strech and tension

hey guys!

I'm trying to make a surface act like lycra fiber and strch on top of an object. i'v maneged to lay the fiber on top of an object but i just wasnt able to find how to strech the fiber.

i'd be greatfull if anyone could help me understand what i'm doing wrong. i'm on this issue for 48 hours straight.

i'm adding the a picture of a 1:1 model that shows the final target.

thanks in advance