are there any articles(books) where i could learn index free tensor calculus?

Question

the main point is that it uses direct abstract calculations without refering to a basis or using abstract index language.

https://link.springer.com/article/10.3103/S0025654414040037

for example:

Calculatation of the Einstein-Laub force density for linear dielectrics:

http://community.wolfram.com/groups/-/m/t/1127218

Answer 1

Have a look e.g. at these GR lecture notes by Winitzki and at this discussion on Physics Forums.

Answer 2

Among many others but this one is free, more general, clear and complete, including the didactic comparison with the Lorentz-Minkowski formula :

Electromagnetic force distribution inside matter

by Mansuripur, Zakharian & Wright