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This paper addresses the numerical simulation of self-piercing rivetting processes to join fibre reinforced polymers and sheet metals. Special emphasis is placed on the modelling of the deformation and failure behaviour of the composite material. Different from the simulation of rivetting processes in metals, which requires the modelling of large plastic deformations, the mechanical response of composites is typically governed by intra- and interlaminar damage phenomena. Depending on the polymeric matrix, viscoelastic effects can interfere particularly with the long-term behaviour of the joint. We propose a systematic approach to the modelling of composite laminates, discuss limitations of the used model, and present details of parameter identification. Homogenisation techniques are applied to predict the mechanical behaviour of the composite in terms of effective anisotropic elastic and viscoelastic material properties. In combination with a continuum damage approach this model represents the deformation and failure behaviour of individual laminae. Cohesive zone elements enable the modelling of delamination processes. The parameters of the latter models are identified from experiments. The defined material model for the composite is eventually utilised in the simulation of an exemplary self-piercing rivetting process., Comment: Accepted manuscript