Code_Aster Titre : SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable : KAZYMYRENKO Cyril

Transcription

1 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril Date 13/10/2016 Page 1/28 Clé V SSNP168 - Damage of test-tubes concrete of the type Nooru-Mohamed Summary The goal of this CAS-test is to validate models of damage and to characterize the concrete used within the framework of the Worm projectcors (Checking of the Containment of the Engines). It gathers results of three tests of damage carried out on notched samples. The boundary conditions those are obtaineds by correlation of images Suite with work of A. Carpiuc-Prisacari during its thesis [bib1]. This work SE are founded on the tests of Nooru-Mohamed carried out on test-tubes in double concretelies entaillées and solicited in mixed mode of cracking [bib2]. In this case, its loadings mechanicss are applieds by a hexapode, a testing machine to six degrees of freedom. Pour to obtain the required precision, the machine is pileée in real time in 3D by measurements of field. Fact noncommonplace loading and of one geometry of test-tube complex, this test is very discriminhasnt. It is however rich person because there is one zone of stable propagation of crack but also because measurements of field, at the same time 2D and 3D, are realized by correlation of digital images (CIN) constituting a considerable experimental database. These fields of experimental displacements are used to carry out digital simulations with a model of damage. Modeling is used D_PLAN_GRAD_VARI, which makes it possible to carry out the calculations of damage regularized by the gradient of damage for the problems under assumption of plane deformations. Test n 1 loading proportional on doubly notched test-tube Modeling A loading proportional on face A and law ENDO_SCALAIRE Modeling B loading proportional on face A and law ENDO_FISS_EXP Modeling C loading proportional on the face B and law ENDO_SCALAIRE Modeling D Chargement proportional on the face B and law ENDO_FISS_EXP Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

2 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril Date 13/10/2016 Page 2/28 Clé V Test n 2 non-proportional loading on doubly notched test-tube Modeling E loading notproportional on face A and law ENDO_SCALAIRE Modeling F non-proportional loading on face A and law ENDO_FISS_EXP Modeling G loading notproportional on the face B and law ENDO_SCALAIRE Modeling H non-proportional loading on the face B and law ENDO_FISS_EXP Test n 3 non-proportional loading in zigzag on simply notched test-tube Modeling I Chargement nonproportional in zigzag on face A and law ENDO_SCALAR Modeling J Chargement nonproportional in zigzag on face A and law ENDO_FISS_EXP Modeling K Chargement nonproportional in zigzag on the face B and law ENDO_SCALAR Modeling L Chargement nonproportional in zigzag on the face B and law ENDO_FISS_EXP Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

3 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 1 Problem of reference 1.1 GeometryS Date 13/10/2016 Page 3/28 Clé V Geometry test-tubes used for tests expérimentwith is given by figure 1 hereafter 200 This test-tube of dimension 200 mm 200 mm and thickness 50 mm have one or two notches of width and depth varied according to the tests carried out. During the tests, the test-tube is embedded according to FACE_INF and the loadings are applied to FACE_SUP thanks to the hexapode. FACE_SUP Z X FACE_INF Y Figure 1 Geometry of the test-tube real used for the experimental tests Measurements of fields of experimental displacements, obtained by correlation of images, are usedes to carry out the digital simulations. However, because of complexity of the experiment, the recovered values of displacement are not exactly those extractes of FACE_SUP and FACE_INF but of FC_HIGH and FC_LOW nearers center of the test-tube like illustrates it below figure 2 FACE_SUP FC_HAUT FC_BAS FACE_INF Figure 2 Boundary conditions measured then applied with simulations digital So the geometries retained for the two digital simulations are slightly different (reduction height). 200owing to the fact that the fields of displacements are extracted Moreover, 200 on FC_LOW instead of FACE_INF and because of elasticity of the concrete, FC_BAS is not any more embedded and FC_HAUT FC_HAUT undergoes from now on a field of displacements Geometries retaineds for the digital simulations, dependent on measurements of correlation of images, are presented in the following figures FC_BAS Y Y Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Z Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http// X FC_BAS Z X

4 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril Date 13/10/2016 Page 4/28 Clé V of Figure 3 Geometry of test-tube tests 1 and 2 Figure 4 Geometry of test-tube test 3 For more legibility, the total reference mark of the test-tube was modified between the experimental tests and the digital simulations so that the tractive efforts evolve according to the axis Y and the shearing forces according to axis X. Test n 1 and 2 doubly notched test-tube (modelisation A B C D E F G and H ) One considers a plate 2D dimension L=200 mm H =100 mm doubly notched. Each of the two notches has a height of 5 mm and one depth of 40 mm ET is symmetrical compared to the horizontal median axis and vertical. Test n 3 test-tube simply notched and loading in zigzag (modelisation I J K and L ) One considers a plate 2D dimension L=200 mm H =150 mm doubly notched. notch is positioned on the right side of the test-tube, has a height of 5 mm and one depth of 25 mm ET is symmetrical compared to the horizontal median axis. 1.2 Properties of material The material considered is compared to the concrete (one works on a millimetre-length scale). Characteristics rubber bands E =2.1E10 Pa =2.1E4 N/mm 2 =0.2 Elastic limit in traction of the law of damage σ t =3.9E6 Pa=3.9 N/mm 2 Elastic limit in compression of the law of damage σ c =85.E6 Pa=85 N/mm 2 for the law ENDO_SCALAIRE σ c =28.5E6 Pa=28.5 N/mm 2 for the law ENDO_FISS_EXP Elastic limit in pure shearing of the law of damage τ=3.25e6 Pa=3.25 N/mm 2 Rate of refund of energy by surface of crack (constant of Griffith) G f =100 J/m2 =0.1 N/mm Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

5 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 1.3 Date 13/10/2016 Page 5/28 Clé V Boundary conditions and loadings LoadingS As considering previously, the loadings (fields of displacements) are extracted from experimental tests by correlation of images. These loadings those are not really extracteds of FACE_SUP ET FACE_INF but of sections closer to the center of the test-tube named FC_HIGH ET FC_LOW. Rigid edge Lbe first digital simulations reveal damage parasite on the edges of the test-tube. By the continuation, the damage will be propagated while following the two horizontal interfaces as illustrated in the figure 5. This damage is not observed on the experimental tests. Figure 5 Starting of the damage parasitizes with interfaces So that this damage is artificially blocked, one crée two layers on the level of the interfaces FC_HIGH ET FC_LOW. These two layers, named respectively SINGU_H and SINGU_B in the grid, consist of a material more resistant than the concrete. This method perhaps equivalent to the real case via the treatments of surfaces. Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

6 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 2 Reference solution 2.1 Method of calculating Date 13/10/2016 Page 6/28 Clé V The results are experimental. The images below show the propagation of cracks in the test-tube according to the test considered. Test n 1 Loading proportional (modelisation A B C and D ) (A) (b) Figure 6 Comparison enters the ways of cracking of the model of damage (thick black lines) and of the experiment (fine black lines) face 1 (A), and of face 2 (b). Essai n 3 Loading not proportional zigzag (modelisation (A) I J K and L ) (b) Figure 7 Trajets of cracking obtained expérimentally for a loading nonproportional of the face 1 (A), Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

7 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril Date 13/10/2016 Page 7/28 Clé V and of face 2 (b). Answer force-displacement Essai n 1 Loading proportional (modelisation A B C and D ) (A) (b) Figure 8 Curve force-déplacement experimental in traction (a) and shearing (b). E ssai n 3 Loading nonproportional zigzag (m odelisation (A) I J K and L ) (b) Figure 9 Curve force-déplacement experimental in traction (a) and shearing (b). 2.2 Sizes and results of reference Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

8 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril Date 13/10/2016 Page 8/28 Clé V One notes respectively and F s (δs ) the two answers force-displacement in traction and shearing. The values of reference result from experimental data Essai n 1 Loading proportional (modelisation Modelisation A A B C and D ) δ s=4, μ m kn δ s= μ m kn δ s= μ m kn δn = μ m kn δn = μ m kn δn = μ m kn Modelisation B δ s= μ m kn δ s= μ m kn δ s= μ m kn δn = μ m kn δn = μ m kn δn = μ m kn Modelisation C δ s= μ m kn δ s= μ m kn δ s= μ m kn δn = μ m kn δn = μ m kn δn = μ m kn Modelisation D Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

9 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril Date 13/10/2016 Page 9/28 Clé V δ s= μ m kn δ s= μ m kn δ s= μ m kn δn = μ m kn δn = μ m kn δn = μ m kn Essai n 2 Loading notproportional (m odelisation Modelisation E E F G and H ) δ s= μ m kn δ s= μ m kn δ s= μ m kn δn = μ m kn δn = μ m kn δn = μ m kn Modelisation F δ s= μ m kn δ s= μ m kn δ s= μ m kn δn = μ m kn δn = μ m kn δn = μ m kn Modelisation G Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

10 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril Date 13/10/2016 Page 10/28 Clé V δ s= μ m kn δ s= μ m kn δ s= μ m kn δn = μ m kn δn = μ m kn δn = μ m kn Modelisation H δ s= μ m kn δ s= μ m kn δ s= μ m kn δn = μ m kn δn = μ m kn δn = μ m kn Essai n 3 Loading notproportional zigzag (modelisation Modelisation I I J K and L ) δ s= μ m kn δ s= μ m kn δ s= μ m kn δn = μ m kn δn = μ m kn δn = μ m kn Modelisation J Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

11 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril kn δ s= μ m kn δ s= μ m kn δn = μ m kn δn = μ m kn δn = μ m kn Modelisation K δ s= μ m kn δ s= μ m kn δ s= μ m kn δn = μ m kn δn = μ m kn δn = μ m -10,857 kn Modelisation L δ s= μ m δ s= μ m kn δ s= μ m kn δ s= μ m kn 2.3 Date 13/10/2016 Page 11/28 Clé V δn = μ m kn δn = μ m kn δn = μ m -10,857 kn Uncertainties on the solution Experimental results. 2.4 [bib1] ReferenceS bibliographicals A. Carpiuc-Prisacari Innovative tests for characterizing mixed-mode fractures of concrete from pre-defined to interactive and hybrid tests, Thesis of doctorate, EDF R & D, ENS Cachan, 2015 Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

12 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril [bib2] Date 13/10/2016 Page 12/28 Clé V M.B. Nooru-Mohamed, Mixed-mode fractures of concrete experimental year approach. Thesis of Doctorate, Technische Universiteit Delft (1992). Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

13 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 3 Modeling A 3.1 Characteristics of modeling Date 13/10/2016 Page 13/28 Clé V One consider a modeling of damage D_PLAN_GRAD_VARI who, under the assumption of plane deformation, a Lagrangian mixed formulation of damage is regularized by the gradient of damage. Law of damage (material) ENDO_SCALAIRE Characteristics related to the not-local law of damage c= N ; p=1.5 ; m= ; pena=25 ; c volu = ;, c comp= ; CE which corresponds to the zone of damage 1 D equalize with D=3 mm. The correspondence with the physical parameters is the following one c=3 /8 D G f ; k = 3G f 2kE ; m= 2 ; 4D ft [( 2 ] 2(1+ν) (σ c +σ t )τ 3 1+ν (σc σ t )τ 3 c comp= ; cvolu = 1 ; 1 2 ν 2 σt σ c 1 2 ν 2 σt σ c 3.2 ) Characteristics of the grid grid contains 3278 elements TRIA6. The zone of propagation of crack is refined of advantage. Figure 10 Grid of the zone of propagation of crack of refined advantage 3.3 Sizes tested and results One test curved force-displacement for weak damage where the variations compared to the experiment are acceptable. Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

14 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril (A) Date 13/10/2016 Page 14/28 Clé V (b) Figure 11 Comparison curves force-displacement for the law ENDO_SCALAIRE in traction (A) and shearing (b) One notes the two answers force-displacement in traction and shearing. δ s=4, μ m kn 6% δ s= μ m kn 7% δ s= μ m kn 2% δn = μ m kn 2% δn = μ m kn 4% δn = μ m kn Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

15 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 4 Modeling B 4.1 Characteristics of modeling Date 13/10/2016 Page 15/28 Clé V One consider a modeling of damage D_PLAN_ GRAD_VARI who, under the assumption of plane deformation, a Lagrangian mixed formulation of damage is regularized by the gradient of damage. Law of damage (material) ENDO_FISS_EXP Properties materials are defined using the order DEFI_MATER_GC. 4.2 Characteristics of the grid L E grid is identical to that of m odelisation A. 4.3 Sizes tested and results One test curved force-displacement for weak damage where the variations compared to the experiment are acceptable. (A) (b) Figure 12 Comparison curves force-displacement for the law ENDO_MADES_EXP in traction (A) and shearing (b) way of cracking also seems to be close to the experimental results. Figure 1 3 Comparison of the way of cracking between digital and experimental test One notes the two answers force-displacement in traction and shearing. Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

16 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril Date 13/10/2016 Page 16/28 Clé V δ s= μ m kn 4% δ s= μ m kn δ s= μ m kn 7 δn = μ m kn 2% δn = μ m kn δn = μ m kn Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

17 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 5 Modeling C 5.1 Characteristics of modeling Date 13/10/2016 Page 17/28 Clé V Modelisation identical to modeling A by considering the mechanical loading of the face B of the testtube. 5.2 Characteristics of the grid LE grid is identical to that of modelisation 5.3 A. Sizes tested and results One notes F s (δs ) the two answers force-displacement in traction and shearing. δ s= μ m kn 5% δ s= μ m kn 10% δ s= μ m kn 8% δn = μ m kn 2% δn = μ m kn δn = μ m kn 3% Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

18 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 6 Modeling D 6.1 Characteristics of modeling M odelisation identical to modeling tube. 6.2 Date 13/10/2016 Page 18/28 Clé V B by considering the mechanical loading of the face B of the test- Characteristics of the grid LE grid is identical to that of modelisation A. 6.3 Sizes tested and results One notes the two answers force-displacement in traction and shearing. δ s= μ m kn 3% δ s= μ m kn δ s= μ m kn 2% δn = μ m kn 2% δn = μ m kn δn = μ m kn 2% Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

19 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 7 Modeling E 7.1 Characteristics of modeling Date 13/10/2016 Page 19/28 Clé V One consider a modeling of damage D_PLAN_ GRAD_VARI who, under the assumption of plane deformation, a Lagrangian mixed formulation of damage is regularized by the gradient of damage. Law of damage (material) ENDO_SCALAIRE 7.2 Characteristics of the grid LE grid is identical to that of modelisation A. 7.3 Sizes tested and results One notes the two answers force-displacement in traction and shearing. δ s= μ m kn 10% δ s= μ m kn δ s= μ m kn δn = μ m kn 3% δn = μ m kn 5% δn = μ m kn 12% Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

20 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 8 Modeling F 8.1 Characteristics of modeling Date 13/10/2016 Page 20/28 Clé V One consider a modeling of damage D_PLAN_ GRAD_VARI who, under the assumption of plane deformation, a Lagrangian mixed formulation of damage is regularized by the gradient of damage. Law of damage (material) ENDO_ FISS_EXP 8.2 Characteristics of the grid LE grid is identical to that of modelisation A. 8.3 Sizes tested and results One notes the two answers force-displacement in traction and shearing. δ s= μ m kn δ s= μ m kn 2% δ s= μ m kn 8% δn = μ m kn 3% δn = μ m kn 2% δn = μ m kn 5% Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

21 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 9 Modeling G 9.1 Characteristics of modeling Modelisation identical to modeling tube. 9.2 Date 13/10/2016 Page 21/28 Clé V E by considering the mechanical loading of the face B of the test- Characteristics of the grid LE grid is identical to that of modelisation A. 9.3 Sizes tested and results One notes the two answers force-displacement in traction and shearing. δ s= μ m kn 9% δ s= μ m kn 1 δ s= μ m kn 5% δn = μ m kn 13% δn = μ m kn 6% δn = μ m kn 7% Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

22 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 10 Date 13/10/2016 Page 22/28 Clé V Modeling H 10.1 Characteristics of modeling Modelisation identical to modeling tube. F by considering the mechanical loading of the face B of the test Characteristics of the grid LE grid is identical to that of modelisation A Sizes tested and results One notes the two answers force-displacement in traction and shearing. δ s= μ m kn 4% δ s= μ m kn 8% δ s= μ m kn 8% δn = μ m kn 8% δn = μ m kn 5% δn = μ m kn Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

23 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 11 Date 13/10/2016 Page 23/28 Clé V Modeling I 11.1 Characteristics of modeling One consider a modeling of damage D_PLAN_ GRAD_VARI who, under the assumption of plane deformation, a Lagrangian mixed formulation of damage is regularized by the gradient of damage. Law of damage (material) ENDO_SCALAIRE 11.2 Characteristics of the grid LE grid contains 1684 elements TRIA6. The zone of propagation of crack is refined of advantage. Figure 1 4 Grid of the zone of propagation of crack of refined advantage 11.3 Sizes tested and results One test curved force-displacement for UN weak damage where the variations compared to the experiment are acceptable. Figure 15 Comparaison Courbe force-déplacement experimental in traction (a) and shearing (b). One notes the two answers force-displacement in traction and shearing. Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

24 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril Date 13/10/2016 Page 24/28 Clé V δ s= μ m kn δ s= μ m kn 6% δ s= μ m kn 4% δn = μ m kn 3% δn = μ m kn δn = μ m kn Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

25 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 12 Date 13/10/2016 Page 25/28 Clé V Modeling J 12.1 Characteristics of modeling One consider a modeling of damage D_PLAN_ GRAD_VARI who, under the assumption of plane deformation, a Lagrangian mixed formulation of damage is regularized by the gradient of damage. Law of damage (material) ENDO_FISS_EXP Properties materials are defined using the order DEFI_MAT ER _GC Characteristics of the grid LE grid is identical to that of modeling I Sizes tested and results One test curved force-displacement for weak damage where the variations compared to the experiment are acceptable. Figure 15 Comparaison Courbe force-déplacement experimental in traction (a) and shearing (b). One Nexcept the two answers force-displacement in traction and shearing. δ s= μ m kn 2% δ s= μ m kn 7% δ s= μ m kn 4% δn = μ m kn 3% δn = μ m kn 6% δn = μ m kn 3% Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

26 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 13 Date 13/10/2016 Page 26/28 Clé V Modeling K 13.1 Characteristics of modeling Modelisation identical to modeling tube. I by considering the mechanical loading of the face B of the test Characteristics of the grid LE grid is identical to that of modeling I Sizes tested and results One notes F s (δs ) the two answers force-displacement in traction and shearing. δ s= μ m kn 2% δ s= μ m kn 4% δ s= μ m kn 6% δn = μ m kn 9% δn = μ m kn δn = μ m -10,857 kn 2% Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

27 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 14 Date 13/10/2016 Page 27/28 Clé V Modeling L 14.1 Characteristics of modeling Modelisation identical to modeling tube. J by considering the mechanical loading of the face B of the test Characteristics of the grid LE grid is identical to that of modeling I Sizes tested and results One notes the two answers force-displacement in traction and shearing. δ s= μ m kn 2% δ s= μ m kn 4% δ s= μ m kn 7% δn = μ m kn 8% δn = μ m kn 3% δn = μ m -10,857 kn 3% Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//

28 Titre SSNP168 - Endommagement d'éprouvettes béton de typ[...] Responsable KAZYMYRENKO Cyril 15 Date 13/10/2016 Page 28/28 Clé V Summary of the results This test shows the robustness and the performance of modeling GRAD_VARI. Laws ENDO_SCALAIRE and ENDO_FISS_EXP reproduce the way of cracking well obtained in experiments, nevertheless the answer in force-displacement is coherent only for one level of damage weak. Warning The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is Copyright 2018 EDF R&D - Licensed under the terms of the GNU FDL (http//