TY - GEN A1 - Hütter, Geralf T1 - Interpretation of micromorphic constitutive relations for porous materials at the microscale via harmonic decomposition T2 - Journal of the Mechanics and Physics of Solids N2 - 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. KW - Micromorphic theory KW - Homogenization KW - Size effect in torsion KW - Harmonic decomposition KW - Foam material Y1 - 2023 U6 - https://doi.org/10.1016/j.jmps.2022.105135 VL - 171 SP - 1 EP - 24 ER - TY - GEN A1 - Malik, Alexander A1 - Hütter, Geralf A1 - Abendroth, Martin A1 - Kiefer, Bjoern T1 - Micromorphic FE2 simulation of plastic deformations of foam structures T2 - International Journal of Mechanical Sciences N2 - Capturing and predicting the effective mechanical properties of highly porous cellular media still represents a significant challenge for the research community, due to their complex structural interdependencies and known size effects. Micromorphic theories are often applied in this context to model the inelastic deformation behavior of foam-like structures, in particular to incorporate such size effect into the investigation of structure–property correlations. This raises the problems of formulating appropriate constitutive relations for the numerous non-classical stress measures and determining the corresponding material parameters, which are usually difficult to assess experimentally. The present contribution therefore alternatively employs a hierarchical micromorphic multi-scale approach within the direct FE2 framework to simulate the complex irreversible behavior of foam-like porous solids. The predictions of Cosserat (micropolar) and a fully-micromorphic theory are compared with conventional FE2 results and direct numerical simulations (DNS) for complex loading scenarios with elastic, elastic–plastic, and creep deformations. Therein, non-classical deformation modes of the microstructure resulting from the introduced micromorphic kinematics are visualized, as are the macroscopic hyperstresses and deformations. KW - Multi-scale KW - Homogenization KW - Size effects KW - Generalized continuum KW - Micromorphic theory KW - FE Y1 - 2024 U6 - https://doi.org/10.1016/j.ijmecsci.2024.109551 SN - 0020-7403 VL - 282 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 - 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 - TY - GEN A1 - Kirchhof, Stephan A1 - Ams, Alfons A1 - Hütter, Geralf T1 - On the question of the sign of size effects in the elastic behavior of foams T2 - Journal of Elasticity N2 - 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. KW - Foam KW - Cellular material KW - Elastic size effect KW - Bending KW - Torsion KW - Virtual testing Y1 - 2023 UR - https://link.springer.com/article/10.1007/s10659-023-10037-6 U6 - https://doi.org/10.1007/s10659-023-10037-6 SN - 1573-2681 ER - 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 -