Page 107 - Introduction to Continuum Mechanics

92 Kinematics of a Continuum

Similarly,

3.5 Displacement Field

The displacement of a particle from position P to position Q is the vector PQ, Thus, the
displacement vector of a particle, from the reference position to the position at time t, is given
by

From the above equation, it is clear that whenever the pathline x(X,*) of a particle is known,
its displacement field is also known. Thus, the motion of a continuum can be described either
by the pathlines equation Eq. (3.1.1) or by its displacement vector field as given by Eq. (3.5.1).

Example 3.5.1

s yen
The position at time t, of a particle initially at (ATi^^s) * gi by

Find the displacement field.
Solution.

Example 5.2
The deformed configuration of a continuum is given by

Find the displacement field.
Solution. The displacement components are:

This displacement field represents a uniaxial contraction (the state of confined compression).