This work presents a continuum thermomechanical approach for modelling the behaviour of a laser powder bed fusion manufactured AlSi10Mg. Thermomechanical means that the analysis methods include the material’s self-heating effect during inelastic deformations. This effect is directly coupled to the deformation process and can additionally be used for the parameter identification. The research introduces a method for the coupled thermomechanical experimental observation, the enhancement of the theoretical framework for a fully thermomechanical material description, and an approach for the parameter identification and validation. To describe the rate-dependent behaviour under consideration of damage effects, a coupled Chaboche–Gurson–Tvergaard–Needleman (GTN) model was utilised. For modelling high complex stress states with a good accuracy between the experiment and the simulation, the Chaboche–GTN model was enhanced with an approach that includes the effects of low stress triaxialities. In order to enable a fully coupled simulation of the deformation and temperature field for complex geometries, the model is implemented in the finite element programme Abaqus via a user material subroutine (UMAT).