A well-known Achilles' heel of laser powder bed fusion (L-PBF) additive manufactured lattice structures is the difficulty in predicting fatigue properties. The presence of manufacturing-induced defects significantly affects the fatigue resistance of the porous component and must be accurately captured by predictive models. To tackle this challenge, the as-built geometry of the lattice needs to be modeled, which introduces another challenge on the computational front. For the first time, a model based on the computer tomography (μ-CT) reconstruction of the as-built lattice geometry is simulated with the efficient finite cell method and combined with the average strain energy density (ASED) to obtain accurate fatigue predictions. This work presents a workflow for determining the fatigue resistance of lattice metamaterial, followed by a case study for method validation. The validation shows a good agreement between the predicted fatigue life and the experimental results.

An accurate prediction of the fatigue life of metallic additively manufactured lattice structures is still a challenging task. The proposed work addresses this challenge of industrial relevance through the computation of an as-built geometry of a lattice structure directly from its X-ray computed tomography reconstruction. The computation is carried out by taking advantage of the Finite Cell Method and applies the average strain energy density method to predict fatigue failure. The proof of concept provided in this work shows an excellent agreement in the fatigue prediction, paving the way for a computationally accurate fatigue life prediction of other types of metamaterials.

The advancements in additive manufacturing (AM) technology have allowed for the production of geometrically complex parts with customizable designs. This versatility benefits large-scale space-frame structures, as the individual design of each structural node can be tailored to meet specific mechanical and other functional requirements. To this end, however, the design and analysis of such space-frames with distinct structural nodes needs to be highly automated. A critical aspect in this context is automated integration of the local 3D features into the 1D large-scale models. In the present work, a two-scale modeling approach is developed to improve the design and linear-elastic analysis of space frames with complex additively manufactured nodes. The mechanical characteristics of the 3D nodes are numerically reduced through an automated dimensional reduction process based on the Finite Cell Method (FCM) and substructuring. The reduced stiffness quantities are assembled in the large-scale 1D model which, in turn, enables efficient structural analysis. The response of the 1D model is passed on to the local model, enabling fully resolved 3D linear-elastic analysis. The proposed approach is numerically verified on a simplified beam example. Furthermore, the workflow is demonstrated on a tree canopy structure with additively manufactured nodes with bolted connections. The form of the large-scale structure is found based on the Combinatorial Equilibrium Modeling framework, and the different designs of the local structural nodes are based on generative exploration of the design space. It is demonstrated that the proposed methodology effectively automates the design and analysis of space-frame structures with complex, distinct structural nodes.

Combining the additive manufacturing (AM) process of extrusion with lightweight concrete, mono-material but multi-functional elements with an internal cellular structure can be created to achieve good thermal performance of a wall at low resource consumption. The aim of this paper is to analyze and optimize the actual thermal performance of such a component. A sensitivity analysis and a parametric optimization were conducted based on a mathematical description of heat transfer in cellular structures. To investigate the thermal performance, 2D and 3D heat transfer simulations were used and validated by heat flux measurements on an existing prototype. A geometric optimization led to a further reduction of the U-value by up to 24%, reaching 0.58 W/m2 K. The ratio of solid material to air inside the cells (relative density) was identified as the main driver, in addition to cell diameter, cell height, and cell wall thickness. The comparison of analytical and numerical results showed high correspondence with deviations of 3–10%, and for the experimental results 25%. These remaining deviations can be traced back to simplifications of the theoretical models and discrepancies between as designed and as built. The presented approach provides a good basis for optimizing the thermal design of complex AM components by investigating practical thermal problems with the help of 2D and 3D simulations, and thus offers a great potential for further applications.

This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis functions utilized in the finite cell method and the multi-level hp-method, which is attributed to the use of high-order integrated Legendre basis functions and overlay meshes, to yield a simple and elegant multigrid scheme. This simplicity is reflected in the fact that all restriction and prolongation operators reduce to binary matrices that do not need to be explicitly constructed. The coarse spaces are constructed over the different polynomial orders and refinement levels of the immersed discretization. Elementwise and patchwise additive Schwarz smoothing techniques are used to mitigate the influence of the cut cells leading to convergence rates that are independent of the cut configuration, mesh size and in certain scenarios even the polynomial order. The multigrid approach is applied to second-order problems arising from the Poisson equation and linear elasticity. A series of numerical examples demonstrate the applicability of the scheme for solving large immersed systems with multiple millions and even billions of unknowns on massively parallel machines.