Let us consider rotation about the center of the cube. Since the problem concerns a pure rotation, a cylindrical co-ordinate system is appropriate. This problem also provides us a easy way of trying out Maple. Here are the steps that you can follow to find the strains at a point in the cube.
r := sqrt(x^2+y^2);
theta := arctan(y/x);
x1 := r*cos(theta);
y1 := r*sin(theta);
x2 := r*cos(theta+Pi/2);
y2 := r*sin(theta+Pi/2);
u := x2 - x1;
v := y2 - y1;
epsx := simplify(diff(u,x));
epsy := simplify(diff(v,y));
gamxy := simplify(diff(u,y) + diff(v,x));
From the above Maple calculation, and noting that there is no motion
in the direction, the strains in the cube are
A pure rigid body rotation should not result in any non-zero strains.
Therefore, the measure of strain we have used is not appropriate for
large rigid body motions.