The deformation mechanism of cold rolling thin foil is investigated wi
th the aid of the slab method in conjunction with an incremental analy
sis. The interaction between the rolls and foil is explored thoroughly
. The effects of initial thickness and yield stress of foil materials
are discussed in detail. Extensive numerical studies show that the pre
ssure and shearing force profiles in the rolling bite vary significant
ly with the increment of reduction ratio. The distribution of slip and
no-slip zones is much more complex than that predicted previously. In
the regime of rolling extremely thin foils with a constant reduction
ratio, the rolling load increases and the rolling torque decreases mon
otonically with decreasing inlet foil thickness. It is found, however,
that the change of the central elastic/plastic no-slip zones has very
little effect on the resultant rolling forces.