Ran one's hand over the material (4)
I believe the answer is:
felt
I believe this clue is a double definition.
'ran one's hand over' is the first definition.
(I've seen this before)
'the material' is the second definition.
(felt is a kind of material)
(Other definitions for felt that I've seen before include "checked by hand" , "Fabric - perceived by touch" , "Fabric of matted wool fibres" , "investigated in touching way" , "Touched; a soft material" .)