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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-07-01
|
| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.584/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206230044377088 |
|---|---|
| author | Hauret, Patrice |
| author_facet | Hauret, Patrice |
| author_sort | Hauret, Patrice |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-57a4154abf8049eb8f2a3c275ecf334a |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-57a4154abf8049eb8f2a3c275ecf334a2025-02-07T11:21:51ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-07-01362G659360510.5802/crmath.58410.5802/crmath.584Multiplicative reduced bases for hyperelasticityHauret, Patrice0Centre de Technologies Michelin, Place des Carmes, 63000 Clermont-Ferrand, France; SiMatLab, Campus Universitaire des Cézeaux, 24 Avenue Blaise Pascal, TSA 60026 / CS 60026, 63178 Aubière Cedex, FranceThe 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.584/ |
| spellingShingle | Hauret, Patrice Multiplicative reduced bases for hyperelasticity Comptes Rendus. Mathématique |
| title | Multiplicative reduced bases for hyperelasticity |
| title_full | Multiplicative reduced bases for hyperelasticity |
| title_fullStr | Multiplicative reduced bases for hyperelasticity |
| title_full_unstemmed | Multiplicative reduced bases for hyperelasticity |
| title_short | Multiplicative reduced bases for hyperelasticity |
| title_sort | multiplicative reduced bases for hyperelasticity |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.584/ |
| work_keys_str_mv | AT hauretpatrice multiplicativereducedbasesforhyperelasticity |