Nature of displacement and the deformation tensor

[mohammed El-Kady]

If we have two points P and Q in undeformed material and after deformation they become P' and Q'. The deformation tensor is the derivative of the displacement. What is the displacement? vector PP'? or the change from PQ to P'Q'?
is the second question is the strain "change in length".
Why the deformation is the derivative of displacement, why not the displacement itself? does it has scientific reason or just choice?

 

[Chestermiller]

If we have two points P and Q in undeformed material and after deformation they become P' and Q'. The deformation tensor is the derivative of the displacement. What is the displacement? vector PP'? or the change from PQ to P'Q'?
is the second question is the strain "change in length".
Why the deformation is the derivative of displacement, why not the displacement itself? does it has scientific reason or just choice?

The deformation gradient tensor maps the differential vector between P and Q into the differential vector between P'and Q'.