A strain based Lipschitz regularization for materials undergoing damage
Data Driven Computational Mechanics (DDCM) solves the boundary value problem by directly relying on the strain-stress data, bypassing the need for a constitutive model. In presence of materials exhibiting a softening response, Finite Element analyses performed with a constitutive model typically use...
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Académie des sciences
2023-03-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.176/ |
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| author | Kamasamudram, Vasudevan Stainier, Laurent |
| author_facet | Kamasamudram, Vasudevan Stainier, Laurent |
| author_sort | Kamasamudram, Vasudevan |
| collection | DOAJ |
| description | Data Driven Computational Mechanics (DDCM) solves the boundary value problem by directly relying on the strain-stress data, bypassing the need for a constitutive model. In presence of materials exhibiting a softening response, Finite Element analyses performed with a constitutive model typically use a length scale, which can be introduced into the problem in multiple ways. A few commonly used ways include the addition of the gradient of damage variable in the energy density functional, using the gradient of strain while evaluating the internal variable, and so on. However, in the context of DDCM, these techniques may not be effective as the internal variables are not explicitly defined. Hence, the current article introduces a regularization technique, where the gradient of strain is constrained to lie within some interval. This prevents strain localization within an element by introducing a length scale into the problem. This article demonstrates the effectiveness of such a regularization technique in the case of 1D problems using a constitutive model while comparing its performance with strain gradient (SG) models. |
| format | Article |
| id | doaj-art-5aa730d7617f4bd7b0adafddae5570ac |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-5aa730d7617f4bd7b0adafddae5570ac2025-02-07T13:46:51ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-03-01351G112514910.5802/crmeca.17610.5802/crmeca.176A strain based Lipschitz regularization for materials undergoing damageKamasamudram, Vasudevan0Stainier, Laurent1Nantes Université, Ecole Centrale de Nantes, CNRS, GeM, 1 rue de la Noë, 44000 Nantes, FranceNantes Université, Ecole Centrale de Nantes, CNRS, GeM, 1 rue de la Noë, 44000 Nantes, FranceData Driven Computational Mechanics (DDCM) solves the boundary value problem by directly relying on the strain-stress data, bypassing the need for a constitutive model. In presence of materials exhibiting a softening response, Finite Element analyses performed with a constitutive model typically use a length scale, which can be introduced into the problem in multiple ways. A few commonly used ways include the addition of the gradient of damage variable in the energy density functional, using the gradient of strain while evaluating the internal variable, and so on. However, in the context of DDCM, these techniques may not be effective as the internal variables are not explicitly defined. Hence, the current article introduces a regularization technique, where the gradient of strain is constrained to lie within some interval. This prevents strain localization within an element by introducing a length scale into the problem. This article demonstrates the effectiveness of such a regularization technique in the case of 1D problems using a constitutive model while comparing its performance with strain gradient (SG) models.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.176/LocalizationStrain gradient limiterRegularizationSofteningDamage |
| spellingShingle | Kamasamudram, Vasudevan Stainier, Laurent A strain based Lipschitz regularization for materials undergoing damage Comptes Rendus. Mécanique Localization Strain gradient limiter Regularization Softening Damage |
| title | A strain based Lipschitz regularization for materials undergoing damage |
| title_full | A strain based Lipschitz regularization for materials undergoing damage |
| title_fullStr | A strain based Lipschitz regularization for materials undergoing damage |
| title_full_unstemmed | A strain based Lipschitz regularization for materials undergoing damage |
| title_short | A strain based Lipschitz regularization for materials undergoing damage |
| title_sort | strain based lipschitz regularization for materials undergoing damage |
| topic | Localization Strain gradient limiter Regularization Softening Damage |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.176/ |
| work_keys_str_mv | AT kamasamudramvasudevan astrainbasedlipschitzregularizationformaterialsundergoingdamage AT stainierlaurent astrainbasedlipschitzregularizationformaterialsundergoingdamage AT kamasamudramvasudevan strainbasedlipschitzregularizationformaterialsundergoingdamage AT stainierlaurent strainbasedlipschitzregularizationformaterialsundergoingdamage |