Upper bounds estimates of the distance to cubic or orthotropic elasticity
We address the problem, not of the determination–which usually needs numerical methods–but of an accurate analytical estimation of the distance of a raw elasticity tensor to cubic symmetry and to orthotropy. We point out that there are not one but several second-order tensors that carry the likely c...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-06-01
|
| Series: | Comptes Rendus. Mécanique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.246/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825205962660642816 |
|---|---|
| author | Desmorat, Rodrigue Kolev, Boris |
| author_facet | Desmorat, Rodrigue Kolev, Boris |
| author_sort | Desmorat, Rodrigue |
| collection | DOAJ |
| description | We address the problem, not of the determination–which usually needs numerical methods–but of an accurate analytical estimation of the distance of a raw elasticity tensor to cubic symmetry and to orthotropy. We point out that there are not one but several second-order tensors that carry the likely cubic/orthotropic coordinate system of the raw tensor. Since all the second-order covariants of an (exactly) cubic elasticity tensor are isotropic, distance estimates based only on such covariants are not always accurate. We extend to cubic symmetry and to orthotropy the technique recently suggested by Klimeš for transverse isotropy: solving analytically an auxiliary quadratic minimization problem whose solution is a second-order tensor that carries the likely cubic coordinate system. Numerical examples are provided, on which we evaluate the accuracy of different upper bounds estimates of the distance to cubic or orthotropic symmetry. |
| format | Article |
| id | doaj-art-d52616f08aa34e57ac5450ada3d58c07 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-d52616f08aa34e57ac5450ada3d58c072025-02-07T13:48:46ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342024-06-01352G116920010.5802/crmeca.24610.5802/crmeca.246Upper bounds estimates of the distance to cubic or orthotropic elasticityDesmorat, Rodrigue0Kolev, Boris1Université Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, Laboratoire de Mécanique Paris-Saclay, 91190, Gif-sur-Yvette, France.Université Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, Laboratoire de Mécanique Paris-Saclay, 91190, Gif-sur-Yvette, France.We address the problem, not of the determination–which usually needs numerical methods–but of an accurate analytical estimation of the distance of a raw elasticity tensor to cubic symmetry and to orthotropy. We point out that there are not one but several second-order tensors that carry the likely cubic/orthotropic coordinate system of the raw tensor. Since all the second-order covariants of an (exactly) cubic elasticity tensor are isotropic, distance estimates based only on such covariants are not always accurate. We extend to cubic symmetry and to orthotropy the technique recently suggested by Klimeš for transverse isotropy: solving analytically an auxiliary quadratic minimization problem whose solution is a second-order tensor that carries the likely cubic coordinate system. Numerical examples are provided, on which we evaluate the accuracy of different upper bounds estimates of the distance to cubic or orthotropic symmetry.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.246/Symmetry classElasticityDistance to a symmetry classCubic symmetryOrthotropyUpper bounds |
| spellingShingle | Desmorat, Rodrigue Kolev, Boris Upper bounds estimates of the distance to cubic or orthotropic elasticity Comptes Rendus. Mécanique Symmetry class Elasticity Distance to a symmetry class Cubic symmetry Orthotropy Upper bounds |
| title | Upper bounds estimates of the distance to cubic or orthotropic elasticity |
| title_full | Upper bounds estimates of the distance to cubic or orthotropic elasticity |
| title_fullStr | Upper bounds estimates of the distance to cubic or orthotropic elasticity |
| title_full_unstemmed | Upper bounds estimates of the distance to cubic or orthotropic elasticity |
| title_short | Upper bounds estimates of the distance to cubic or orthotropic elasticity |
| title_sort | upper bounds estimates of the distance to cubic or orthotropic elasticity |
| topic | Symmetry class Elasticity Distance to a symmetry class Cubic symmetry Orthotropy Upper bounds |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.246/ |
| work_keys_str_mv | AT desmoratrodrigue upperboundsestimatesofthedistancetocubicororthotropicelasticity AT kolevboris upperboundsestimatesofthedistancetocubicororthotropicelasticity |