  We prove the $\Gamma$-convergence of sequences of differentially constrained,
random integral functionals of the form \begin{equation*} \int_{U}
f\Big(\omega, x/\varepsilon, \mathbb{A} u\Big) \mathrm{d} x \end{equation*} for
the class of vectorial differential operators $\mathbb{A}$ with
finite-dimensional nullspaces. This work is intended to generalise results for
the full gradient and to cover the cases of symmetric gradients and the
deviatoric operator. The homogenisation procedure is carried out by employing a
variant of the blow-up method in the setting of $\mathbb{A}$-weakly
differentiable maps along with the Akcloglu-Krengel subadditive ergodic
theorem.
