Page 96 - Introduction to Continuum Mechanics

Description of Motions of a Continuum 81

e
where X = jt 1e 1+jt 2e2+*3 3 is the position vector at time t for a particle which was at
X = XTPI+XTFV+X&S at f = 0. Sketch the configuration at time t for a body which at t - 0
has the shape of a cube of unit sides as shown in Fig. 3.2.
Solution. In component form, Eq. (i) becomes

Fig. 3.2

At t = 0, the particle O is located at (0,0,0). Thus, for this particle, the material coordinates are

Substituting these values for X\ in Eq. (ii), we get, for all time t, (jtj, x^, £3) = (0,0,0). In other
words, this particle remains at (0,0,0) at all times.
Similarly, the material coordinates for the particle ^4 are

and the position for ,4 at time t is

Thus, the particle^ also does not move with time. In fact, since the material coordinates for
the points along the material line OA are

Therefore, for them, the positions at time t are