Hello Taiwo,

You made a valiant effort to obtain the component representation of the third invariant of the second-order tensor. You are generally on the right track but you did not express the scalar product completely in the component form as you should have done. Since a scalar triple product is a scalar, you should be able to express it completely without any vector basis. I have decided to work it out fully for the class and my notes from now on will carry the explanation I am supplying below:

This should provide a complete answer to what you were trying to do. If you have further questions, please comment below.

Please can anybody help me find the page that contains question 2.11.1 Ά̲̣̥πϑ 2.13.1 refered †̥o in homework 2.2, ℓ̊’ve searched through gurtin but can’†̥ find ℓ̊†̥. ℓ̊ saw equation 2.111 which Ȋ̝̊̅§ not an excercise. Help please

In the recommended textbook: Gurtin, here is the way I reference questions: the first number is the chapter number, the second number is the section after which the questions are placed. Lastly, the third number is the number of the question itself. You will see therefore that Question 2.11.1 is question 1 on page 23; and question 2.13.1 is also question 1 on page 27.

Sir, this explanation completely answers my question. I can now see what I should have done. Thanks Prof.

Speaking of your comment here, I fell into the same trouble in the last assignment submitted. Instead of referring to the referred exercises, I was solving the equations that corresponds to the label( eg 2.61 instead of 2.6.1). They annoyingly looked worthy of proving. It was after I saw my marked script I discovered I was showing a different thing which earned me no mark. My bad! Because I should asked this same question earlier.

Good Afternoon Sir,

I’d like to know the mutation that happened to the second kronecker delta l i (line 2 of the proof), on slide 73 of the tensor algebra class note.

My concern is the location of l

Thank you

Charles, It does not appear that you have been sufficiently specific in your question. As the numbering of the slides I have may be different from yours, it may be necessary to include the slide header or say something more about the problem. I am sure the only thing that can lead to the “disappearance” of a Kronecker Delta in a subsequent equation is that it was used as a substitution operator as I had taught in class. If you get more specific, I may be able to say more.

On a second look, I think I have seen the problem you are referring to. Take a look at the six-symbol Kronecker Delta. You will see that the first two symbols (up and down) became i – i rather than l – i as a result of the substitution operation of the Kronecker delta you are talking about. Anytime a Kronecker Delta disappears, it has been used as a substitution symbol!