I'm studying elasticity theory and for the problem "Finite Bending of an incompressible elastic block" I have the following first Piola-Kirchoff stress tensor:
$$S=\left(\frac{\pi + \mu_0}{\lambda_1} + \mu_0 \lambda_1\!\right)e_r \otimes e_1 + \left(\frac{\pi + \mu_0}{\lambda_2} + \mu_0 \lambda_2\!\right) e_\theta \otimes e_2$$
where $e_r = cos(\theta) e_1 + \sin(\theta) e_2$ and $e_\theta = - \sin(\theta) e_1 + \cos(\theta) e_2$
The author writes (see here at page 186 formula (5.95)):
$$Div(S) = \frac{\partial }{\partial x_1^0} S_{r1} e_r + \frac{\partial}{\partial x_2^0} S_{\theta 2} e_{\theta} = 0$$
but I can't understand what are the steps to get this result.
I mean, I know that in cartesian coordinates the divergence of a tensor $S$ is defined as $(Div(S))_i = S_{ij,j}$ but I don't know why he wrote that expression with $e_r$ and $e_\theta$. How can I compute that divergence? What are the steps I have to do?