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Purpose This paper aims to present a systematic approach in the literature survey related to metal additive manufacturing (AM) processes and its multi-physics continuum modelling approach for its better understanding. Design/methodology/approach A systematic review of the literature available in the area of continuum modelling practices adopted for the powder bed fusion (PBF) AM processes for the deposition of powder layer over the substrate along with quantification of residual stress and distortion. Discrete element method (DEM) and finite element method (FEM) approaches have been reviewed for the deposition of powder layer and thermo-mechanical modelling, respectively. Further, thermo-mechanical modelling adopted for the PBF AM process have been discussed in detail with its constituents. Finally, on the basis of prediction through thermo-mechanical models and experimental validation, distortion mitigation/minimisation techniques applied in PBF AM processes have been reviewed to provide a future direction in the field. Findings The findings of this paper are the future directions for the implementation and modification of the continuum modelling approaches applied to PBF AM processes. On the basis of the extensive review in the domain, gaps are recommended for future work for the betterment of modelling approach. Research limitations/implications This paper is limited to review only the modelling approach adopted by the PBF AM processes, i.e. modelling techniques (DEM approach) used for the deposition of powder layer and macro-models at process scale for the prediction of residual stress and distortion in the component. Modelling of microstructure and grain growth has not been included in this paper. Originality/value This paper presents an extensive review of the FEM approach adopted for the prediction of residual stress and distortion in the PBF AM processes which sets the platform for the development of distortion mitigation techniques. An extensive review of distortion mitigation techniques has been presented in the last section of the paper, which has not been reviewed yet.

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