Laser additive manufacturing processes are used for the production of highly complex geometric structures due to their high geometric freedom. Additive manufacturing processes, in particular powder-based selective laser melting, are used to produce metallic additive manufactured components for the automotive and aerospace industries. Different materials are often joined together to realize sustainable lightweight construction. The production of such mixed construction joints is often realized using mechanical joining technology (e.g. self-piercing riveting). However, there is currently very little experience with the mechanical joining of metallic additive manufacturing components. Furthermore, there is insufficient knowledge about the effects that occur during the mechanical joining of additive manufacturing components. In this article, a method is presented to investigate the joinability of additively manufactured components with conventionally manufactured components using a numerical simulation of the self-piercing riveting process. For this purpose, the additive manufacturing materials are characterized experimentally, the simulation model is configured, and the joining process with additive manufacturing materials is represented in the numerical simulation. Furthermore, the influence of the building direction on the mechanical properties is shown using miniature tensile specimens. Besides the configuration of the simulation model, the influence of heat treatment on the self-piercing riveting process is presented.