Preface on mechanics of additive manufacturing—Part I

Additive manufacturing processes—often referred to as 3D printing—have developed since the 1980s into a promising and groundbreaking way of producing components and workpieces with geometries of almost any complexity. And the developments continue to advance! In the meantime, various methods that can be divided into different categories have been introduced. To cover just a few of the most common methods, inkjet technologies, material extrusion, powder bed fusion, direct energy deposition, and stereolithography shall be mentioned here. The latter is considered in some sources to be virtually the starting point of additive manufacturing. The category “powder bed fusion” includes processes such as selective laser sintering, selective laser melting, and electron beam melting. Laser cladding is an example of direct energy deposition. In conventional subtractive manufacturing processes, the final contour of the component is achieved by material removal. In contrast, additive manufacturing processes are characterized by the targeted addition of the respective material to the component layer by layer. The great potential of these processes is evident in the aerospace and automotive industries as well as in biomedical technology, and especially in the manufacturing of custom-made products and lightweight constructions. Developments have even gone so far that local material properties can be specifically adjusted by, for example, adapting the material feed. Moreover, no tools or joining processes are in principle required for direct manufacturing. Additive manufacturing processes can thus be initiated and adapted in a much faster and straight-forward way. For applied mathematics and mechanics, additive manufacturing opens up numerous new perspectives and opportunities, but also major challenges. Particularly in the field of topology optimization, additive manufacturing seems to overcome a previously existing and seemingly insurmountable limitation, namely that of realizability. Until recently, the mathematically optimal structure, for example, in the sense of an optimum density distribution within a given design space, was always subjected to the constraint that the structure must also be manufacturable via conventional methods. Among other things, voids were not allowed to become too small and the density distribution had to be binary—either “no material” or “full material”. Nowadays, additive manufacturing processes indeed enable the production of the mathematically/physically optimal structures. With regard to the modeling of the material and structural behavior of additively manufactured components, numerous new challenges arise. In order to be able to perform load-bearing capacity verifications, the constitutive behavior of the material finally obtained must be modeled and predicted as accurately as possible. In this context, the manufacturing process results in specific and spatially highly inhomogeneously distributed residual stresses, which can have a drastic effect on the long-term behavior of the component or workpiece, for example. The manufacturing process represents a physically highly complex problem. It is strongly thermomechanically coupled, with both the temperature itself and its spatial and temporal gradient taking up a very large range of values in case of powder bed fusion and direct energy deposition, for example. Temperatures alone can reach over 2000◦C in selective laser melting and typical cooling rates are in the order of 100 K/s. For such processes, the transitions between the states “powder” to “molten” and “molten” to “resolidified” must also be taken into account in the modeling and simulation. The contributions of this Special Issue of the Surveys for Applied Mathematics and Mechanics (GAMM-Mitteilungen) directly address many of these challenges: The demanding endeavor of modeling Selective Laser Sintering of polymers, more precisely Polyamide 12, is addressed in [4]. In this contribution, the focus is placed on the necessity to accurately model both melting and crystallization processes and their interactions. In particular, the modeling approach was designed to allow for negative crystallization rates, which in this case are physically possible/observable due to remelting of the material. The topology optimization aspect described above is reflected in [1]. The general problem is tackled by a phase field approach, wherein adaptive isogeometric analysis is used in terms of the numerical implementation. The contribution of [2] covers a wide range of aspects, emphasizing the large number and variety of challenges related to the modeling and simulation of powder bed fusion additive manufacturing. More precisely, the mesoscale,