Code_Aster. Law of behavior BETON_REGLE_PR

Transcription

1 Titre : Loi de comportement BETON_REGLE_PR Date : 21/07/2017 Page : 1/5 Law of behavior BETON_REGLE_PR Summary: This documentation presents the law BETON_REGLE_PR established by the company Sixense-NECS within the framework of the community Code_hasster free. It is about a lawful law [bib1], written by combining two laws 1D.

2 Titre : Loi de comportement BETON_REGLE_PR Date : 21/07/2017 Page : 2/5 Contents 1 Presentation of the law BETON_REGLE_PR Description of the internal variables MatrixS of elementary rigiditys Limitations of the law Features and validation Functionality Checking & Validation Bibliography Description of the versions of the document...5

3 Titre : Loi de comportement BETON_REGLE_PR Date : 21/07/2017 Page : 3/5 1 Presentation of the law BETON_REGLE_PR The law of behavior is of type twice 1D in the clean reference mark of deformation (confused with the clean reference mark of constraint). Only one behavior 1D is described, which is of elastic type nonlinear. In compression, it is the law in the regular manner definite right-angled parabola [bib1]; the constraint is given by the following relations: {σ=σ c y [ 1 ( 1 ε ε 0 ) n ] si 0<ε ε 0 σ=σ y c si ε>ε 0 (partie rectangle) In traction the law is of standard triangle [bib2]: σ=e ε si ε σ t y E avec σ=σ t y+e T [ The parameters materials associated are the following: (partie parabole) E : Young modulus; t y : the constraint with the peak in traction ( f t ); E T : the tangent module (generally understood enters E 3 y c : the maximum constraint in compression ( f c ); n : the exhibitor of the law of work hardening in compression; c : the deformation to which one reaches y c. The answer stress-strain is given on the following figure: (1) ε σ t y E ] (2) and E 10 ); Figure 1-a: stress-strain curve in 1D So that slopes at the origin in traction and in compression are identical, one can choose the parameters in such way that: =0 =E = f n c (3) c

4 Titre : Loi de comportement BETON_REGLE_PR Date : 21/07/2017 Page : 4/5 2 Description of the internal variables There is no internal variable for this model. 3 MatrixS of elementary rigiditys The matrices of rigidity of the type tangent and secant are available for this law. By in Code_hasster, the tangent matrix is used. To use the secant matrix, or stamps of discharge, it is necessary to add the keyword PAS_MINI_ELAS with a value larger than the interval between two moments of calculation in the keyword factor NEWTON non-linear operators. The secant matrix is calculated starting from the secant module in each principal direction i : E i s = i / i if ε i 0 E i s =E if ε i =0 4 Limitations of the law The law BETON_REGLE_PR present two important limitations: the model is elastic: the discharge is thus not taken into account in the formulation of the law. S ways of load and discharge are thus identicals. It is thus disadvised using this law for cases of nonmonotonous, cyclic or dynamic loading. the model does not represent the Fish effect: the law is of type twice 1D where the behavior in the two principal directions of deformation is treated independently. 5 Features and validation 5.1 Functionality The law is available only in 2D and is accessible with modelings D_PLAN, C_PLAN and DKT. 5.2 Checking & Validation The law BETON_REGLE_PR is checked bys case following tests : SSNP129 [V ] Validation of the law BETON_REGLE_PR on an element DKT SSNS114 [V ] Degradation of a reinforced concrete plate under requests varied with the law BETON_REGLE_PR The validation of the law was also made by comparison with the experimental results got on a reinforced concrete flagstone subjected to its actual weight and a pressure in the center of the flagstone [bib1]. 6 Bibliography

5 Titre : Loi de comportement BETON_REGLE_PR Date : 21/07/2017 Page : 5/5 1. BAEL 91 revised 99 (NF P ) 2. VB. Zhang, R. Masmoudi, B. Benmokrane, Behaviour of one-way concrete slabs reinforced with CFRP grid reinforcements, Constructions and Materials Buildings, 18, pp Description of the versions of the document Aster Author (S) Organization (S) 11.3 S. Michel S. Michel S. Michel- Description of the modifications Initial text Addition Stamps secant Update of the cases tests and section on the limitations of the law