  In this paper we study the asymptotic behaviour of phase-field functionals of
Am brosio and Tortorelli type allowing for small-scale oscillations both in the
volume and in the diffuse surface term. The functionals under examination can
be interpreted as an instance of a static gradient damage model for
heterogeneous materials. Depending on the mutual vanishing rate of the
approximation and of the oscillation parameters, the effective behaviour of the
model is fully characterised by means of Gamma-convergence.
