In an elastic collision, 2 processes can be said to take place as mentioned here in the accepted answer: Why does a billiard ball stop when it hits another billiard ball head on?
First by the interacting force and then when the deformation is undone.
But why would the the latter process ('expanding back to original shape') cause changes in the energy/velocity of the same whole body ? Wouldn't it only cause changes in the local area where the deformation had taken place ?