•A modelling framework for multi-track, multi-layer and multi-material SLM.•Simulation of multi-material powder deposition in various patterns.•Effect of process parameters on balling effect, keyhole and lack of fusion.•Molten pool evolution of multi-material SLM on the same and across different layers.•Modelling of phase migration at the interface between two different materials. Selective laser melting (SLM) is a promising powder-based additive manufacturing technology due to its capability to fabricate metallic components with complex geometries. While most previous investigations focus on printing with a single material, recent industry-orientated studies indicate the need for multi-material SLM in several high-value manufacturing sectors including medical devices, aerospace and automotive industries. However, understanding the underlying physics in multi-material SLM remains challenging due to the difficulties of experimental observation. In this paper, an integrated modelling framework for multi-track, multi-layer and multi-material SLM is developed to advance the in-depth understanding of this process. The main novelty is in modelling the molten pool evolvement and track morphology of multiple materials deposited on the same and across different layers. Discrete element method (DEM) is employed to reproduce the powder deposition process of multiple materials in different deposition patterns, with particle size distribution imported from a particle size analyser. Various phenomena including balling effect, keyhole depression, and lack of fusion between layers are investigated with different laser energy inputs. As a result of the different thermal properties, several process parameters including energy density and hatch spacing are optimised for different powder materials to obtain a continuous track profile and improved scanning efficiency. The interface between two layers of different materials is visualised by simulation; it was found that the phase migration at the interface is related to the convection flow inside the molten pool, which contributes to the mixing of the two materials and elemental diffusion. This study significantly contributes to the challenging area of multi-material additive manufacturing by providing a greater in-depth understanding of the SLM process from multi-material powder deposition to laser interaction with powders across multiple scanning tracks and different building layers than can be achieved by experimentation alone.