Through the emergence of additive manufacturing technologies, there has been an increasing interest in the design and fabrication of architected and microstructured materials in recent years. In particular, open-cell foams and lattice-type periodic metamaterials with truss- or beam-like struts have been extensively investigated, covering aspects such as high stretchability and compressibility, resilience, damage-tolerance and failure, uncertainties, instabilities and rate-dependence, energy absorption and dissipation, or specific functionalities (e.g., shape memory effect, self-assembly). In terms of modelling and simulation, depending on the type of microstructure, base materials (metals, polymers, etc.), and applications, this requires complex nonlinear and inelastic effects, such as large deformations, instabilities, rate-dependence, plasticity, fracture, or damage, to be considered, which remains a major challenge. In this contribution \cite{aml}, we present a geometrically nonlinear, shear-deformable 3D beam formulation with inelastic material behaviour and its numerical discretization by a mixed isogeometric collocation method \cite{iga}. In particular, the constitutive model captures elasto-visco-plasticity with damage/softening from Mullin’s effect. Thus, the formulation can be applied to the modelling of stiffer metallic and more flexible polymeric materials. The method is demonstrated numerically for the simulation of additively manufactured beam lattice structures subject to highly nonlinear and inelastic behaviour, including large deformations with instabilities, rate-dependence and plasticity. Furthermore, it is validated in application to beam-lattice structures additively fabricated from PA12 by selective laser sintering and from a tough polymer resin via masked stereolithography. For compression tests executed until densification or with unloading and at different rates, the beam simulations are in very good agreement with experiments. These results strongly indicate that the consideration of all nonlinear and inelastic effects is crucial to accurately model the finite deformation behavior of lattice structures. It can be concluded that this can be effectively attained using inelastic beam models, which opens the perspective for simulation-based design and optimization of lattices for practical applications.