FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse design
Auxetic structures, known for their negative Poisson's ratio, exhibit effective elastic properties heavily influenced by their underlying geometry and base material properties. While periodic homogenization of auxetic unit cells can be used to investigate these properties, it is computationally...
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Elsevier
2024-12-01
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| Series: | Materials & Design |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S0264127524008669 |
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| author | Hooman Danesh Daniele Di Lorenzo Francisco Chinesta Stefanie Reese Tim Brepols |
| author_facet | Hooman Danesh Daniele Di Lorenzo Francisco Chinesta Stefanie Reese Tim Brepols |
| author_sort | Hooman Danesh |
| collection | DOAJ |
| description | Auxetic structures, known for their negative Poisson's ratio, exhibit effective elastic properties heavily influenced by their underlying geometry and base material properties. While periodic homogenization of auxetic unit cells can be used to investigate these properties, it is computationally expensive and limits design space exploration and inverse analysis. In this paper, the fast Fourier transform (FFT)-based homogenization approach is adopted to efficiently generate data for developing surrogate models, bypassing concerns about periodic mesh generation and boundary conditions typically associated with the finite element method (FEM). Surrogate models are developed for the real-time prediction of the effective elastic properties of auxetic unit cells with orthogonal voids of different shapes. The generated surrogate models accept geometric parameters and base material properties as inputs to predict the effective elastic constants in real-time. This rapid evaluation enables a practical inverse analysis framework for obtaining the optimal design parameters that yield the desired effective response. The performance of the generated surrogate models is rigorously examined through a train/test split methodology, a parametric study, and an inverse problem. Finally, a graphical user interface (GUI) is developed, offering real-time prediction of the effective tangent stiffness and performing inverse analysis to determine optimal geometric parameters. |
| format | Article |
| id | doaj-art-acff5b8e68ad486e99152c6601273ef8 |
| institution | DOAJ |
| issn | 0264-1275 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Materials & Design |
| spelling | doaj-art-acff5b8e68ad486e99152c6601273ef82025-08-20T02:52:35ZengElsevierMaterials & Design0264-12752024-12-0124811349110.1016/j.matdes.2024.113491FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse designHooman Danesh0Daniele Di Lorenzo1Francisco Chinesta2Stefanie Reese3Tim Brepols4Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany; Corresponding author.ESI Group, Symbiose 2, 10 Av. Aristide Briand, 92220 Bagneux, France; PIMM Lab, ENSAM Institute of Technology, 151 Boulevard de l'Hôpital, 75013 Paris, FranceESI Group, Symbiose 2, 10 Av. Aristide Briand, 92220 Bagneux, France; PIMM Lab, ENSAM Institute of Technology, 151 Boulevard de l'Hôpital, 75013 Paris, France; CNRS @CREATE, 1 CREATE Way, 04-05 CREATE Tower, 138602, SingaporeInstitute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany; University of Siegen, Adolf-Reichwein-Str. 2a, 57076 Siegen, GermanyInstitute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, GermanyAuxetic structures, known for their negative Poisson's ratio, exhibit effective elastic properties heavily influenced by their underlying geometry and base material properties. While periodic homogenization of auxetic unit cells can be used to investigate these properties, it is computationally expensive and limits design space exploration and inverse analysis. In this paper, the fast Fourier transform (FFT)-based homogenization approach is adopted to efficiently generate data for developing surrogate models, bypassing concerns about periodic mesh generation and boundary conditions typically associated with the finite element method (FEM). Surrogate models are developed for the real-time prediction of the effective elastic properties of auxetic unit cells with orthogonal voids of different shapes. The generated surrogate models accept geometric parameters and base material properties as inputs to predict the effective elastic constants in real-time. This rapid evaluation enables a practical inverse analysis framework for obtaining the optimal design parameters that yield the desired effective response. The performance of the generated surrogate models is rigorously examined through a train/test split methodology, a parametric study, and an inverse problem. Finally, a graphical user interface (GUI) is developed, offering real-time prediction of the effective tangent stiffness and performing inverse analysis to determine optimal geometric parameters.http://www.sciencedirect.com/science/article/pii/S0264127524008669Auxetic structuresSurrogate modelsEffective propertiesInverse analysisFFT-based homogenization |
| spellingShingle | Hooman Danesh Daniele Di Lorenzo Francisco Chinesta Stefanie Reese Tim Brepols FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse design Materials & Design Auxetic structures Surrogate models Effective properties Inverse analysis FFT-based homogenization |
| title | FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse design |
| title_full | FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse design |
| title_fullStr | FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse design |
| title_full_unstemmed | FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse design |
| title_short | FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse design |
| title_sort | fft based surrogate modeling of auxetic metamaterials with real time prediction of effective elastic properties and swift inverse design |
| topic | Auxetic structures Surrogate models Effective properties Inverse analysis FFT-based homogenization |
| url | http://www.sciencedirect.com/science/article/pii/S0264127524008669 |
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