In the last decade, the additive manufacturing based on fused deposition modelling has become increasingly attractive in diverse engineering fields. For successful application of 3D printed structural elements as end-user parts, reliable performance in terms of stiffness and strength properties has to be ensured. There are numerous experimental studies that mainly investigate the stiffness properties of the 3D printed materials as a function of several printing parameters. However, only few studies, have characterized the failure mechanisms of 3D printed samples and the crucial role of the bond properties between adjacent filaments on the overall strength of printed elements \cite{gao}. This work aims to propose different techniques able to describe the overall mechanical response of 3D printed materials taking into account the plastic behaviour and the occurrence of failure. In both cases, the 3D printed material is described as a laminate consisting of different layers of filaments that assume an elasto-plastic behavior \cite{mon1}. In the first approach, at the layer level, a non-local orthotropic damage and plasticity phenomenological model is developed to describe the crack propagation that occur in the material. Two different damage variables that take into account the intra-layer and the inter-layer damage are introduced. In the second approach, a multiscale model is developed introducing at each point of the lamina a homogenization procedure to solve the micromechanical problem of the representative volume element (RVE) of the 3D printed material. A plastic model is introduced to model the filament behavior. The de-cohesion between filaments that constitute the printed material is described introducing a cohesive damage interface model that takes into account also the unilateral contact. In particular, a homogenization procedure based on the PieceWise Uniform Transformation Field Analysis properly extended to the case of interfaces is developed. In detail, the plastic strains in the filaments and the inelastic relative displacements along the interfaces are approximated as piecewise constant functions and then are computed solving the evolutive problem. The pros and cons of the two procedures are critically discussed. Some numerical applications are carried out, comparing numerical results with the experimental ones \cite{mon2}, to show the potentiality of the proposed techniques.