  We study the limit behaviour of singularly-perturbed elliptic functionals of
the form \[ \mathcal F_k(u,v)=\int_A v^2\,f_k(x,\nabla
u)\.dx+\frac{1}{\varepsilon_k}\int_A g_k(x,v,\varepsilon_k\nabla v)\.dx\,, \]
where $u$ is a vector-valued Sobolev function, $v \in [0,1]$ a phase-field
variable, and $\varepsilon_k>0$ a singular-perturbation parameter, i.e.,
$\varepsilon_k \to 0$, as $k\to +\infty$.
  Under mild assumptions on the integrands $f_k$ and $g_k$, we show that if
$f_k$ grows superlinearly in the gradient-variable, then the functionals
$\mathcal F_k$ $\Gamma$-converge (up to subsequences) to a brittle
energy-functional, i.e., to a free-discontinuity functional whose surface
integrand does not depend on the jump-amplitude of $u$. This result is achieved
by providing explicit asymptotic formulas for the bulk and surface integrands
which show, in particular, that volume and surface term in $\mathcal F_k$
decouple in the limit.
  The abstract $\Gamma$-convergence analysis is complemented by a stochastic
homogenisation result for stationary random integrands.

Analysis of PDEs