@article{FrankeWagnerKrause, author = {Franke, Markus and Wagner, Marcus and Krause, Tom Janis}, title = {Data-driven model order reduction with surrogate elements for transient simulations}, series = {Engineering Computations : International journal for computer-aided engineering and software}, volume = {2025}, journal = {Engineering Computations : International journal for computer-aided engineering and software}, publisher = {Emerald Publishing}, address = {Leeds}, doi = {10.1108/EC-06-2024-0511}, pages = {26}, abstract = {Purpose - The purpose of this study is to introduce surrogate elements for static and transient finite element simulations. These elements are designed to replace regions of several conventional solid elements with a single artificial element that possesses a reduced number of degrees of freedoms (dofs). A notable advantage of our surrogate elements is their seamless integration into standard finite element meshes. Design/methodology/approach - The construction of the surrogate elements stiffness and mass matrices is achieved through an optimization process wherein displacements serve as the optimization objective. Moreover, the matrices are designed to possess properties analogous to those of standard finite elements. A particular focus is placed on ensuring that the artificial stiffness matrices are positive semi-definite. Furthermore, artificial degrees of freedom are introduced. Findings - The efficacy of the proposed technique is demonstrated through its application to two different use cases. It is demonstrated that, despite being trained on examples comprising a single surrogate element, the surrogate elements can be employed multiple times within complex and practical models. The degree of accuracy achieved in these applications is noteworthy. Moreover, the proposed method is considerably faster than the fully discretized models. Originality/value - The study expands the field of substructuring and model order reduction by incorporating artificial surrogate elements built by neural networks, which enables seamless integration with standard finite element analysis via positive semi-definite matrices. Furthermore, the introduction of artificial degrees of freedom, which are detached from the computational domain, is proposed. Once trained, the surrogate elements can be utilised in load and support independent scenarios.}, language = {en} } @inproceedings{SwidergalWagnerLubsederetal., author = {Swidergal, Krzysztof and Wagner, Marcus and Lubseder, C. and von Wurmb, I. and Meinhardt, Josef and Marburg, Steffen}, title = {Investigation of the forming tool dynamics by means of numerical simulation}, series = {Advanced Metal Forming Processes in Automotive Industry, AutoMetForm 2016}, booktitle = {Advanced Metal Forming Processes in Automotive Industry, AutoMetForm 2016}, publisher = {Fraunhofer}, pages = {335 -- 340}, abstract = {In the forming tools for pressing car body parts, heavy blankholders are used to prevent buckling and wrinkling of the blank. During each press cycle, those large masses need to be lifted, raising thereby the structural dynamic load on the forming tool and on the press. Therefore a detailed knowledge about the forming tool dynamics is essential for an accurate and robust design of forming tools. In this paper, a dynamic finite element method (FEM) simulation of selected automotive forming tool is presented enabling identification of regions of critical stresses. For validation of the simulation results, the kinematic responses of the tool's components are compared with the measurements obtained in an experiment.}, language = {en} } @article{ThumannMarburgMeinhardtetal., author = {Thumann, Philipp and Marburg, Steffen and Meinhardt, Josef and Saubiez, Jean-Marc and Hoogen, Michael and Suck, Bertram and Wagner, Marcus}, title = {Frequency Dependent Fatigue Strength Investigations on Tempered Steel and Nodular Cast Iron}, series = {steel research international}, volume = {90}, journal = {steel research international}, number = {7}, publisher = {Wiley}, doi = {10.1002/srin.201800620}, abstract = {This paper presents experimental fatigue tests on specially shaped specimens made from quenched and tempered steel 42CrMoS4 and nodular cast iron EN-GJS-600-3. The specimens are geometrically designed to resemble actual subcomponents of forming and cutting dies for sheet metal manufacturing. These subcomponents have failed in the past.Experiments are carried out using a fictive load-time function, which is a modification of an actually measured load curve and has variable mean and amplitude values. This first test series serves as a general validation of a subsequent fatigue analysis. A second test series is carried out with constant mean and amplitude values with a load ratio 𝑅≈0. Here, the load frequencies in the individual test runs are varied between f = 5 Hz and f = 45 Hz in order to investigate the influence of the frequency. Both series are performed on a servo-hydraulic testing machine.The experimental data is then statistically evaluated. The values for the scatter correlate with data from the literature. The data from the test series with the fictive load-time function can thus be used for subsequent validation of a fatigue calculation, which will be addressed in a future publication. Most significant are the findings from the second series of experiments with varied load frequencies, as a significant frequency influence could be detected. Furthermore, the hardening and softening behavior under cyclic loading and the fracture behavior of the materials are analyzed and compared with data from the literature.}, language = {en} } @article{ThumannBuchnerMarburgetal., author = {Thumann, Philipp and Buchner, Stefan and Marburg, Steffen and Wagner, Marcus}, title = {A comparative study of Glinka and Neuber approaches for fatigue strength assessment on 42CrMoS4-QT specimens}, series = {Strain}, volume = {2023}, journal = {Strain}, number = {e12470}, publisher = {Wiley}, issn = {1475-1305}, doi = {10.1111/str.12470}, pages = {21}, abstract = {In fatigue strength assessment, the methods based on ideal elastic stresses according to Basquin and the less established method based on elastic-plastic stress quantities according to Manson, Coffin and Morrow are applied. The former calculates loads using linear-elastic stresses, the latter requires elasticplastic evaluation parameters, such as stresses and strains. These can be determined by finite element analysis (FEA) with a linear-elastic constitutive law, and subsequent conversion to elastic-plastic loads, using the macro support formula by Neuber. In this contribution, an alternative approach to approximate elastic-plastic parameters proposed by Glinka is compared to the the strain-life method using Neuber's formula, as well as the stress-life method of Basquin. Several component tests on 42CrMoS4-QT specimens are investigated. To determine the input data for the fatigue strength evaluations, the entire test setup is computed by FEA. The nodal displacements from these validated full-model simulations are used as boundary conditions for a submodel simulation of a notch, whose results serve as input for the fatigue strength assessments. It is shown that all approaches provide a reliable assessment of components. Our key result is that the strain-life method using the concept by Glinka for notch stress computation, yields improved results in fatigue strength assessments.}, language = {en} } @article{SwidergalLubesederWurmbetal., author = {Swidergal, Krzysztof and Lubeseder, Christian and Wurmb, Ingo von and Lipp, Arnulf and Meinhardt, Josef and Wagner, Marcus and Marburg, Steffen}, title = {Experimental and numerical investigation of blankholder's vibration in a forming tool}, series = {Production Engineering - Research and Development}, volume = {9}, journal = {Production Engineering - Research and Development}, number = {5-6}, publisher = {Springer}, issn = {0944-6524}, doi = {10.1007/s11740-015-0640-9}, pages = {634}, abstract = {In order to achieve the energy and efficiency goals in modern automotive press shops, press systems with increasingly high stroke rates are being implemented (Meinhardt in proceedings of ACI forming in car body engineering. Bad Nauheim, Germany 2012). As a side effect, the structural dynamic loads on the press and especially on the forming tool increase. Hence, to design reliable and withstanding forming tools, a detailed knowledge of the vibrations and resulting critical loads is essential. In this paper, the main focus is put on the vibration of the blankholder—the heaviest moving component in the forming tool. To predict those vibrations, a coupled multibody-finite element simulation (MBS-FEM) is conducted, which combines rigid and elastic modeling approaches. Also, an experimental validation of the blankholder vibration under operational load is carried out. To compare the numerical and experimental results—both in time and frequency domain—an 1/3-octave analysis of a blankholder's vibrational speed is performed. The test measurements agree well with the MBS-FEM simulation.}, language = {en} } @article{SittlMarburgWagner, author = {Sittl, Christopher and Marburg, Steffen and Wagner, Marcus}, title = {Application of a Krylov subspace method for an efficient solution of acoustic transfer functions}, series = {Mechanical Systems and Signal Processing}, volume = {148}, journal = {Mechanical Systems and Signal Processing}, publisher = {Elsevier}, doi = {10.1016/j.ymssp.2020.107135}, abstract = {Solving acoustic radiation problems, arising from systems including fluid-structure interaction, is of interest in many engineering applications. Computing frequency response functions over a large frequency range is a concern in such applications. A method which solves the Helmholtz equation for multiple frequencies in one step is the matrix-Pad{\´e}-via-Lanczos connection for unsymmetric systems, as presented by Wagner et al. [1]. The present work is based on Ref. [1] and presents a method for efficiently computing frequency responses over a frequency range for coupled structural-acoustic problems, where the structure and the acoustic near field are discretized with finite elements and an analytical Dirichlet-to-Neumann map approximates the far field. The method is based on a Krylov-subspace projection technique which derives a matrix-valued Pad{\´e} approximation for a restricted area in the near field and the pressure field on a spherical boundary. On the spherical boundary, where the finite domain is truncated, the non-local modified Dirichlet-to-Neumann operator is applied as a low-rank update matrix. The present contribution extends this method and incorporates new techniques for a more stable model reduction through the Lanczos algorithm and a novel weighted adaptive windowing technique. Further, structural damping is incorporated, for computing the acoustic radiation of a harmonically excited plate. These computed results are compared with acoustic measurements in an anechoic chamber and verified with computational results obtained with a commercial code that uses the perfectly matched layer method.}, language = {en} } @inproceedings{ThumannWagnerSucketal., author = {Thumann, Philipp and Wagner, Marcus and Suck, Bertram and Meinhardt, Josef and Marburg, Steffen}, title = {Explicit and Implicit FE Simulations of Material Tests for Subsequent Durability Analyses}, series = {11th European LS-DYNA Conference, Salzburg}, booktitle = {11th European LS-DYNA Conference, Salzburg}, abstract = {Because of increased stroke rates the loads on forming tools increase too. To ensure a save design of components, durability analyses are intended. For this, simulation results from FE analyses are necessary. Therefore, it is desirable to use elements with quadratic function, because of a good stress approximation.The goal of the described investigation is to show if calculation results created by LS-DYNA [1] can be used for durability analyses. Especially the use of quadratic elements is investigated. For the evaluation, on the one hand explicit FE analyses of a special durability test are carried out. These analyses are validated by available test data. To create results for later durability analyses further FE analyses with implicit time discretisation are carried out. In this paper results of the investigations are presented and evaluated critically.}, language = {en} } @inproceedings{SwidergalWagnerLubesederetal., author = {Swidergal, Krzysztof and Wagner, Marcus and Lubeseder, Christian and Wurmb, Ingo von and Meinhardt, Josef and Marburg, Steffen}, title = {Finite element simulation of blankholder's lift-off in a deep drawing tool using Abaqus/Standard}, series = {SIMULIA Community Conference, 19 - 21 May 2015, Berlin, Germany}, booktitle = {SIMULIA Community Conference, 19 - 21 May 2015, Berlin, Germany}, abstract = {In the deep drawing tools for forming car body parts, heavy blankholders are used to prevent buckling and wrinkling of the blank. During each press cycle, those large masses need to be lifted, raising thereby the structural dynamic load on the deep drawing tool and on the press. Therefore a detailed knowledge about the blankholder's lift-off event is essential for an accurate and robust design of forming tools. In this paper, a dynamic finite element method (FEM) simulation of a blankholder's lift-off in a selected automotive deep drawing tool is presented enabling identification of regions of critical stresses. The FEM model is built within the Abaqus/CAE environment and solved with Abaqus/Standard. Each dynamic analysis is preceded by a static analysis where the gravity load is applied and the lifting bolts are pre-stressed. A special emphasis is put on modeling the elastomer dampers, which are installed between lifting bolts and the blankholder to avoid hard impacts during the lift-off event. Those dampers are modelled using a hyperelastic material with hysteresis. In addition, an experimental validation of a blankholder's vibration under operating loading was carried out. The simulation results are in good agreement with the measurements.}, language = {en} } @inproceedings{SwidergalLubesederWurmbetal., author = {Swidergal, Krzysztof and Lubeseder, Christian and Wurmb, Ingo von and Meinhardt, Josef and Wagner, Marcus and Marburg, Steffen}, title = {Vibration analysis of an automotive forming tool using coupled MBS-FEM simulation and experimental validation}, series = {Proceedings of the 26th International Conference on Noise and Vibration Engineering (ISMA2014), Leuven, Belgium}, booktitle = {Proceedings of the 26th International Conference on Noise and Vibration Engineering (ISMA2014), Leuven, Belgium}, pages = {2931 -- 2942}, abstract = {To improve efficiency in automotive press shops, press systems with increasingly high stroke rates are beingimplemented, raising thereby the structural dynamic load on the press and especially on the forming tool. Adetailed knowledge of the vibrations and resulting critical loads is thus essential for accurate and reliable de-signs of forming tools. In this paper, multibody simulation (MBS) of a selected automotive tool is presentedenabling the identification of the vibration of its components. Starting from a pure rigid modelling approach,the MBS model is extended by adding finite element (FE) component to allow extra flexibility in the sys-tem. As an example, a detailed vibrational analysis - both in time and frequency domain - is performed ona blankholder. Also an experimental validation of a blankholder vibration under operational load is carriedout, with test signal data gained by piezoelectric accelerometers.}, language = {en} } @inproceedings{SwidergalLubesederWurmbetal., author = {Swidergal, Krzysztof and Lubeseder, Christian and Wurmb, Ingo von and Lipp, Arnulf and Meinhardt, Josef and Wagner, Marcus and Marburg, Steffen}, title = {Structural analysis of an automotive forming tool for large presses using LS-DYNA}, series = {10th European LS-DYNA Conference, W{\"u}rzburg}, booktitle = {10th European LS-DYNA Conference, W{\"u}rzburg}, language = {en} } @inproceedings{SwidergalLubesederWurmbetal., author = {Swidergal, Krzysztof and Lubeseder, Christian and Wurmb, Ingo von and Meinhardt, Josef and Wagner, Marcus and Marburg, Steffen}, title = {Effiziente Methode zur Bestimmung von dynamischen strukturellen Belastungen in Großpresswerkzeugen}, series = {36. EFB-Kolloquium Blechverarbeitung 2016, Fellbach}, booktitle = {36. EFB-Kolloquium Blechverarbeitung 2016, Fellbach}, language = {de} } @inproceedings{SwidergalThumannLubesederetal., author = {Swidergal, Krzysztof and Thumann, Philipp and Lubeseder, Christian and Wurmb, Ingo von and Meinhardt, Josef and Wagner, Marcus and Marburg, Steffen}, title = {Modeling and simulation of carbon black filled elastomer damper using LS-DYNA}, series = {LS-DYNA Forum 2014, Bamberg}, booktitle = {LS-DYNA Forum 2014, Bamberg}, language = {en} } @article{WagnerFrankeKrauseetal., author = {Wagner, Marcus and Franke, Markus and Krause, Tom Janis and Heinle, Ingo}, title = {Data augmentation of material properties for machine learning in industrial production - a case study in an automotive press shop}, series = {Engineering Computations : International journal for computer-aided engineering and software}, journal = {Engineering Computations : International journal for computer-aided engineering and software}, publisher = {Emerald Publishing}, address = {Leeds}, doi = {10.1108/EC-08-2024-0787}, pages = {18}, abstract = {In the context of industrial production, the utilisation of data recording and processing techniques is becoming increasingly prevalent across the manufacturing sector. The solutions integrate sensors, facilitate the transmission of data, and enable data-driven decision-making, thereby reducing downtime and optimising quality. However, challenges emerge due to the limited non-transferable data or models between processes. Alterations to the production process can render collected data invalid, resulting in restricted datasets and potential overfitting. To address these issues, techniques such as data augmentation are employed. This study aims to develop a data augmentation methodology applicable in dynamic, data-scarce production environments, enhancing the robustness of regressor predictions.}, subject = {Data augmentation}, language = {en} } @inproceedings{StockerLehrerDuddecketal., author = {Stocker, Philipp and Lehrer, Tobias and Duddeck, Fabian and Wagner, Marcus}, title = {Face-wise prediction of sheet-metal drawability using graph neural networks}, series = {Journal of Physics: Conference Series}, volume = {3104}, booktitle = {Journal of Physics: Conference Series}, number = {1}, publisher = {IOP Publishing}, issn = {1742-6588}, doi = {10.1088/1742-6596/3104/1/012053}, pages = {11}, abstract = {The early design phase of deep-drawn structural components involves time-consuming iterative development. Traditional drawability assessments rely on finite element simulations, which are computationally expensive and slow the design process. Alternative machine learning (ML) approaches show promise in accelerating this process but face challenges with existing methods. Existing low-dimensional ML models only provide global predictions without identifying specific geometric regions prone to failure. High-dimensional models provide local predictions but require significant amounts of training data. We propose a data-driven approach leveraging graph neural networks (GNNs) for face-wise drawability prediction of sheet metal components in their computer-aided design (CAD) representation. Our method aims to bridge the gap between the computational efficiency of ML and the spatial resolution of simulation by providing face-wise insight into potential failure regions. This study utilises a dataset of parametric U-channel geometries with variability in both geometry and topology. Ground-truth labels are generated using inverse analysis simulations. Geometric entities are represented through the use of UV parameterisations, whereby 3D surfaces are mapped into 2D space to facilitate geometric encoding. Concurrently, the topological relationships are captured using a face adjacency graph. To address data scarcity, we evaluate how different amounts of training data affect model performance and perform ablation studies to analyse the impact of different CAD representation features. Our results show that the proposed approach achieves high accuracy even with limited training data. In addition, the ablation studies provide insights into the most critical CAD features, guiding future research. These results highlight the potential of our GNN to predict face-wise drawability in the early design phase.}, language = {en} } @article{HollweckLeidingerHartmannetal., author = {Hollweck, Christoph and Leidinger, Lukas and Hartmann, Stefan and Wagner, Marcus and W{\"u}chner, Roland}, title = {An analysis of the critical time step size for explicit dynamics using trimmed B-splines, LR-splines, and THB-splines}, series = {Computer Methods in Applied Mechanics and Engineering}, volume = {450}, journal = {Computer Methods in Applied Mechanics and Engineering}, publisher = {Elsevier}, issn = {0045-7825}, doi = {10.1016/j.cma.2025.118656}, pages = {36}, abstract = {Isogeometric analysis (IGA) combined with explicit dynamics is increasingly used in academia and has already been successfully applied in industrial simulations, including crash and sheet-metal forming. Since explicit schemes are only conditionally stable, accurate estimation of the critical time step is essential for both stability and efficiency. Adaptive mesh refinement is widely used to balance accuracy and computational cost. In IGA, THB- and LR-splines break the tensor-product structure of standard B-splines and enable local refinement, but their effect on the critical time step under trimming has not been systematically studied - a key requirement for reliable time step estimation. We investigate the critical time step in explicit dynamic simulations using trimmed B-splines, LR-splines, and THB-splines, based on a lumped mass matrix obtained by simple row summation. One-dimensional bar, two-dimensional membrane, and trimmed shell models are analyzed to determine how trimming and local refinement influence element and system eigenfrequencies, which directly control the stable time step. Refined boundary elements in open knot vectors are identified as the main bottleneck. Trimming these elements can increase the stable time step, though certain trimming configurations introduce new restrictions. Results show that LR- and THB-splines impose time step constraints similar to B-splines, making them equally suitable for explicit simulations. We also present a general method for computing element-wise B{\´e}zier extraction operators for LR- and THB-splines, enabling straightforward integration into standard finite element solvers. The findings are validated through nonlinear sheet-metal forming simulations in LS-DYNA using shells discretized with trimmed B-, LR-, and THB-splines. This represents the first such application and demonstrates their practical feasibility for industrial use.}, language = {en} } @unpublished{LehrerStockerDuddecketal., author = {Lehrer, Tobias and Stocker, Philipp and Duddeck, Fabian and Wagner, Marcus}, title = {UCSM: Dataset of U-Shaped Parametric CAD Geometries and Real-World Sheet Metal Meshes for Deep Drawing}, publisher = {SSRN}, doi = {10.2139/ssrn.5268323}, pages = {19}, abstract = {The development of machine learning (ML) applications in deep drawing is hindered by limited data availability and the absence of open-access benchmarks for validating novel approaches, including domain generalization over distinct geometries. This paper addresses these challenges by introducing a comprehensive U-shaped dataset tailored to this manufacturing process. Our U-Channel sheet metal (UCSM) dataset combines 90 real-world meshes with an infinite number of synthetic geometry samples generated from four parametric Computer-Aided Design (CAD) models, ensuring extensive geometry variety and data quantity. Additionally, a ready-to-use dataset for drawability assessment and segmentation is provided. Leveraging CAD and mesh data sources bridges the gap between sparse data availability and ML requirements. Our analysis demonstrates that the proposed parametric models are geometrically valid, and real-world and synthetic data complement each other effectively, providing robust support for ML model development. While the dataset is confined to U-shaped, thin-walled, deep drawing scenarios, it considerably aids in overcoming data scarcity. Thereby, it facilitates the validation and comparison of new geometry-generalizing ML methodologies in this domain. By providing this benchmark dataset, we enhance the comparability and validation of emerging methods for ML advancements in sheet metal forming.}, language = {en} } @article{SittlMarburgDeckersetal., author = {Sittl, Christopher and Marburg, Steffen and Deckers, Elke and Wagner, Marcus}, title = {Model order reduction for unbounded second-order vibroacoustic systems using infinite elements and Dirichlet-to-Neumann map}, series = {Computer Methods in Applied Mechanics and Engineering}, volume = {453}, journal = {Computer Methods in Applied Mechanics and Engineering}, publisher = {Elsevier}, doi = {10.1016/j.cma.2026.118846}, pages = {22}, abstract = {This work addresses the efficient numerical simulation of time-harmonic vibroacoustic problems in unbounded domains, with a focus on fluid-structure interaction. The underlying mathematical model is a second-order dynamical system arising from the coupling of structural and acoustic domains, incorporating material damping effects, relevant in structural acoustics and noise control applications. A central novelty of the proposed method is its unified computational framework that supports two distinct strategies for treating unbounded fluid domains: (1) non-local absorbing boundary conditions based on Dirichlet-to-Neumann map, and (2) infinite elements, which extend the computational domain rather than truncate it. Both approaches are integrated into a consistent formulation that enables flexible and accurate modeling of exterior wave propagation. To efficiently evaluate frequency-domain transfer functions, the method employs model order reduction using the Pad{\´e}-via-Lanczos technique. While this algorithm typically targets first-order systems, the present approach uses a Schur complement strategy to reduce the second-order system in a way that maintains computational efficiency and storage requirements comparable to first-order formulations. Importantly, the framework seamlessly embeds both interior structural damping and the additional dissipation introduced by the acoustic-domain truncation into the model-order reduction process. The exterior acoustic field is represented via spherical harmonic expansions, with expansion coefficients computed from the reduced system. Numerical results demonstrate the method's accuracy, efficiency, and scalability, making it well-suited for high-fidelity vibroacoustic analysis in unbounded domains.}, language = {en} } @misc{LehrerStockerDuddecketal., author = {Lehrer, Tobias and Stocker, Philipp and Duddeck, Fabian and Wagner, Marcus}, title = {Parametric CAD Models to Create an Infinite Number of Structural U-Shaped Sheet Metal Geometries [Data set]}, doi = {10.5281/ZENODO.14191374}, abstract = {The U-Channel Software is a python package containing four parametric models of U-shaped Sheet metals. The parameters refer to geometric dimensions, angles, fillet radii. Using the models, one can generate an infinite number of U-shaped sheet metal geometries, e.g. as STEP files. The parametric models are inspired by real-world shapes. A feasibility check is provided to ensure plausiblity of the shapes. Further features of the code are creating images of the geometries and generating geometries and images in parallel. For more details, refer to the repository and associated publications.}, language = {en} }