AbstractA framework for damage modelling based on the fast Fourier transform (FFT) method is proposed to combine the variational phase-field approach with a cohesive zone model. This combination enables the application of the FFT methodology in composite materials with interfaces. The composite voxel technique with a laminate model is adopted for this purpose. A frictional cohesive zone model is incorporated to describe the fracture behaviour of the interface including frictional sliding. Representative numerical examples demonstrate that the proposed model is able to predict complex fracture behaviour in composite microstructures, such as debonding, frictional sliding of interfaces, crack deviation and coalescence of interface cracking and matrix cracking.