The Cauchy stress tensor is given by:
$T_{11} = x_1^2 + x_2^2$, $T_{22} = x_1x_2x_3$, $T_{33} = x_1^2 + x_2^2$
$T_{12} = x_1x_2$, $T_{13} = x_1x_3$, $T_{23} = x_2x_3$
The body force is given by $b = ge_3$.
a) Write the stress tensor, T, in matrix form.
b) Show that this body cannot be in a state of static equilibrium.
c) Calculate the acceleration field in the body to satisfy the balance of linear momentum.
d) Find the tractions acting on the plane $x_1 + 2x_2 + 3x_3 = 8$, at location $x = (1,2,1)$.
