Mechanics

I believe, I could summarize my eight years in mechanical engineering (bachelors and master) in this single post.

Most of our physical world is related with solids and fluids. So, what is a good definition of solids and fluids?

This one:

  • Solids: Is that state of matter which stress \sigma, is function of deformation \epsilon. We represent this as: \sigma = f(\epsilon).
  • Fluids: Is that state of matter which stress \sigma is function deformation rate \dot{\epsilon}. We represent this as \sigma = f(\dot{\epsilon}).

The best of all, is that we could model both behaviors with just one equation. This is the damped motion equation:

m\ddot{\epsilon}+\lambda\dot{\epsilon}+k\epsilon=0

Re-arranging:

m\ddot{\epsilon}=-\lambda\dot{\epsilon}-k\epsilon

Which means:

Stress = rate of  deformation (fluid behavior) + deformation (solid behavior)

So we can model a vast quantity of physical cases solving this single equation. Watch me doing it for underground mining here using Discrete Element Method (DEM). By the way, DEM really rocks.

So, the important things to be noticed are:

  • Stress depends on deformation and rate of deformation.
  • Stress depends on time.
  • Stress is not the most fashion way to start a year :S

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