Multiplicative reduced bases for hyperelasticity
The present paper introduces multiplicative reduced bases for hyperelasticity relying on a truncated version of the Baker–Campbell–Hausdorff’s expansion. We show such a construction is equally interpolatory (in a multiplicative way) for the fields of deformation gradients, surfacic and volumetric de...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-07-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.584/ |
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| Summary: | The present paper introduces multiplicative reduced bases for hyperelasticity relying on a truncated version of the Baker–Campbell–Hausdorff’s expansion. We show such a construction is equally interpolatory (in a multiplicative way) for the fields of deformation gradients, surfacic and volumetric deformation measures involved in large deformation mechanics. The method is naturally derived from a fully consistent variational setting and we establish an upper bound of the error in the energy norm. From a computational standpoint, the approach achieves efficient Kolmogorov $n$-width decay when very large rotations and incompressibility are involved. |
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| ISSN: | 1778-3569 |