Plastic strain depens on loading path

[progiangbk]

Hi there,

My teacher gave me a homework, but this Theory of Plasticity is new and difficult to me.

He has calculated the strain according to path (1), now I have to do with the path (2) and (3).

This is what he did with path (1):

ε11=∫(1/E)dσ11 + ∫[(σ11/S)(σ11dσ11+3σ12dσ12)]/(σ11^2 + 3σ12^2)

the first and second terminals for the above integration are (0,Y) and (0,Y/√3)

Finally he got:

ε11= (Y/E) + (Y/S)ln√2

Please help me with path (2) or pah (3) or both, or tell me how to solve it.

Thanks and best regards

 

[progiangbk]

I forgot the arrow for path (1) and (2):

Path (1): O => B => A
Path (2): O => C => A
Path (3): O => A

 

[progiangbk]

oh, i found it already!, just calculate the path integration!

I was confused because i made error in computing integration so the result was different with my teacher. Now everything's done!