# Make a sample lecture on Elasticity in bars.

While talking about life, the universe and everything with a friend we started to apply chatGPT for a very recurrent task: create a useful lecture for a technical topic.
My friend is a prolific engineer and math champion that is teaching a Mechanical Eng class for computer engineers.
Since eventually all sentient being will be using chatGPT or similar tools, the idea was to present a creative and useful way of applying chatGPT for the class students.

The selected topic, ***Elasticity in Bars***, came out of nowhere, and then we started our prompt.

*Make a sample lecture on Elasticity in bars.*

## Elasticity in Bars

> Elasticity refers to the ability of a material to return to its original shape after it has been deformed by an applied force. When discussing elasticity in bars, we are referring to the extent to which a bar will stretch or compress under a load, and how it will return to its original length once the load has been removed.
>
> Bars are typically made of materials like steel, aluminum, or plastic that have high elastic moduli, which means they are able to resist large amounts of deformation before they break. This is an important property for many structures, as it allows them to support heavy loads while still returning to their original shape.
>
> When a bar is subjected to a load, it will stretch or compress until the load is balanced by the internal force of the material. This internal force is known as stress, and it is proportional to the amount of strain (or deformation) in the bar. The relationship between stress and strain is described by Hooke's Law, which states that stress is directly proportional to strain within the elastic limit of the material.
>
> It is important to note that there is a limit to the amount of strain that a bar can undergo before it reaches its elastic limit and becomes permanently deformed. This limit is known as the proportional limit, and it is a property of the material that determines the maximum stress that can be applied to the bar without causing permanent deformation.
>
> When a bar exceeds its proportional limit and becomes permanently deformed, it is said to have undergone plastic deformation. In this case, the bar will no longer return to its original length when the load is removed, and it may even break.
>
> In conclusion, the elasticity of a bar refers to its ability to stretch or compress under a load and return to its original shape once the load has been removed. The extent of this ability is determined by the elastic modulus of the material, which can be described by Hooke's Law. Understanding the principles of elasticity in bars is crucial for designing safe and reliable structures that can resist large loads without permanent deformation or failure.

Our first reacting was "Fuck. This is it."
To get practical, we asked for a simple experiment.

*Fantastic. Write a sample experiment for a mathematical rhelogic model for elasticity*.

> Experiment: Mathematical Model for Elasticity
>
> Objective: To develop a mathematical model for elasticity by testing the relationship between the applied load and the deformation of a bar.
>
> Materials:
>
> Bar made of a material with a known elastic modulus (e.g. steel, aluminum, or plastic)
> Load cell to measure the applied force
> Dial gauge or micrometer to measure the deformation of the bar
> Computer and data acquisition system for recording and analyzing the data
> Procedure:
>
> Secure the bar between two supports, with the dial gauge or micrometer attached to measure the deformation of the bar.
> Apply a load to the bar using the load cell, starting with a small force and gradually increasing it.
> Measure and record the deformation of the bar at each step.
> Plot the stress (load divided by cross-sectional area of the bar) versus strain (deformation divided by original length of the bar) for the data.
> Compare the results with the predictions of Hooke's Law (stress = elastic modulus * strain) to determine the validity of the mathematical model for elasticity.
> Repeat the experiment for different levels of applied load to further validate the model.
> Expected Results: The results should show a linear relationship between stress and strain within the elastic limit of the material, as described by Hooke's Law. Beyond the proportional limit, the relationship between stress and strain should become non-linear and the bar should become permanently deformed.
>
> Conclusion: This experiment provides a practical demonstration of the mathematical model for elasticity and helps to reinforce the concepts of stress, strain, and the relationship between them described by Hooke's Law. The results can be used to better understand the behavior of materials under load and to design more reliable structures.

*Absurd. Write a sample code illustrating the suggested experiment. try to be concise.*

Yep, absurd. A very simple and effective experiment, useful as hell as a introductory class on the topic.

And then, let´s see the code.

## Sample Code: Elasticity Experiment

import numpy as np
import matplotlib.pyplot as plt

# Define the elastic modulus of the material
E = 210e9 # Pa

# Load data
force = np.array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0]) # N
deformation = np.array([0.0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3]) # m

# Calculate stress and strain
cross_sectional_area = 0.01 # m^2
stress = force / cross_sectional_area
strain = deformation / 1.0 # m

# Plot stress versus strain
plt.plot(strain, stress, 'o-')
plt.xlabel('Strain (m/m)')
plt.ylabel('Stress (Pa)')
plt.title('Elasticity Experiment')

# Plot Hooke's Law predictions
strain_pred = np.linspace(0, 0.3, 100)
stress_pred = E * strain_pred
plt.plot(strain_pred, stress_pred, 'r')

# chatGPT suggested this. We decided to create a file
# plt.show()

plt.savefig("test.png")


> Explanation: This code implements a simple experiment to test the relationship between stress and strain in a bar. It uses the numpy and matplotlib libraries to load the data, calculate stress and strain, and plot the results. The results are compared with the predictions of Hooke's Law, and a graphical representation of the experiment is displayed. This code provides a concise illustration of the suggested experiment, and can be easily modified to accommodate different data or variations in the experimental setup.

Yep. A simple but effective lecture on Elasticity.
It´s clear how useful this tools can be for our daily stuff.
Having so much fun.