For the people who are familar with continuum mechanics:

 

How I can derive a stress tensor T for a chocolate dependent on

- Cauchy-Green deformation tensor E

- Strain rate tensor D (is objective derivative of E)

- The time where the chocolate is exposed mechanical loads or temperatures (denoted by t)

- The state of the chocolate (whether it is solid or liquid)

- etc.?

 

I am very familar with continuum mechanics, I know how to derive material models for viscoelastic, plastic or viscoplastic continua.

But chocolate seems to be more complicated than these, because chocolate will undergo a phase change if it is chewed in the mouth.

I have to use diffusion equations also for deriving the stress tensor, right? Do I need in-between configurations for describing chocolate in different phase states?

 

Are there theories which can describe such complicated material behavior?

 

 

 

 

I am sorry the experts here have declined to help.

 

I cannot paste links from this computer but I googled food rheology and chocolate rheology and found lots.

 

Happy surfing

Oooh, lets have this discussion. I too can generally write these equations down from first principles material frame description and can write fully hyperelastic viscoplastic [properly rate dependent] codes even for the extreme dynamic limit of true shock physics [proof:

] and I thought rock was rock hard... but I just don't have a clue how to do this choccy question. Please do inform us how to contend with solid-liquid transitions.

oh, did not realize the aside link would appear like that in my post!

The margarine and butter industries have done considerable research on this subject related to fats, which also undergo pseudo phase transitions. Chocolate is a large % fat after all. But all are mixtures, so do not exist in single phases in the same way as pure substances.

But in my everyday [not every day!] experience, chocolate is solid and undergoes brittle failures and can be fragmented too.

Does the addition of saliva have something to do with the all important "mouth feel" transition too?

What if its got nuts in?

Nightmare for modellers...

Chocolate is complicated.

 

Yes it may fail in brittle failure at room temperatures in bending but it will more than likely squash rather than fragment to powder under compression. I have never tried triaxial tests on it though.

I would love to see bullets and projectiles fired in to it, videod with high frame rate.

I wonder how it spalls?

Is dark choc much more brittle than white choc?

Is Belgian Chocolate [real chococlate] completely different to American Candy cocoa solids [faux-choccy]?

What an interesting piece of materials science.

Well, if your organisation needs a consultant to spearhead your investigation, let me know.