TY - GEN A1 - Lange, Nils A1 - Hütter, Geralf A1 - Kiefer, Bjoern T1 - A monolithic hyper ROM FE2 method with clustered training at finite deformations T2 - Computer Methods in Applied Mechanics and Engineering N2 - The usage of numerical homogenization to obtain structure–property relations by applying the finite element method at both the micro- and macroscale has gained much interest in the research community. The computational cost of this so-called FE2 method, however, is typically so high that algorithmic modifications and reduction methods are essential. In the present contribution, a monolithic solution algorithm is combined with reduced order modeling (ROM) and the empirical cubature method (ECM) for hyper integration. It is further complemented by a clustered training strategy, which lowers the training effort and the number of necessary ROM modes immensely. The applied methods can be combined modularly as desired in finite element approaches. An implementation in terms of an extension to the previously established MonolithFE2 code is provided. Numerical examples show the efficiency and accuracy of the monolithic hyper ROM FE2 method and the advantages of the clustered training strategy. Even for two-scale problems with complex geometry and complex, inelastic material behaviors it was shown that speedup factors of almost 1000 (i.e., three orders of magnitude) regarding the online simulation time and of up to 30 regarding all necessary computing effort are obtainable in comparison to the conventional FE2 scheme. The training stage requires only around 3% of that time, meaning that the offline phase is relatively inexpensive, in contrast to many Neural Network approaches, whose employment, in terms of total computational efficiency, only pays off if a large number of online simulations is to be conducted, without requiring additional training. KW - Homogenization KW - Multiscale KW - FE2 KW - Reduced Order Modelling (ROM) KW - Hyper integration KW - Monolithic scheme Y1 - 2024 UR - https://www.sciencedirect.com/science/article/pii/S0045782523006461?via%3Dihub U6 - https://doi.org/10.1016/j.cma.2023.116522 SN - 0045-7825 VL - 418 ER - TY - GEN A1 - Pham, Dinh Rinh A1 - Hütter, Geralf A1 - Henkel, S. A1 - Seupel, Andreas A1 - Biermann, H. A1 - Kiefer, Bjoern T1 - Experimentelle und numerische Untersuchungen des Einflusses der Mehrachsigkeit auf das Risswiderstandsverhalten von duktilem Gusseisen T2 - 54. Tagung des Arbeitskreises Bruchmechanik und Bauteilsicherheit N2 - Bei der Ermittlung statischer bruchmechanischer Kennwerte wird versucht, eine möglichst hohe Spannungsmehrachsigkeit vor der Rissspitze sicherzustellen. Im Bereich der Zähbruchmechanik (J Integral- und CTOD-Konzept) werden dazu auf ca. halbe Ligamenttiefe angerissene Proben hinreichender Größe mit Seitenkerben verwendet. Die an solchen Proben bestimmten Risswiderstandskurven bilden eine untere Schranke und erlauben somit eine sichere Bewertung von Rissen in Bauteilen. Je nach Geometrie des Bauteils und der zu bewertenden Risskonfiguration können diese Schranken allerdings sehr konservativ sein. Deshalb haben eine Vielzahl von Studien in den letzten 30 Jahren den Einfluss der Spannungsmehrachsigkeit auf das Risswiderstandsverhalten von Stählen untersucht, um ihn bei der Bauteilwertung berücksichtigen zu können. Im Gegensatz dazu liegen für duktiles Gusseisen kaum entsprechende Daten vor. Der Beitrag zeigt den Einfluss der Mehrachsigkeit auf das Risswiderstandsverhalten von duktilem Gusseisen mit Kugelgraphit. Dazu wurden 3-Punkt-Biegeversuche an SEN(B)-Proben mit unterschiedlich tiefen Anrissen und mit Variation der Seitenkerben sowie ein Vergleich mit Mittenrissproben durchgeführt. Weiterhin wird untersucht, inwiefern sich dieser Einfluss der Mehrachsigkeit mittels des schädigungsmechanischen Modells von Gurson-Tvergaard-Needleman numerisch vorhersagen lässt. KW - Risswiderstand KW - duktiles Gusseisen KW - Mehrachsigkeit KW - GTN-Modell Y1 - 2023 U6 - https://doi.org/10.48447/BR-2023-014 ER - TY - GEN A1 - El Khatib, Omar A1 - Hütter, Geralf A1 - Pham, Rinh-Dinh A1 - Seupel, Andreas A1 - Kuna, Meinhard A1 - Kiefer, Bjoern T1 - A non-iterative parameter identification procedure for the non-local Gurson–Tvergaard–Needleman model based on standardized experiments T2 - International Journal of Fracture N2 - Damage mechanics models exhibit favorable properties such as the intrinsic influence of stress triaxiality on damage evolution and the prediction of crack initiation as well as propagation leading to structural failure. However, their application requires advanced expertise hindering the transfer of these models into industrial practice, especially since the parameter calibration is a key obstacle. In this paper, a simplified procedure is proposed for a non-local extension of the Gurson–Tvergaard–Needleman model (GTN), which is a highly accepted model for ductile failure of metals. The procedure is iteration free and requires experimental input data from only two standardized tests. The parameters are determined using look-up diagrams created on the basis of systematic simulations and made available for different material behavior covering the majority of ductile metals. Benchmark tests for three different steels are conducted to evaluate the robustness of the proposed procedure. The reliability of the GTN model is validated for all investigated materials. KW - Ductile fracture KW - Non-local GTN KW - Finite element analysis KW - Damage mechanics KW - Fracture mechanics Y1 - 2023 U6 - https://doi.org/10.1007/s10704-023-00689-9 SN - 0376-9429 VL - 241 IS - 1 SP - 73 EP - 94 ER - TY - GEN A1 - Pham, Dinh Rinh A1 - El Khatib, Omar A1 - Seupel, Andreas A1 - Hütter, Geralf A1 - Kiefer, Bjoern ED - Vormwald, Michael T1 - Iterationslose Bestimmung der Parameter des Gurson-Modells aus zwei genormten Versuchen T1 - Non-iterative determination of the parameters for the Gurson model from two standard tests T2 - 54. Tagung des Arbeitskreises Bruchmechanik und Bauteilsicherheit: Bruchmechanische Werkstoff- und Bauteilbewertung: Beanspruchungsanalyse, Prüfmethoden und Anwendungen N2 - Das schädigungsmechanische Modell nach Gurson wird seit vielen Jahren in der Forschung erfolgreich für die Simulation des duktilen Versagensmechanismus und der anschließenden Rissausbreitung eingesetzt. Als Schwierigkeit, insbesondere im Hinblick auf eine breite Anwendung, hat sich dabei die Bestimmung der großen Anzahl von Materialparametern herausgestellt. Diesbezüglich wurden im Schrifttum verschiedenste Ansätze verfolgt, um die Parameter aus einer gewissen Anzahl von mehr oder minder aufwändigen Experimenten zu bestimmen, meist iterativ in einer Schleife aus FEM-Simulationen. Die Autoren hatten in einer Reihe von Untersuchungen Sensitivitätsstudien durchgeführt und eine Prozedur vorgeschlagen, um die Parameter ausschließlich aus dem Zugversuch und einem genormten Bruchmechanikversuch zu bestimmen. Dieses Vorgehen wurde weiter vereinfacht, indem Diagramme bereitgestellt werden, aus welchen die Parameter des Gurson-Modells ohne Iteration und ausschließlich unter Verwendung der Daten der beiden genannten genormten Versuche abgelesen werden können. Diese Prozedur wird im vorliegenden Beitrag für verschiedene Werkstoffe evaluiert und die Vorhersagequalität überprüft. N2 - The damage mechanics model of Gurson has been successfully applied in research for many years to simulate ductile failure mechanism and crack propagation. The determination of the large number of material parameters has turned out to be a problem, particularly with regard to broad application. In this respect, various approaches have been pursued in the literature in order to determine the parameters from a certain number of more or less complex experiments, mostly through iterative FE simulations. The authors had carried out sensitivity studies in a series of investigations and proposed a procedure to determine the parameters only from a tensile test and a standardized fracture mechanics test. This procedure has been further simplified by providing diagrams, from which the parameters of the Gurson model can be obtained without iteration and exclusively using the experimental data of two standardized tests mentioned above. In this article, this procedure is applied for various materials and the prediction quality is checked. KW - Schädigungsmechanik KW - GTN-Modell KW - Kalibrierungsprozedur KW - Anwendung KW - damage mechanics KW - GTN-Model KW - calibration procedure KW - application Y1 - 2022 U6 - https://doi.org/10.48447/BR-2022-005 VL - 2022 IS - 254 SP - 43 EP - 52 PB - DVM e.V. CY - Berlin ER - TY - GEN A1 - El Khatib, Omar A1 - Pham, Rinh-Dinh A1 - Hütter, Geralf A1 - Seupel, Andreas A1 - Kiefer, Bjoern T1 - On the predictive capabilities of non-local models for ductilecrack propagation under different levels of stress triaxiality T2 - Proceedings in applied mathematics and mechanics : PAMM N2 - Ductile materials are used in many applications such as hydrogen storage andtransport, energy plants and additively manufactured components. High safetystandards are vital for such applications, which underline the necessity of thor-oughly investigating ductile failure to ensure safety and increase componentsefficiency. Ductile failure is mainly prompted by the evolution of the so-calledductile damage, characterized by the nucleation, growth and coalescence ofmicrovoids due to plastic deformation. Moreover, the plastic zones formed at thecrack tip of ductile materials exhibit high sensitivity to the stress triaxiality level,which in turn distinctly depends on the geometry of the considered component.The quantification of the stress triaxiality at the crack tip is therefore essential tobetter understand and predict ductile crack propagation and failure. For that rea-son, a non-local ductile damage model is employed in this work to simulate theductile crack propagation under different stress triaxiality conditions. Differentgeometries are considered, such as constrained geometries of notched bendingspecimens and unconstrained geometries of center cracked tension specimens,which characterize the different triaxiality levels. To address the effects of thick-nessandinitialcracklength,three-dimensionalgeometriesaresimulated,whichaccount for the out-of-plane crack-tip constraints. Finally, to evaluate the predic-tion quality of the simulations, corresponding experiments have been carried outand direct comparisons are conducted, with respect to the crack length, ductilecrack propagation and resistance curves. KW - nonlocal GTN model KW - crack tip constraint KW - fracture mechanics KW - ductile crack propagation Y1 - 2023 UR - https://onlinelibrary.wiley.com/doi/10.1002/pamm.202300274 U6 - https://doi.org/10.1002/pamm.202300274 SN - 1617-7061 N1 - 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), December 2023 VL - 23 IS - 4 ER -