Let $BV(\mathbb R^n; \mathbb R^n)$ be the space of (vector-valued) functions of bounded variation and let $BD(\mathbb R^n;\mathbb R^n)$ the space of functions with bounded deformation. They are made up respectively of functions $u$ for which the full distributional derivative $$ Du \in \mathcal M(\mathbb R^n) $$ is represented by a measure with finite total variation and of the functions for which the symmetric part of the distributional derivative $$ Eu := \frac{Du+(Du)^t}{2} \in \mathcal M(\mathbb R^n) $$ is represented by a measure with finite total variation.

If $n=1$ of course the two definitions coincide. For $n\ge 2$ they are different, but I do not find an explicit example.

Q.Let $n\ge 2$. Find an element in $BD \setminus BV$.

Is a characterization of such functions available somewhere in the literature?