Additive manufacturing (AM) is nowadays more than a promising technology for creating solid structures of virtually any shape, and its impact in engineering is increasing at a very fast rate. AM allows to produce more complex shapes than those obtained through classical manufacturing techniques, and, as a consequence, applications for AM products range across many engineering fields, from design models to lightweight components for automotive or aerospace industry, from patient-specific medical implants to civil engineering structural and/or architectural components. The exponential growth of the AM world clearly raises new questions for numerical simulations, computational models, and design optimizations of the involved products and processes. The seven research articles published within this special issue are aimed at addressing such questions, identifying some of the most challenging topics in this modern and exciting research field.

In Dorussen et al. [2], the authors investigate the potential of the discrete element method to simulate the physics of particle bed-based additive manufacturing. The proposed method naturally captures the discrete aspects of AM processes, such as material addition and the discrete element framework uses constitutive relations for loose powder, bonding kinematics and the thermo-mechanical behavior of bonded particles. In this article, a heat conducting rod of both powder and bonded material is simulated and compared to a continuum finite element simulation. Numerical results show that the proposed discrete model is able to simulate a complete printing process, accurately capturing the solid material behavior. Finally, a simulation of a printed sample shows various AM aspects such as: the deposited powder layer, G-code input, heat source interaction, contact, bonding, thermal conduction and the accumulation of residual stresses and deformations.

Lu et al. [6] present a thermo-mechanical finite element model for directed energy deposition (DED) process simulations. Such a numerical tool is used to study the effect of the baseplate dimensions and the energy density on both residual stresses and microstructure evolution. On the one hand, the results indicate that the large baseplate causes higher residual stresses but produces more uniform microstructures, and contrariwise for the smaller baseplate. On the other hand, increasing the energy density favors stress relief, but its effect fails to prevent the stress concentration at the built basement. In this contribution, the authors propose also two approaches to control both stress accumulation and metallurgical evolution during the DED processes.

The local nature of the thermo-mechanical phenomena occurring in AM processes calls for effective adaptive mesh strategies. Moreira et al. [7] present an h-adaptive finite element strategy to address the numerical simulation of large-scale AM parts produced by means of wire-arc additive manufacturing (WAAM). The approach presented by the authors is suitable for industrial applications and can be applied to AM processes other than WAAM. To identify the location in the mesh of the heat-affected zone (HAZ), a collision detection algorithm based on the separating axis theorem is used. The mesh is continuously adapted to guarantee the necessary mesh resolution to capture the phenomena inside and outside the HAZ by means of a multi-criteria adaptive mesh refinement and coarsening strategy based on an a-posteriori error estimator. Thanks to this approach, the number of active finite elements is controlled and mesh manipulation by the end-user is avoided. Numerical simulations comparing the h-adaptive strategy with the (reference) fixed fine meshes are performed to prove the computational cost efficiency and the solution accuracy.

The often complex geometry of laser powder bed fusion (LPBF) AM-produced components make these kinds of analyses computationally very challenging since the small geometrical features of the part usually require non-trivial conform mesh generation processes. Immersed boundary methods offer an alternative to deal with this kind of complexity, without requiring a part-conform meshing. In Carraturo et al. [1], the numerical simulation of a large-scale LPBF AM process is performed by using an immersed boundary method suitable to deal with multi-scale problems. In their contribution, the authors apply a modified version of the recently introduced two-level method to part-scale thermal analysis of LPBF manufactured components, validating the proposed part-scale model with respect to experimental measurements from the literature and applying the presented numerical framework to simulate a full-scale LPBF process of a topologically optimized structure.

In Liang et al. [5], a novel multiphysics-based topology optimization framework is developed to maximize the performances in 3D cross-flow heat exchangers (HXs), and concurrently limit the pressure drop between the fluid inlet and outlet. In particular, an isogeometric analysis solver is developed to solve the coupled steady-state Navier–Stokes and heat convection–diffusion equations. Non-body-fitted control mesh is adopted instead of dynamically remeshing the design domain during the evolution of the boundary interface. The method of moving morphable voids is employed to represent and track boundary interface between the hot and the remaining regions. In addition, various constraints are incorporated to guarantee manufacturability of the optimized structures with respect to practical considerations in AM, such as removing sharp corners, controlling channel perimeters, and minimizing overhangs. By means of a set of numerical examples, the authors show that the HXP of the optimized structure is greatly improved compared with its corresponding initial design, and the PD between the fluid inlet and outlet is controlled concurrently. Moreover, a smooth boundary interface between the channel and the cold fluid, and improved manufacturability are simultaneously obtained for the optimized structures.

Fuchs et al. [3] propose a versatile computational modeling framework for simulating such coupled microfluid-powder dynamics problems involving thermo-capillary flow and reversible phase transitions. In particular, a liquid and a gas phase are interacting with a solid phase that consists of a substrate and mobile powder particles while simultaneously considering temperature-dependent surface tension and wetting effects. In case of laser–metal interactions, the effect of rapid evaporation is incorporated through additional mechanical and thermal interface fluxes. All phase domains are spatially discretized using smoothed particle hydrodynamics. The method’s Lagrangian nature is beneficial in the context of dynamically changing interface topologies due to phase transitions and coupled microfluid-powder dynamics. While the underlying model equations are of a very general nature, the proposed framework is especially suitable for the mesoscale modeling of various AM processes. To this end, the generality and robustness of the computational modeling framework is demonstrated by several application-motivated examples representing the specific AM processes binder jetting, material jetting, directed energy deposition, and powder bed fusion.

Finally, the course of time integration in AM process simulation is addressed in Kopp et al. [4]. The authors introduce a space–time Galerkin framework suitable for AM process simulations, where the finite element interpolation also includes the temporal dimension. The authors construct four-dimensional meshes that are locally refined toward the laser spot and allow for varying temporal accuracy depending on the position in space. By splitting the mesh into conforming time-slabs, the proposed methodology is able to recover a stepwise solution to solve the space–time problem locally in time at this slab; additionally, it allows to choose time-slab sizes significantly larger than classical time-stepping schemes. Moreover, their space–time Galerkin framework is well suited for large-scale parallelization. The authors use a continuous Galerkin–Petrov formulation of the nonlinear heat equation with an apparent heat capacity model to account for the phase change and validate the proposed approach by computing the AMB2018-02 benchmark. Using the same setup, they also demonstrate the performance potential of their approach by hatching a square area with a laser path length of about one meter.

In summary, the present special issue assembles a representative collection of the state of the art in the research on AM design, modeling, and simulation, showcasing new methodological developments and emerging techniques. However, this is not limited to providing an exhaustive snapshot of the actual landscape in this research area, but it also aims at paving the way toward a full digitalization of AM process and product design.