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A displacement field is an assignment of displacement vectors for all points in a region or 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. For example, a displacement field may be used to describe the effects of deformation on a solid body.
Before considering displacement, the state before deformation must be defined. It is a state in which the coordinates of all points are known and described by the function:
Most often it is a state of the body in which no forces are applied.
Then given any other state of this body in which coordinates of all its points are described as R → 1 {\displaystyle {\vec {R}}_{1}} the displacement field is the difference between two body states: