@misc{LangeHuetterKiefer, author = {Lange, Nils and H{\"u}tter, Geralf and Kiefer, Bjoern}, title = {A monolithic hyper ROM FE2 method with clustered training at finite deformations}, series = {Computer Methods in Applied Mechanics and Engineering}, volume = {418}, journal = {Computer Methods in Applied Mechanics and Engineering}, issn = {0045-7825}, doi = {10.1016/j.cma.2023.116522}, abstract = {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.}, language = {en} } @misc{PhamHuetterHenkeletal., author = {Pham, Dinh Rinh and H{\"u}tter, Geralf and Henkel, S. and Seupel, Andreas and Biermann, H. and Kiefer, Bjoern}, title = {Experimentelle und numerische Untersuchungen des Einflusses der Mehrachsigkeit auf das Risswiderstandsverhalten von duktilem Gusseisen}, series = {54. Tagung des Arbeitskreises Bruchmechanik und Bauteilsicherheit}, journal = {54. Tagung des Arbeitskreises Bruchmechanik und Bauteilsicherheit}, doi = {10.48447/BR-2023-014}, abstract = {Bei der Ermittlung statischer bruchmechanischer Kennwerte wird versucht, eine m{\"o}glichst hohe Spannungsmehrachsigkeit vor der Rissspitze sicherzustellen. Im Bereich der Z{\"a}hbruchmechanik (J Integral- und CTOD-Konzept) werden dazu auf ca. halbe Ligamenttiefe angerissene Proben hinreichender Gr{\"o}ße 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 k{\"o}nnen 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 St{\"a}hlen untersucht, um ihn bei der Bauteilwertung ber{\"u}cksichtigen zu k{\"o}nnen. Im Gegensatz dazu liegen f{\"u}r 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 durchgef{\"u}hrt. Weiterhin wird untersucht, inwiefern sich dieser Einfluss der Mehrachsigkeit mittels des sch{\"a}digungsmechanischen Modells von Gurson-Tvergaard-Needleman numerisch vorhersagen l{\"a}sst.}, language = {de} } @misc{ElKhatibHuetterPhametal., author = {El Khatib, Omar and H{\"u}tter, Geralf and Pham, Rinh-Dinh and Seupel, Andreas and Kuna, Meinhard and Kiefer, Bjoern}, title = {A non-iterative parameter identification procedure for the non-local Gurson-Tvergaard-Needleman model based on standardized experiments}, series = {International Journal of Fracture}, volume = {241}, journal = {International Journal of Fracture}, number = {1}, issn = {0376-9429}, doi = {10.1007/s10704-023-00689-9}, pages = {73 -- 94}, abstract = {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.}, language = {en} } @misc{Huetter, author = {H{\"u}tter, Geralf}, title = {Interpretation of micromorphic constitutive relations for porous materials at the microscale via harmonic decomposition}, series = {Journal of the Mechanics and Physics of Solids}, volume = {171}, journal = {Journal of the Mechanics and Physics of Solids}, doi = {10.1016/j.jmps.2022.105135}, pages = {1 -- 24}, abstract = {Micromorphic theories became an established tool to model size effects in materials like dispersion, localization phenomena or (apparently) size dependent properties. However, the formulation of adequate constitutive relations with its large number of constitutive relations and respective parameters hinders the usage of the full micromorphic theory, which has 18 constitutive parameters already in the isotropic linear elastic case. Although it is clear that these parameters are related to predicted size effects, the individual meaning of single parameters has been rather unclear. The present work tries to elucidate the interpretation of the constitutive relations and their parameters. For this purpose, a harmonic decomposition is applied to the governing equations of micromorphic theory. The harmonic modes are interpreted at the microscale using a homogenization method for a simple volume element with spherical pore. The resulting boundary-value problem at the microscale is solved analytically for the linear-elastic case using spherical harmonics resulting in closed-form expressions for all of the elastic 18 parameters. These values are used to predict the size effect in torsion of slender foam specimens. The predictions are compared with respective experimental results from literature.}, language = {en} } @misc{PhamElKhatibSeupeletal., author = {Pham, Dinh Rinh and El Khatib, Omar and Seupel, Andreas and H{\"u}tter, Geralf and Kiefer, Bjoern}, title = {Iterationslose Bestimmung der Parameter des Gurson-Modells aus zwei genormten Versuchen}, series = {54. Tagung des Arbeitskreises Bruchmechanik und Bauteilsicherheit: Bruchmechanische Werkstoff- und Bauteilbewertung: Beanspruchungsanalyse, Pr{\"u}fmethoden und Anwendungen}, volume = {2022}, journal = {54. Tagung des Arbeitskreises Bruchmechanik und Bauteilsicherheit: Bruchmechanische Werkstoff- und Bauteilbewertung: Beanspruchungsanalyse, Pr{\"u}fmethoden und Anwendungen}, number = {254}, editor = {Vormwald, Michael}, publisher = {DVM e.V.}, address = {Berlin}, doi = {10.48447/BR-2022-005}, pages = {43 -- 52}, abstract = {Das sch{\"a}digungsmechanische Modell nach Gurson wird seit vielen Jahren in der Forschung erfolgreich f{\"u}r 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. Diesbez{\"u}glich wurden im Schrifttum verschiedenste Ans{\"a}tze verfolgt, um die Parameter aus einer gewissen Anzahl von mehr oder minder aufw{\"a}ndigen Experimenten zu bestimmen, meist iterativ in einer Schleife aus FEM-Simulationen. Die Autoren hatten in einer Reihe von Untersuchungen Sensitivit{\"a}tsstudien durchgef{\"u}hrt 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 k{\"o}nnen. Diese Prozedur wird im vorliegenden Beitrag f{\"u}r verschiedene Werkstoffe evaluiert und die Vorhersagequalit{\"a}t {\"u}berpr{\"u}ft.}, language = {en} } @misc{KirchhofAmsHuetter, author = {Kirchhof, Stephan and Ams, Alfons and H{\"u}tter, Geralf}, title = {On the Question of the Sign of Size Effects in the Elastic Behavior of Foams}, series = {Journal of Elasticity}, journal = {Journal of Elasticity}, issn = {1573-2681}, doi = {10.1007/s10659-023-10037-6}, abstract = {Due to their good ratio of stiffness and strength to weight, foam materials find use in lightweight engineering. Though, in many applications like structural bending or tension, the scale separation between macroscopic structure and the foam's mesostructure like cells size, is relatively weak and the mechanical properties of the foam appear to be size dependent. Positive as well as negative size effects have been observed for certain basic tests of foams, i.e., the material appears either to be more compliant or stiffer than would be expected from larger specimens. Performing tests with sufficiently small specimens is challenging as any disturbances from damage of cell walls during sample preparation or from loading devices must be avoided. Correspondingly, the number of respective data in literature is relatively low and the results are partly contradictory. In order to avoid the problems from sample preparation or bearings, the present study employs virtual tests with CT data of real medium-density ceramic foams. A number of samples of different size is "cut" from the resulting voxel data. Subsequently, the apparent elastic properties of each virtual sample are "measured" directly by a free vibrational analysis using finite cell method, thereby avoiding any disturbances from load application or bearings. The results exhibit a large scatter of the apparent moduli per sample size, but with a clear negative size effect in all investigated basic modes of deformation (bending, torsion, uniaxial). Finally, the results are compared qualitatively and quantitatively to available experimental data from literature, yielding common trends as well as open questions.}, language = {en} } @misc{ElKhatibPhamHuetteretal., author = {El Khatib, Omar and Pham, Rinh-Dinh and H{\"u}tter, Geralf and Seupel, Andreas and Kiefer, Bjoern}, title = {On the predictive capabilities of non-local models for ductilecrack propagation under different levels of stress triaxiality}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {23}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {4}, issn = {1617-7061}, doi = {10.1002/pamm.202300274}, abstract = {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.}, language = {en} }