# Tensor Notation

 Register Blogs Members List Search Today's Posts Mark Forums Read

 September 3, 2002, 10:31 Tensor Notation #1 Kevin A. Goodheart Guest   Posts: n/a 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

 September 3, 2002, 11:10 Re: Tensor Notation #2 sylvain Guest   Posts: n/a (?) = 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,

 September 3, 2002, 11:13 Re: Tensor Notation #3 h.jordi Guest   Posts: n/a 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.

 September 3, 2002, 12:30 Re: Tensor Notation #4 Kalyan Guest   Posts: n/a 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.

 September 4, 2002, 02:27 Re: Tensor Notation #5 Kevin A. Goodheart Guest   Posts: n/a 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

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

All times are GMT -4. The time now is 14:57.