A comparison of material models for the simulation of selective beam melting processes - Burkhardt, Christian; Soldner, Dominic; Mergheim, Julia (Procedia CIRP, 2020)
The focus of this contribution lies on the comparison of different material models for the thermo-mechanical simulation of selective laser melting (SLM) processes. A Finite Element (FE) framework for the analysis of residual stresses and distortions in laser beam melting processes is introduced. The FE solver for the thermo-mechanical problem uses a staggered algorithm, is based on the open source finite element library deal.ii and makes use of heavy parallelization. The most important aspects to be investigated here are the mechanical material behavior and stress relaxation in the range of the melting temperature. Material models, which reset certain variables as stress and plastic strain to zero at a critical temperature are compared to a thermo-viscoplastic constitutive law. Simulations, related to the SLM process of Ti-6Al-4V, are performed to compare the residual stresses and plastic strains predicted by different models after melting and cooling. Furthermore, the validity of geometrically linearized material model is analyzed. <br
Keywords: SLM process; Finite Element simulations; residual stresses; viscoplastic material models; melting; solidification

Additive manufacturing of cellular structures: Multiscale simulation and optimization - Mergheim, Julia; Breuning, Christoph; Burkhardt, Christian; Hübner, Daniel; Köpf, Johannes; Herrnböck, Ludwig; Yang, Zerong; Körner, Carolin; Markl, Matthias; Steinmann, Paul; Stingl, Michael (Journal of Manufacturing Processes, 2023)
This paper introduces a multiscale and multi-purpose simulation framework to investigate selective beam melting processes for metallic cellular structures along the complete process chain, up to the topology optimization of components made of cellular materials. Process simulation methods on various length scales are introduced to analyze the relation of process strategies and resulting properties of the cellular materials, as e. g. warpage, residual stresses, material grain structure and surface roughness. Numerical homogenization methods are applied to investigate the influence of the grain structure and the topology of the cellular materials on their mechanical properties. Based on these process-dependent mechanical properties, a two-scale optimization of components made of cellular material is performed, aiming in particular on optimizing the buckling resistance of the structures. The interfaces between the different simulation tools are specified and illustrate the flexibility of the numerical framework. It is shown that consistent simulations of additive manufacturing of cellular materials - from the manufacturing process to the optimized component - provide important insights into process-structure interactions and enable tailored additive manufacturing processes.
CRIS-Team WoS Importer:2023-06-02

An energetically consistent heat input model for additive manufacturing - Burkhardt, Christian; Soldner, Dominic; Steinmann, Paul; Mergheim, Julia (Proceedings in Applied Mathematics and Mechanics, 2019)
Additive manufacturing offers the ability to design parts more freely and to realize complex geometries that would not have been manufacturable with conventional processes. In powder bed‐based beam melting processes parts are build in a layer‐by‐layer fashion by selectively melting the powder material to generate the part. The energy input of the laser beam and the temperature distribution during the process strongly influence the quality of the produced part and can be studied by means of macroscopic thermal simulations. Due to the non‐linearity of the material behaviour and the diverging time and length scales huge computational costs arise. In the present contribution a temporal integration of the heat input model is used to allow for larger time step sizes. In order to reduce the errors due to the spatial discretization in the heat affected zone, a correction term is introduced, rendering an energetically consistent heat input. A numerical example shows the success of this strategy.<br

Geometrical Influence on Material Properties for Ti6Al4V Parts in Powder Bed Fusion - Nahr, Florian; Rasch, Michael; Burkhardt, Christian; Renner, Jakob; Baumgärtner, Benjamin; Hausotte, Tino; Körner, Carolin; Steinmann, Paul; Mergheim, Julia; Schmidt, Michael; Markl, Matthias (Journal of Manufacturing and Materials Processing, 2023)
One major advantage of additive manufacturing is the high freedom of design, which supports the fabrication of complex structures. However, geometrical features such as combined massive volumes and cellular structures in such parts can lead to an uneven heat distribution during processing, resulting in different material properties throughout the part. In this study, we demonstrate these effects, using a complex structure consisting of three conic shapes with narrow cylinders in between hindering heat flux. We manufacture the parts via powder bed fusion of Ti6Al4V by applying a laser beam (PBF-LB/M) as well as an electron beam (PBF-EB). We investigate the impact of the different thermal regimes on the part density, microstructure and mechanical properties aided by finite element simulations as well as by thermography and X-ray computed tomography measurements. Both simulations and thermography show an increase in inter-layer temperature with increasing part radius, subsequently leading to heat accumulation along the build direction. While the geometry and thermal history have a minor influence on the relative density of the parts, the microstructure is greatly affected by the thermal history in PBF-LB/M. The acicular martensitic structure in the narrow parts is decomposed into a mix of tempered lath-like martensite and an ultrafine 𝛼 + 𝛽 microstructure with increasing part radius. The EBM part exhibits a lamellar 𝛼 + 𝛽 microstructure for both the cylindric and conic structures. The different microstructures directly influence the hardness of the parts. For the PBF-LB part, the hardness ranges between 400 HV0.5 in the narrow sections and a maximum hardness of 450 HV0.5 in the broader sections, while the PBF-EB part exhibits hardness values between 280 and 380 HV0.
Keywords: PBF-LB/M; PBF-EB; Ti6Al4V; simulation; thermography

Macroscopic Modeling, Simulation, and Optimization - Burkhardt, Christian; Soldner, Dominic; Steinmann, Paul; Mergheim, Julia (Springer Nature, 2025)
During the repeated melting and cooling of (initially) powder material in powder bed based additive manufacturing (AM), high temperatures and large temperature gradients arise. These lead to thermal expansion and contraction of the material, for both metals and polymers and to shrinkage during crystallization in the case of semi-crystalline polymers. The heterogeneous temperature field, temperature-dependent mechanical behavior, and heterogeneous crystallization result in warpage and residual stresses during powder bed fusion (PBF).
CRIS-Team Scopus Importer:2025-06-06

Memory-based meso-scale modeling of Covid-19 - Kergaßner, Andreas; Burkhardt, Christian; Lippold, Dorothee; Kergaßner, Matthias; Pflug, Lukas; Budday, Dominik; Steinmann, Paul; Budday, Silvia (Computational Mechanics, 2020)
The COVID-19 pandemic has lead to an unprecedented world-wide effort to gather data, model, and understand the viral spread. Entire societies and economies are desperate to recover and get back to normality. However, to this end accurate models are of essence that capture both the viral spread and the courses of disease in space and time at reasonable resolution. Here, we combine a spatially resolved county-level infection model for Germany with a memory-based integro-differential approach capable of directly including medical data on the course of disease, which is not possible when using traditional SIR-type models. We calibrate our model with data on cumulative detected infections and deaths from the Robert-Koch Institute and demonstrate how the model can be used to obtain county- or even city-level estimates on the number of new infections, hospitality rates and demands of intensive care units. We believe that the present work may help guide decision makers to locally fine-tune their expedient response to potential new outbreaks in the near future.<br

Numerical and experimental investigation of the isothermal assumption in selective laser sintering of PA12 - Soldner, Dominic; Greiner, Sandra; Burkhardt, Christian; Drummer, Dietmar; Steinmann, Paul; Mergheim, Julia (Additive Manufacturing, 2020)

Spatiotemporal modeling of first and second wave outbreak dynamics of COVID‐19 in Germany - Lippold, Dorothee; Kergaßner, Andreas; Burkhardt, Christian; Kergaßner, Matthias; Loos, Jonas; Nistler, Sarah; Steinmann, Paul; Budday, Dominik; Budday, Silvia (Biomechanics and Modeling in Mechanobiology, 2021)
The COVID-19 pandemic has kept the world in suspense for the past year. In most federal countries such as Germany, locally varying conditions demand for state- or county-level decisions to adapt to the disease dynamics. However, this requires a deep understanding of the mesoscale outbreak dynamics between microscale agent models and macroscale global models. Here, we use a reparameterized SIQRD network model that accounts for local political decisions to predict the spatiotemporal evolution of the pandemic in Germany at county resolution. Our optimized model reproduces state-wise cumulative infec- tions and deaths as reported by the Robert Koch Institute and predicts the development for individual counties at convincing accuracy during both waves in spring and fall of 2020. We demonstrate the dominating effect of local infection seeds and identify effective measures to attenuate the rapid spread. Our model has great potential to support decision makers on a state and community politics level to individually strategize their best way forward during the months to come.
Keywords: COVID-19 · SIQRD model · Mesoscale outbreak dynamics · Germany

Thermo-mechanical simulations of powder bed fusion processes: accuracy and efficiency - Burkhardt, Christian; Steinmann, Paul; Mergheim, Julia (Advanced Modeling and Simulation in Engineering Sciences, 2022)
In this contribution, the accuracy and efficiency of various modeling assumptions and numerical settings in thermo-mechanical simulations of powder bed fusion (PBF) processes are analyzed. Thermo-mechanical simulations are used to develop a better understanding of the process and to determine residual stresses and distortions based on the temperature history. In these numerically very complex simulations, modeling assumptions are often made that reduce computational effort but lead to inaccuracies. These assumptions include the omission of the surrounding powder or the use of geometrically linearized material models. The numerical setting, in particular the temporal and spatial discretizations, can further lead to discretization errors. Here, a highly parallelized and adaptive finite element method based on the open source C++ library deal.II is validated and utilized, to investigate some of these modeling assumptions and to identify the required temporal and spatial discretizations for the simulation of PBF of Ti-6Al-4V. The insights initially gained on a simple wall-like geometry are transferred to a larger open rectangular profile where the results of a detailed simulation are compared with those of a more efficient one. The results for the efficient approach show a maximum deviation of ≈8%" role="presentation">≈8% in the displacements and ≈3.5%" role="presentation">≈3.5% in the residual stresses while significantly reducing the computational tim