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## Homework Statement

I am following a textbook "Seismic Wave Propagation in Stratiﬁed Media" by Kennet, I was greeted by the fact that he decided to use cylindrical coordinates to compute the Stress and Strain tensor, so given these two relations, that I believed to be constitutive given an isotropic elastic medium =

$$\nabla (\textbf{u}) = \bar{\bar{\epsilon}}_{ij}$$

$$\tau_{ij}=\lambda \delta_{ij} \epsilon_{kk} + 2\mu \epsilon_{ij}$$

Given epsilon Strain and tau Stress tensors I was then surprised to see this

https://imgur.com/x4PG3iN

Equation 2.1.4, the shear stresses (crossed derivatives) and strains hold water to what I did, but the diagonals have an extra something...it looks like a divergence, multiplied by lambda, Am I missing basic calculus knowledge to solve this problem? I admit to be a bit rusty in my notation, even computing the equation 2.1.2 was tiring, but now I'm really surprised by this.

Any feedback would be greatly appreciated, thanks :)

## Homework Equations

$$\nabla (\textbf{u}) = \bar{\bar{\epsilon}}_{ij}$$

$$\tau_{ij}=\lambda \delta_{ij} \epsilon_{kk} + 2\mu \epsilon_{ij}$$

## The Attempt at a Solution

Stated above

P.S. [/B]= I posted it here because it is a mixture of math and physics, if it's wrong please let me know