Displacement field (mechanics)

A displacement field is an assignment of displacement vectors for all points in a body that is displaced from one state to another.

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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:

$\vec{R}_0: \Omega \rightarrow P$

where

$\vec{R}_0$ is a placement vector

Ω

are all the points of the body

P

are all the points in the space in which the body is present

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 $\vec{R}_1$ the displacement field is the difference between two body states: