Here is the problem:

T_ij = S_ij - .3*S_kk + S_ik*S_kj-.3*S_kl*S_kl

The first term is i=1,j=1,k=1

T_11 = S_11 -.3(S_11+S_22+S_33) + S_11*S_11 - .3*(?)

What do I do with this kl. I am trying to implement the explicit algebraic stress model, one could argue that if I can't figure out the tensor notation then I shouldn't be trying to implement an EASM model but that is just one of many problems.

Thank You, Kevin

(?) = S11*S11+S12*S12+S13*S13

+ S21*S21+S22*S22+S23*S23

+ S31*S31+S32*S32+S33*S33

It's the same for any ij. Was not it written S_kl*S_lk ? Which is the same if S is symetric,

hi kevin.

if i understand your question.........

T_ij = S_ij - (S_kk) + [S_ik*S_kj] - {S_kl*S_kl}

you understood the first bracketed term ( ) was an implied sumation.

well the second bracketed term [ ] is also an implied summation on k. so you get =

S_i1*S_1j + S_i2*S_2j + S_i3*S_3j

and, the third term { }. this has a double repeated index, l and k and so you sum on both. giving =

S_11*S_11 + S_12*S_12 + S_13*S_13 + S_21*S_21 + S_22*S_22 + S_23*S_32 + S_31*S_31 + S_32*S_32 + S_33*S_33

H.

Kevin,

The expression

T_ij = S_ij - .3*S_kk + S_ik*S_kj-.3*S_kl*S_kl

is not tensorially consistent because there are scalars (2ns and 4th terms on the right) mixed in with tensors (other terms). A correct form would be

T_ij = S_ij - (.3*S_kk) delta_ij + S_ik*S_kj - (.3*S_kl*S_kl) delta_ij

Terms involving repeated indices (k and l) have an implicit double summation.

Thank You all for you help with my Tensor Notation and also catching my two mistakes, not summing the second term and leaving out the delta_ij function.

Now time to have fun solving this equaiton.

Kevin