A displacement field is an assignment of displacement vectors for all points in a body that is displaced from one state to another.
A displacement vector specifies the position of a point or a particle in reference to an origin or to a previous position.
Before considering displacement, the body state before deformation must be defined. It is a state in which the coordinates of all body's points are known and described by function:
Most often it is a state of body to which no forces are applied.
Then given any other state of this body in which coordinates of all its points are described as the displacement field is the difference between two body states: