I have done some problems in current electricity where you stretch or squeeze a wire, the length and area of cross section change but the volume remains same.
A question on math.stackexchange.com tries to answer it mathematically( https://math.stackexchange.com/questions/1125781/does-the-volume-of-a-ball-remain-constant-under-deformation)
But why it is thee physical reason behind volume being unchanged and on what physical limits the stretching & squeezing (and other sort of deformation) will leave the volume unchanged?
P.S. As per Mike Dunlavey's comment I am not talking about incompressible objects.