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.
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Vasudevan Kamasamudram 1; Laurent Stainier 1
CC-BY 4.0
@article{CRMECA_2023__351_G1_125_0,
author = {Vasudevan Kamasamudram and Laurent Stainier},
title = {A strain based {Lipschitz} regularization for materials undergoing damage},
journal = {Comptes Rendus. M\'ecanique},
pages = {125--149},
publisher = {Acad\'emie des sciences, Paris},
volume = {351},
year = {2023},
doi = {10.5802/crmeca.176},
language = {en},
}
TY - JOUR AU - Vasudevan Kamasamudram AU - Laurent Stainier TI - A strain based Lipschitz regularization for materials undergoing damage JO - Comptes Rendus. Mécanique PY - 2023 SP - 125 EP - 149 VL - 351 PB - Académie des sciences, Paris DO - 10.5802/crmeca.176 LA - en ID - CRMECA_2023__351_G1_125_0 ER -
Vasudevan Kamasamudram; Laurent Stainier. A strain based Lipschitz regularization for materials undergoing damage. Comptes Rendus. Mécanique, Volume 351 (2023), pp. 125-149. doi : 10.5802/crmeca.176. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.176/
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