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2. Using a penalty term to deal with spurious oscillations in second gradient finite elements.

Author

Soufflet, Marc, Jouan, Gwendal, Kotronis, Panagiotis, and Collin, Frédéric

Subjects
*FINITE element method, *STRAINS & stresses (Mechanics), *COMPUTER simulation, *FRACTURE mechanics, *ELASTICITY
Abstract

It is well known that it is necessary to introduce a length scale parameter in a continuum damage mechanics model to correctly simulate strain localization. The second gradient model, a special case of kinematically enriched continua, considers an internal length parameter by taking into account the second-order derivatives of the displacements in the virtual power principle. In this paper, we show that the original second gradient finite element of Chambon and co-workers can present spurious oscillations, especially for mode I crack propagation problems. After providing the plane stress second gradient constitutive law, we propose to add a penalty term in the original formulation in order to improve numerical convergence and to avoid spurious oscillations in the local variables distributions. Two numerical examples using classical damage mechanics laws, a three-point reinforced concrete beam and a trapezoidal notched specimen are used to test the performance of the formulation. Parametrical studies are also shown on the influence of the penalty parameter. The problem of unrealistic damage spreading for damage values close to 1, occurring often in mode I crack propagation problems, is finally discussed. [ABSTRACT FROM AUTHOR]

Published
2019
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3. A Plane Stress Second-Gradient Finite Element

Author

Soufflet, Marc, Kotronis, Panagiotis, Collin, Frédéric, Institut de Recherche en Génie Civil et Mécanique (GeM), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Département des Géoressources, Géotechnologies et Matériaux de construction (GEOMAC), and Université de Liège

Subjects
[SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph], [SPI.MAT]Engineering Sciences [physics]/Materials
Published
2013

4. Applying a second gradient theory on reinforced concrete structural elements

Author

Soufflet, Marc, Jouan, Gwendal, Kotronis, Panagiotis, Collin, Frédéric, Institut de Recherche en Génie Civil et Mécanique (GeM), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Département des Géoressources, Géotechnologies et Matériaux de construction (GEOMAC), and Université de Liège

Subjects
[SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph], [SPI.MAT]Engineering Sciences [physics]/Materials
Published
2013

5. Modélisation de structures voiles en béton armé soumises à du cisaillement

Author

Soufflet, Marc, Kotronis, Panagiotis, Collin, Frédéric, Institut de Recherche en Génie Civil et Mécanique (GeM), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Département des Géoressources, Géotechnologies et Matériaux de construction (GEOMAC), and Université de Liège

Subjects
lois d'endommagement, fissuration, [SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph], cisaillement, [SPI.MAT]Engineering Sciences [physics]/Materials
Abstract

Within the French National Program CEOS.fr reinforced concrete shear walls were tested in order to create a database and thereby compare and improve the numerical tools to characterize cracks under severe shear stresses. In this article we present the numerical simulation of the specimen 3 of the program using a stress plane model and two different constitutive laws: the Mazars and the Damage_TC models. Although these laws are extensively validated in traction-compression conditions, it is necessary to evaluate their performances under important shear stresses.; Dans le cadre du programme CEOS.fr, des campagnes expérimentales sur des voiles en béton armé soumis à des chargements statiques sévères ont établi une importante base de données permettant la calibration et l'amélioration des outils numériques pour caractériser l'ouverture de fissures sous l'effet de contraintes de cisaillement. L'étude numérique présentée dans ce rapport consiste à reproduire l'essai du voile 3 grâce à une modélisation élément fini 2D en contraintes planes en étudiant la performance de deux lois d'endommagement du code Cast3M : La loi Mazars et la loi Damage_TC. Si ces lois sont extensivement validées dans le passé dans des cas de modèles soumis à des contraintes de traction-compression, il convient de les évaluer sur des structures soumises à de fortes contraintes en cisaillement.

Published
2013

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