# Transformation - strain tensor matrix

A question from a continuum mechanics beginner... If the stress $$\sigma_{xx}$$ is applied to an isotropic, three-dimensional body, the following strain tensor results:

$$\boldsymbol\epsilon=\left(\begin{matrix}\frac{1}{E}\sigma _{xx} & 0 & 0 \\0 & -\frac{\nu}{E}\sigma _{xx} & 0 \\0 & 0 & -\frac{\nu}{E}\sigma _{xx}\end{matrix}\right)$$

Now the tensor should be rotated in the xy-plane by the angle $$\alpha$$.

How is the transformation matrix calculated to get the strain components in the x', y', z'-coordinate system?

$$A' = Q A Q^T\, ,$$
where $$Q$$ is the transformation. In this case, your $$Q$$ should look something like
$$Q = \begin{bmatrix} \cos\alpha &\sin\alpha &0\\ -\sin\alpha &\cos\alpha &0\\ 0 &0 &1 \end{bmatrix}\, .$$