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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.
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.
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.
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.
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.