ponjavic
Feb19-08, 01:59 PM
1. The problem statement, all variables and given/known data
1a) Confirm that grad dot (y x sigma) = y x grad dot sigma + grad*sigma x sigma
where y is a vector and sigma a second order tensor
2. Relevant equations
(a x b)_i = e_ipq a_p b_q
(A x B)_i = e_ipq A_pl B_ql
(a x B)_ij = e_ipq a_p B_qj
(caps are tensors)
3. The attempt at a solution
I get:
e_ipq y_p sigma_qj = e_ipq y_p sigma_qj,j + e_ipq y_p,l sigma_ql
if it is correct I'm not quite sure how to add the third and second term together
1a) Confirm that grad dot (y x sigma) = y x grad dot sigma + grad*sigma x sigma
where y is a vector and sigma a second order tensor
2. Relevant equations
(a x b)_i = e_ipq a_p b_q
(A x B)_i = e_ipq A_pl B_ql
(a x B)_ij = e_ipq a_p B_qj
(caps are tensors)
3. The attempt at a solution
I get:
e_ipq y_p sigma_qj = e_ipq y_p sigma_qj,j + e_ipq y_p,l sigma_ql
if it is correct I'm not quite sure how to add the third and second term together