stress derivative of von misses stress 1

[shazar]

Hi to All ,
as you know VM=(2/3*S:S)^-1 i wanr to calculate partial derivative of VM WRT sigma. Could you help be about derivation i am not sure if i am right but first i have to calculate (sigma-1/3trsigma*I)sigma-1/3trsigma*I) ?

 

[TERIO]

See the section in the link below "Differentiating the yield criterion"

[URL unfurl="true"]http://solidmechanics.org/text/Chapter3_7/Chapter3_7.htm[/url]