Comptes Rendus
Spontaneous articles
A strain based Lipschitz regularization for materials undergoing damage
Comptes Rendus. Mécanique, Volume 351 (2023), pp. 125-149.

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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmeca.176
Keywords: Localization, Strain gradient limiter, Regularization, Softening, Damage

Vasudevan Kamasamudram 1; Laurent Stainier 1

1 Nantes Université, Ecole Centrale de Nantes, CNRS, GeM, 1 rue de la Noë, 44000 Nantes, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@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  - 
%0 Journal Article
%A Vasudevan Kamasamudram
%A Laurent Stainier
%T A strain based Lipschitz regularization for materials undergoing damage
%J Comptes Rendus. Mécanique
%D 2023
%P 125-149
%V 351
%I Académie des sciences, Paris
%R 10.5802/crmeca.176
%G en
%F CRMECA_2023__351_G1_125_0
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/

[1] Ron H. J. Peerlings Enhanced damage modelling for fracture and fatigue, Ph. D. Thesis, Technische Universiteit Eindhoven, Eindhoven, Deutschland (1999) | DOI

[2] Ron H. J. Peerlings; Marc G. D. Geers; René De Borst; W. A. M. Brekelmans A critical comparison of nonlocal and gradient-enhanced softening continua, Int. J. Solids Struct., Volume 38 (2001) no. 44-45, pp. 7723-7746 | DOI | Zbl

[3] Ron H. J. Peerlings; René De Borst; W. A. M. Brekelmans; Marc G. D. Geers Localisation issues in local and nonlocal continuum approaches to fracture, Eur. J. Mech., A, Solids, Volume 21 (2002) no. 2, pp. 175-189 | DOI | MR | Zbl

[4] Gilles Pijaudier-Cabot; Zdeněk P. Bažant Nonlocal damage theory, J. Eng. Mech., Volume 113 (1987) no. 10, pp. 1512-1533 | DOI

[5] Raymond David Mindlin; N. N. Eshel On first strain-gradient theories in linear elasticity, Int. J. Solids Struct., Volume 4 (1968) no. 1, pp. 109-124 | DOI | Zbl

[6] Z. Cedric Xia; John W. Hutchinson Crack tip fields in strain gradient plasticity, J. Mech. Phys. Solids, Volume 44 (1996) no. 10, pp. 1621-1648 | DOI

[7] Trung Le Duc; Jean-Jacques Marigo; Corrado Maurini; Stefano Vidoli Strain-gradient vs damage-gradient regularizations of softening damage models, Comput. Methods Appl. Mech. Eng., Volume 340 (2018), pp. 424-450 | DOI | MR | Zbl

[8] Eric Lorentz; Stéphane Andrieux Analysis of non-local models through energetic formulations, Int. J. Solids Struct., Volume 40 (2003) no. 12, pp. 2905-2936 | DOI | MR | Zbl

[9] Kim Pham; Jean-Jacques Marigo; Corrado Maurini The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models, J. Mech. Phys. Solids, Volume 59 (2011) no. 6, pp. 1163-1190 | DOI | MR | Zbl

[10] Jean-Jacques Marigo; Corrado Maurini; Kim Pham An overview of the modelling of fracture by gradient damage models An overview of the modelling of fracture by gradient damage models An overview of the modelling of fracture by gradient damage models, Meccanica (2016) no. 12, p. 51 | DOI | Zbl

[11] Christian Miehe; Lisa Marie Schänzel Phase field modeling of fracture in rubbery polymers. Part I: Finite elasticity coupled with brittle failure, J. Mech. Phys. Solids, Volume 65 (2014) no. 1, pp. 93-113 | DOI | MR | Zbl

[12] Christian Miehe; Lisa Marie Schänzel; Heike Ulmer Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids, Comput. Methods Appl. Mech. Eng., Volume 294 (2015), pp. 449-485 | DOI | MR | Zbl

[13] N. Moës; Claude Stolz; P. E. Bernard; Nicolas Chevaugeon A level set based model for damage growth: The thick level set approach, Int. J. Numer. Methods Eng., Volume 86 (2011) no. 3, pp. 358-380 | DOI | MR | Zbl

[14] Nunziante Valoroso; Claude Stolz Graded damage in quasi-brittle solids, Int. J. Numer. Methods Eng., Volume 123 (2022) no. 11, pp. 2467-2498 | DOI | MR

[15] Nicolas Moës; Nicolas Chevaugeon Lipschitz regularization for softening material models: The Lip-field approach, Comptes Rendus. Mécanique, Volume 349 (2021) no. 2, pp. 415-434 | DOI

[16] T. Kirchdoerfer; Michael Ortiz Data-driven computational mechanics, Comput. Methods Appl. Mech. Eng., Volume 304 (2016), pp. 81-101 | DOI | MR | Zbl

[17] Robert Eggersmann; T. Kirchdoerfer; Stefanie Reese; Laurent Stainier; Michael Ortiz Model-Free Data-Driven inelasticity, Comput. Methods Appl. Mech. Eng., Volume 350 (2019), pp. 81-99 | DOI | MR | Zbl

[18] K. Karapiperis; Laurent Stainier; Michael Ortiz; J. E. Andrade Data-Driven multiscale modeling in mechanics, J. Mech. Phys. Solids, Volume 147 (2021), 104239 | DOI | MR

[19] K. Karapiperis; Michael Ortiz; J. E. Andrade Data-Driven nonlocal mechanics: Discovering the internal length scales of materials, Comput. Methods Appl. Mech. Eng., Volume 386 (2021), 114039 | DOI | MR | Zbl

[20] Alexander Mielke Evolution of rate-independent systems, Handbook of differential equations: Evolutionary equations. Vol. II, Volume 2, Elsevier, 2005, pp. 461-559 | Zbl

[21] Bernard Halphen; Quoc Son Nguyen Sur les matériaux standards généralisés, J. Méc., Paris, Volume 14 (1975), pp. 39-63 | Zbl

[22] Harm Askes; Miguel A. Gutiérrez Implicit gradient elasticity, Int. J. Numer. Methods Eng., Volume 67 (2006) no. 3, pp. 400-416 | DOI | MR | Zbl

[23] Franco Brezzi On the Existence, Uniqueness and Approximation of Saddle-Point Problems Arising from Lagrangian Multipliers, Publications des séminaires de mathématiques et informatique de Rennes (1974) no. S4, 1 | Numdam | Zbl

[24] Dieter Kraft A software package for sequential quadratic programming, DFVLR Forschungsber., Volume 28 (1988) | Zbl

[25] N. Singh; C. V. Verhoosel; René De Borst; E. H. Van Brummelen A fracture-controlled path-following technique for phase-field modeling of brittle fracture, Finite Elem. Anal. Des., Volume 113 (2016), pp. 14-29 | DOI | MR

Cited by Sources:

Comments - Policy