(a) Consider a W = that is pure expansion: Using Eq. (11.3) show that, in the vicinity of a chosen point, the displacement vector

(a) Consider a W = ∇ξ that is pure expansion: 

Using Eq. (11.3) show that, in the vicinity of a chosen point, the displacement vector is 

Draw this displacement vector field.

(b) Similarly, draw ξ(x) for a W that is pure rotation.

(c) Draw ξ(x) for a W that is pure shear. To simplify the drawing, assume that the shear is confined to the x-y plane, and make your drawing for a shear whose only nonzero components are Σ_xx = −Σ_yy. Compare your drawing with Fig. 11.3.

Eq.11.3

Figure 11.3

Wij = @gij.