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[Jan Stránský <question690521@xxxxxxxxxxxxxxxxxxxxx>]

Question #690521 on Yade changed:
https://answers.launchpad.net/yade/+question/690521

Jan Stránský proposed the following answer:
There are some misconceptions in your formulas.
Specifically, do not use scalars where there should be vectors or even tensors (then you will not end with a scalar while expecting a vector).

below (to make it mode readable) s=stress, u=displacement, up=plastic
displacement, k=stiffness

> (dF/ds)=sign(s)=+1
> dup=d_lambda*(dg/ds)
F,g ... scalar
s ... vector
dF/ds and gd/ds ... has to be vector
dF/ds = d(|s|)/ds = s / |s| 

try a re-derivation. If the re-derivation does not help, I suggest to
switch to personal conversation, as the topic is not really Yade
related..

> (dsigma_S/dUs_Pl)=k_s*(1-D_old)

shouldn't D be treated as a function of us_pl?

cheers
Jan

d(|s|) / ds = 
= d(sqrt(s.dot(s)) / ds = 
= 1/2 * 1/sqrt(s.dot(s)) * d(s.dot(s)) / ds =
= 1/2 * 1/|s| * d(s.dot(s)) / ds =
= 1/2 * 1/|s| * (1*s + s*1) =
= s / |s|

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