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I am reading through Fung and Tong's "Classical and Computational Solid Mechanics", and feel that the Einstein summation convention saves a few symbols, at the expense of a lot of clarity. Along with that, there is rampant misuse of superscripts, where they are sometimes used as labels for basis vectors, and sometimes used to denote (as is usually done) a power.

Are there any presentations of tensors/tensor calculus/continuum mechanics I could look into that use a better notation (I am okay with using a few more symbols, for the sake of clarity), or present the currently widespread notation in a better fashion?

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    $\begingroup$ You'll have to get used to the super-script vs exponent if you are going to study tensors. It is a rather widely used notation, and even though it might look crazy in the beginning, in the long run being able to deal with this notation makes life easier. That said, I would say most math books in differential geometry deal with tensors in a coordinate free manner, but then you will need to pay the price by learning more abstract mathematics. $\endgroup$
    – Braindead
    Jan 26, 2014 at 5:08

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My personal favorite notation is the (relatively new) notation adopted in the following excellent review paper,

Kolda & Bader, Tensor Decompositions and Applications (SIAM Review 2009)

I feel it strikes a good balance between some of the more abstract pure math notations on one hand where elements of the tensor are not even considered, and the tedious physics index notation on the other hand.

Beware though, it's only really known/used in the numerical analysis and computational mathematics communities, but not the physics or geometry communities.

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  • $\begingroup$ Thanks for this recommendation! I'll give it a read through, and be sure to either accept your answer, or ask you further questions, depending on how well I am able to understand the paper. $\endgroup$
    – bzm3r
    Jan 18, 2014 at 18:40
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    $\begingroup$ Could you show the notation here, to make the answer more self-contained? $\endgroup$
    – mr_e_man
    Jan 26, 2022 at 19:14

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