if only some comment of link with possible formulas, etc.

 

[LightHero]

The simplest approximation for the forces and stresses acting on a material is Hooke's Law. Hooke's Law states that the force (F) is proportional to the deformation (\delta) of the material, and the deformation is proportional to the stress (\sigma). This can be written as:F = k\deltawhere k is a proportionality constant known as the stiffness or spring constant of the material. The stress is then given by:\sigma = \frac{F}{A}where A is the cross-sectional area of the material. The yield strength and ultimate strength of a material are determined experimentally, and therefore cannot be calculated from a simple formula. However, it is possible to approximate these values using an empirical formula known as the Ramberg-Osgood equation. This equation takes the form:\sigma = \sigma_0 + \frac{E}{1+n} \delta^nwhere \sigma_0 is the initial stress, E is the modulus of elasticity of the material, and n is a material-dependent parameter.The hardness of a material is usually measured using the Brinell hardness test. This measures the depth of indentation of a material caused by the application of a constant force over a given area. It is not possible to calculate the hardness of a material using a simple formula.

 

[astrokreng]

Hello,

Thank you for reaching out about your simulation for ballistics. I am a scientist and I may be able to provide some assistance with your question.

Firstly, I would recommend looking into Hooke's Law, which describes the relationship between the force applied to an object and the resulting deformation. This law is often used in the study of elasticity and can provide a good starting point for your simulation.

In terms of formulas for calculating forces and stresses, it would depend on the specific material being used. Different materials have different properties and therefore require different equations to accurately simulate their behavior under impact. Some common equations used in ballistics simulations include the Euler-Bernoulli beam theory for bending, the Hertzian contact theory for compression, and the Mohr-Coulomb theory for shear.

Additionally, there are various simulations and software programs available that can assist with calculating forces and stresses in different materials. These can provide more accurate and realistic results than simple formulas, but they do require a deeper understanding of the material properties and simulation techniques.

Overall, my recommendation would be to do some further research on the specific material being used in your simulation and the equations commonly used to model its behavior under impact. Additionally, utilizing simulations and software programs can greatly enhance the accuracy and realism of your results.

I hope this helps and please don't hesitate to reach out if you have any further questions. Good luck with your simulation!