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for \"Spectral Normalization and Voigt\u2013Reuss net: A universal approach to microstructure\u2010property forecasting with physical guarantees\"", "user" : "ffritzen", "description" : "", "date" : "2025-06-30 15:01:07", "changeDate" : "2025-06-30 15:01:07", "count" : 6, "pub-type": "dataset", "publisher":"DaRUS", "year": "2025", "url": "https://doi.org/10.18419/DARUS-5120", "author": [ "Sanath Keshav","Julius Herb","Felix Fritzen" ], "authors": [ {"first" : "Sanath", "last" : "Keshav"}, {"first" : "Julius", "last" : "Herb"}, {"first" : "Felix", "last" : "Fritzen"} ], "doi" : "10.18419/DARUS-5120", "bibtexKey": "https://doi.org/10.18419/darus-5120" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2cfbde65aa3a22a8d402353dd7de8e3cb/ffritzen", "tags" : [ "myown","heisenberg","dae","aisa","pn3-a2","exc2075" ], "intraHash" : "cfbde65aa3a22a8d402353dd7de8e3cb", "interHash" : "41677861e35f71ea7db00da9f47a2401", "label" : "Spectral Normalization and Voigt-Reuss 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"ffritzen", "description" : "", "date" : "2025-02-04 10:04:56", "changeDate" : "2025-02-04 10:04:56", "count" : 5, "pub-type": "article", "journal": "Advanced Modeling and Simulation in Engineering Sciences","publisher":"Springer Science and Business Media LLC", "year": "2024", "url": "http://dx.doi.org/10.1186/s40323-024-00275-1", "author": [ "Julian Lißner","Felix Fritzen" ], "authors": [ {"first" : "Julian", "last" : "Lißner"}, {"first" : "Felix", "last" : "Fritzen"} ], "volume": "11","number": "1", "issn" : "2213-7467", "doi" : "10.1186/s40323-024-00275-1", "bibtexKey": "Julian_2024" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2fd87968a17654040b972560bdcbb1c67/ffritzen", "tags" : [ "heisenberg","pn3","pn3-1","dae","exc2075" ], "intraHash" : "fd87968a17654040b972560bdcbb1c67", "interHash" : "5e0181f8438cbc5e91f196ebf20e46c2", "label" : "Double U\u2010Net: Improved multiscale modeling via fully convolutional neural networks", "user" : "ffritzen", "description" : "", "date" : "2023-09-22 13:21:00", "changeDate" : "2023-09-22 13:24:55", "count" : 6, "pub-type": "article", "journal": "Proceedings in Applied Mathematics & Mechanics (PAMM)", "year": "2023", "url": "https://doi.org/10.1002/pamm.202300205", "author": [ "Julian Lißner","Felix Fritzen" ], "authors": [ {"first" : "Julian", "last" : "Lißner"}, {"first" : "Felix", "last" : "Fritzen"} ], "doi" : "10.1002/pamm.202300205", "bibtexKey": "lissner2023double" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/26a374c4bd7b57bfd033a9b7bfc7728b2/ffritzen", "tags" : [ "myown","heisenberg","pn3","dae","pn3-a3","exc2075" ], "intraHash" : "6a374c4bd7b57bfd033a9b7bfc7728b2", "interHash" : "c22fa4b8ffec8eadd04aed0bc821bdf0", "label" : "Reduced order homogenization of thermoelastic materials with strong temperature dependence and comparison to a machine-learned model", "user" : "ffritzen", "description" : "", "date" : "2023-07-20 09:33:41", "changeDate" : "2023-07-20 09:33:41", "count" : 8, "pub-type": "article", "journal": "Archive of Applied Mechanics", "year": "2023", "url": "https://doi.org/10.1007/s00419-023-02411-6", "author": [ "Shadi Sharba","Julius Herb","Felix Fritzen" ], "authors": [ {"first" : "Shadi", "last" : "Sharba"}, {"first" : "Julius", "last" : "Herb"}, {"first" : "Felix", "last" : "Fritzen"} ], "volume": "93","number": "7","pages": "2855--2876","abstract": "In this work, an approach for strongly temperature-dependent thermoelastic homogenization is presented. It is based on computational homogenization paired with reduced order models (ROMs) that allow for full temperature dependence of material parameters in all phases. In order to keep the model accurate and computationally efficient at the same time, we suggest the use of different ROMs at few discrete temperatures. Then, for intermediate temperatures, we derive an energy optimal basis emerging from the available ones. The resulting reduced homogenization problem can be solved in real time. Unlike classical homogenization where only the effective behavior, i.e., the effective stiffness and the effective thermal expansion, of the microscopic reference volume element are of interest, our ROM delivers also accurate full-field reconstructions of all mechanical fields within the microstructure. We show that the proposed method referred to as optimal field interpolation is computationally as efficient as simplistic linear interpolation. However, our method yields an accuracy that matches direct numerical simulation in many cases, i.e., very accurate real-time predictions are achieved. Additionally, we propose a greedy sampling procedure yielding a minimal number of direct numerical simulations as inputs (two to six discrete temperatures are used over a range of around 1000 K). Further, we pick up a black box machine-learned model as an alternative route and show its limitations in view of the limited amount of training data. Using our new method to generate an abundance of data, we demonstrate that a highly accurate tabular interpolator can be gained easily.", "issn" : "1432-0681", "doi" : "10.1007/s00419-023-02411-6", "bibtexKey": "sharba2023" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/237c5677a1c204aae96d3c9275c7ead89/ffritzen", "tags" : [ "postPrint","heisenberg","PN3","peerReviewed","dae","EXC2075","PN3A2" ], "intraHash" : "37c5677a1c204aae96d3c9275c7ead89", "interHash" : "bc89baa806c1c487e235d81d8ce2fc38", "label" : "FFT-based homogenization at finite strains using composite boxels (ComBo)", "user" : "ffritzen", "description" : "", "date" : "2022-10-11 15:46:01", "changeDate" : "2023-06-12 15:17:09", "count" : 6, "pub-type": "article", "journal": "Computational Mechanics", "year": "2023", "url": "https://rdcu.be/cXhLt", "author": [ "Sanath Keshav","Felix Fritzen","Matthias Kabel" ], "authors": [ {"first" : "Sanath", "last" : "Keshav"}, {"first" : "Felix", "last" : "Fritzen"}, {"first" : "Matthias", "last" : "Kabel"} ], "volume": "71","pages": "191-212","abstract": "Computational homogenization is the gold standard for concurrent multi-scale simulations (e.g., FE2) in scale-bridging applications. Often the simulations are based on experimental and synthetic material microstructures represented by high-resolution 3D image data. The computational complexity of simulations operating on such voxel data is distinct. The inability of voxelized 3D geometries to capture smooth material interfaces accurately, along with the necessity for complexity reduction, has motivated a special local coarse-graining technique called composite voxels (Kabel et al. Comput Methods Appl Mech Eng 294: 168--188, 2015). They condense multiple fine-scale voxels into a single voxel, whose constitutive model is derived from the laminate theory. Our contribution generalizes composite voxels towards composite boxels (ComBo) that are non-equiaxed, a feature that can pay off for materials with a preferred direction such as pseudo-uni-directional fiber composites. A novel image-based normal detection algorithm is devised which (i) allows for boxels in the firsts place and (ii) reduces the error in the phase-averaged stresses by around 30\\% against the orientation cf. Kabel et al. (Comput Methods Appl Mech Eng 294: 168--188, 2015) even for equiaxed voxels. Further, the use of ComBo for finite strain simulations is studied in detail. An efficient and robust implementation is proposed, featuring an essential selective back-projection algorithm preventing physically inadmissible states. Various examples show the efficiency of ComBo against the original proposal by Kabel et al. (Comput Methods Appl Mech Eng 294: 168--188, 2015) and the proposed algorithmic enhancements for nonlinear mechanical problems. The general usability is emphasized by examining various Fast Fourier Transform (FFT) based solvers, including a detailed description of the Doubly-Fine Material Grid (DFMG) for finite strains. All of the studied schemes benefit from the ComBo discretization.", "issn" : "1432-0924", "doi" : "10.1007/s00466-022-02232-4", "bibtexKey": "Keshav2022" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2e012cc9969ee46eb82128239f0186ceb/katharinafuchs", "tags" : [ "myown","emma","heisenberg","dae","EXC2075","from:ffritzen" ], "intraHash" : "e012cc9969ee46eb82128239f0186ceb", "interHash" : "f61f8b5059d353dcf74357719c947f8e", "label" : "Construction of a class of sharp Löwner majorants for a set of symmetric matrices", "user" : "katharinafuchs", "description" : "Article ID 9091387", "date" : "2021-12-08 17:10:08", "changeDate" : "2021-12-08 16:10:08", "count" : 8, "pub-type": "article", "journal": "Journal of Applied Mathematics","publisher":"Hindawi", "year": "2020", "url": "https://doi.org/10.1155/2020/9091387", "author": [ "Mauricio Fernández","Felix Fritzen" ], "authors": [ {"first" : "Mauricio", "last" : "Fernández"}, {"first" : "Felix", "last" : "Fritzen"} ], "volume": "2020","pages": "1-18", "language" : "en", "doi" : "10.1155/2020/9091387", "bibtexKey": "fernandez2020_Lowener" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/22515bc88d2935f8b11d5564b28b20368/katharinafuchs", "tags" : [ "myown","postPrint","emma","pn3","peerReviewed","dae","EXC2075","from:ffritzen" ], "intraHash" : "2515bc88d2935f8b11d5564b28b20368", "interHash" : "7b7d86094497dcda15b2bc25b0134764", "label" : "On the generation of periodic discrete structures with identical two-point correlation", "user" : "katharinafuchs", "description" : "2PC correlation, equivalence, generation homogenization of periodic structures, two-point", "date" : "2021-12-08 17:10:08", "changeDate" : "2021-12-08 16:10:08", "count" : 8, "pub-type": "article", "journal": "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences", "year": "2020", "url": "", "author": [ "Mauricio Fernández","Felix Fritzen" ], "authors": [ {"first" : "Mauricio", "last" : "Fernández"}, {"first" : "Felix", "last" : "Fritzen"} ], "volume": "476","number": "2242","pages": "20200568","abstract": "Strategies for the generation of periodic discrete structures with identical two-point correlation\u2014called 2PC-equivalent\u2014are developed. It is shown that starting from a set of 2PC-equivalent root structures, 2PC-equivalent child structures of arbitrary resolution and number of phases (e.g. material phases) can be generated based on phase extension through trivial embeddings, kernel-based extension and phase coalescence. Proofs are provided by means of discrete Fourier transform theory. A Python 3 implementation is offered for reproduction of examples and future applications.", "doi" : "10.1098/rspa.2020.0568", "bibtexKey": "fernandez2020c" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/248a3ac64afcc16966758f3a367b24776/ffritzen", "tags" : [ "myown","heisenberg","pn3","DAE","EXC2075" ], "intraHash" : "48a3ac64afcc16966758f3a367b24776", "interHash" : "803cc3310661ad83b5ee5c6841322466", "label" : "Material modeling for parametric, anisotropic finite strain hyperelasticity based on machine learning with application in optimization of metamaterials", "user" : "ffritzen", "description" : "", "date" : "2021-12-03 14:58:12", "changeDate" : "2021-12-22 12:40:33", "count" : 6, "pub-type": "article", "journal": "International Journal for Numerical Methods in Engineering", "year": "2022", "url": "https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6869", "author": [ "Mauricio Fernández","Felix Fritzen","Oliver Weeger" ], "authors": [ {"first" : "Mauricio", "last" : "Fernández"}, {"first" : "Felix", "last" : "Fritzen"}, {"first" : "Oliver", "last" : "Weeger"} ], "volume": "123","number": "2","pages": "577-609","abstract": "Mechanical metamaterials such as open- and closed-cell lattice structures, foams, composites, and so forth can often be parametrized in terms of their microstructural properties, for example, relative densities, aspect ratios, material, shape, or topological parameters. To model the effective constitutive behavior and facilitate efficient multiscale simulation, design, and optimization of such parametric metamaterials in the finite deformation regime, a machine learning-based constitutive model is presented in this work. The approach is demonstrated in application to elastic beam lattices with cubic anisotropy, which exhibit highly nonlinear effective behaviors due to microstructural instabilities and topology variations. Based on microstructure simulations, the relevant material and topology parameters of selected cubic lattice cells are determined and training data with homogenized stress-deformation responses is generated for varying parameters. Then, a parametric, hyperelastic, anisotropic constitutive model is formulated as an artificial neural network, extending a recent work of the author extending a recent work of the author, Comput Mech., 2021;67(2):653-677. The machine learning model is calibrated with the simulation data of the parametric unit cell. The authors offer public access to the simulation data through the GitHub repository https://github.com/CPShub/sim-data. For the calibration of the model, a dedicated sample weighting strategy is developed to equally consider compliant and stiff cells and deformation scenarios in the objective function. It is demonstrated that this machine learning model is able to represent and predict the effective constitutive behavior of parametric lattices well across several orders of magnitude. Furthermore, the usability of the approach is showcased by two examples for material and topology optimization of the parametric lattice cell.", "eprint" : "https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6869", "doi" : "10.1002/nme.6869", "bibtexKey": "fernandez2022nme" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/24e289cca620543834231d772872449dd/ffritzen", "tags" : [ "myown","emma","pn3","peerReviewed","dae","EXC2075" ], "intraHash" : "4e289cca620543834231d772872449dd", "interHash" : "d463a8b485cc2c2cbd02565f19bf67c0", "label" : "Many-scale finite strain computational homogenization via Concentric Interpolation", "user" : "ffritzen", "description" : "computational homogenization, concentric interpolation, Hencky strain, hyperelasticity, multiscale, reduced basis", "date" : "2020-10-21 15:28:52", "changeDate" : "2021-03-16 07:39:39", "count" : 7, "pub-type": "article", "journal": "International Journal for Numerical Methods in Engineering", "year": "2020", "url": "", "author": [ "Oliver Kunc","Felix Fritzen" ], "authors": [ {"first" : "Oliver", "last" : "Kunc"}, {"first" : "Felix", "last" : "Fritzen"} ], "volume": "121","number": "21","pages": "4689--4716","abstract": "A method for efficient computational homogenization of hyperelastic materials under finite strains is proposed. Multiple spatial scales are homogenized in a recursive procedure: starting on the smallest scale, few high fidelity FE computations are performed. The resulting fields of deformation gradient fluctuations are processed by a snapshot POD resulting in a reduced basis (RB) model. By means of the computationally efficient RB model, a large set of samples of the homogenized material response is created. This data set serves as the support for the Concentric Interpolation (CI) scheme, interpolating the effective stress and stiffness. Then, the same procedure is invoked on the next larger scale with this CI surrogating the homogenized material law. A three-scale homogenization process is completed within few hours on a standard workstation. The resulting model is evaluated within minutes on a laptop computer in order to generate fourth-scale results. Open source code is provided.", "eprint" : "https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6454", "doi" : "10.1002/nme.6454", "bibtexKey": "kunc2020a" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/22515bc88d2935f8b11d5564b28b20368/ffritzen", "tags" : [ "myown","emma","pn3","peerReviewed","dae","EXC2075" ], "intraHash" : "2515bc88d2935f8b11d5564b28b20368", "interHash" : "7b7d86094497dcda15b2bc25b0134764", "label" : "On the generation of periodic discrete structures with identical two-point correlation", "user" : "ffritzen", "description" : "2PC correlation, equivalence, generation homogenization of periodic structures, two-point", "date" : "2020-10-21 15:26:14", "changeDate" : "2021-01-18 17:03:54", "count" : 8, "pub-type": "article", "journal": "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences", "year": "2020", "url": "", "author": [ "Mauricio Fernández","Felix Fritzen" ], "authors": [ {"first" : "Mauricio", "last" : "Fernández"}, {"first" : "Felix", "last" : "Fritzen"} ], "volume": "476","number": "2242","pages": "20200568","abstract": "Strategies for the generation of periodic discrete structures with identical two-point correlation\u2014called 2PC-equivalent\u2014are developed. It is shown that starting from a set of 2PC-equivalent root structures, 2PC-equivalent child structures of arbitrary resolution and number of phases (e.g. material phases) can be generated based on phase extension through trivial embeddings, kernel-based extension and phase coalescence. Proofs are provided by means of discrete Fourier transform theory. A Python 3 implementation is offered for reproduction of examples and future applications.", "doi" : "10.1098/rspa.2020.0568", "bibtexKey": "fernandez2020c" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2e012cc9969ee46eb82128239f0186ceb/ffritzen", "tags" : [ "myown","emma","heisenberg","pn3","dae","EXC2075" ], "intraHash" : "e012cc9969ee46eb82128239f0186ceb", "interHash" : "f61f8b5059d353dcf74357719c947f8e", "label" : "Construction of a class of sharp Löwner majorants for a set of symmetric matrices", "user" : "ffritzen", "description" : "Article ID 9091387", "date" : "2020-01-15 00:02:47", "changeDate" : "2021-12-02 16:04:45", "count" : 8, "pub-type": "article", "journal": "Journal of Applied Mathematics","publisher":"Hindawi", "year": "2020", "url": "https://doi.org/10.1155/2020/9091387", "author": [ "Mauricio Fernández","Felix Fritzen" ], "authors": [ {"first" : "Mauricio", "last" : "Fernández"}, {"first" : "Felix", "last" : "Fritzen"} ], "volume": "2020","pages": "1-18", "language" : "en", "doi" : "10.1155/2020/9091387", "bibtexKey": "fernandez2020_Lowener" } ] }