We're just going to programming everything.

We're just going to stick to some of these.

On what other tools are we going to use?

We are?

We are?

Welcome everybody.

I'm going to start video,

to speak today, you can see is,

I mean, these results are collected in a paper

written with these four colleagues of mine,

Serena Di Piero and Enrico Aldinoci

from the University of Perth in Australia,

and Francesco Maddalena from my same university,

it is the Technical University of Bahrain.

Now, before then we start with the,

really the technicalities and the details of the problem.

Let me briefly give you the background,

the motivations behind these models,

these non-linear pre-dynamic models.

So let us start with really the fundamental things

and the little resume,

which is the classical elasticity theory.

So first of all,

which is the key problem in solving mechanics.

And as you can read here is

the spontaneous formation of singularity.

Now, in these four words,

spontaneous formation of singularity,

we should understand the meaning.

First of all, the word spontaneous,

and second of the word singularity.

When I say spontaneous, I mean a singularity

that was not there at time zero.

So it's not there when you start to look at the dynamics

or at the phenomenon that you are watching,

and there is creating somewhere for some reason.

So no, I mean, no motivation at time zero

to expect the creation of a singularity

and to expect the creation of a singularity

in a precise point.

Now, what I mean by singularity?

Singularity can mean a crack in a homogenous solid,

and you can really fold in ripples,

buckling, evolution of phase boundaries,

and so on and so forth.

So let me show you four pictures that I got from Google.

So I mean, pictures that we all knew,

and pictures of phenomena that we know.

To better understand which kind of phenomena

do we need to consider.