Thank you for this kind introduction.

The last time when I was here and talked about inelasticity already, I had the feeling after

the talk that I was a little bit too stuck in my own engineering perspective, so that

everybody was familiar with what inelasticity means and therefore I brought an experiment

this time.

So you have to know that in my field I'm only on the theory side, so I never did an experiment,

but let's try it out.

So I brought two spheres and they look almost the very same.

You can debate on the color, which is the nicer one, but the structure is almost the

can expect that they might behave the same.

And let's check this out.

So the first, I just drop it, it comes back, everything's fine, and I did it with the second

thing and nothing happened.

So it remains on the ground and it's deformed permanently.

So when I apply here a little bit of force and when I remove the force or remove the

external deformation, it always comes back to its original shape and in contrast this

blue circle here it does not.

So in fact it's modeling clay, so it can deform it and it deforms permanently.

And this is exactly what is the difference between elasticity and inelasticity.

And we want to model that, so therefore we have to talk a little bit about how we do

this in continuum mechanics and usually this takes a year for master students, but I'm

pretty sure we get this done in 10 minutes.

So this is not working at all, I think the battery is.

Then we do it from here.

Okay so in engineering we at the first step want to abstract things and a material scientist

would not agree, but from an engineering perspective this is fine enough.

So what we have seen on a microstructure, if you would really zoom in, you have the

atoms and you have some forces in between.

And what we do is we apply an external deformation, we call this F. It's not a force, it's a deformation.

So this grid here on the microstructure somehow deforms and then we remove the load and get

back to its original shape.

This is what we call elastic behavior and if you want to put this in a mathematical

context we postulate that there exists somehow a Helmholtz free energy.

So this is the scalar function and if you take the derivative with respect to the deformation

you get the stress.

And actually we can only measure the stress, we can never ever measure the energy, we measure

the stress.

So this is the quantity we later on fit our model.

And the nice thing about this approach is that also in 3D this is a scalar function

and scalar functions are more easy to interpret and in fact all of those components, if you

sum this up, all of them have a physical meaning which is quite nice if you want to

interpret the model which comes out.

So let's switch to inelasticity, we start with the very same grid, we deform it and

what you already see is, here's the dislocation.

So there's a slip in this microstructure and what happens is if we remove the load then

this dislocation remains.

So this is obviously not the very same as the original microstructure.

This is then what we call inelasticity, so a permanent or time dependent deformation.

And what is the reason?

What happens in between?