1. Reference problem#

1.1. Geometry and boundary conditions#

_images/10000000000001FE000001EB678C70837458F4BB.png

Figure 1.1-a: Geometry and boundary conditions

1.2. Material properties#

Steel: elastic

\(E\mathrm{=}2.1\mathrm{\times }{10}^{5}\mathit{MPa}\)

\(\nu \mathrm{=}0.3\)

Concrete: elastic

\(E\mathrm{=}1.55\mathrm{\times }{10}^{4}\mathit{MPa}\)

\(\nu \mathrm{=}0.17\)

Joint element:

  • law of behavior ELAS with the following parameters:

\(E\mathrm{=}1.55\mathrm{\times }{10}^{4}\mathit{MPa}\)

\(\nu \mathrm{=}0.17\)

  • law of behavior JOINT_BA with the following parameters:

  • Initial settings:

penetration coefficient:

\(\mathit{Hpen}\mathrm{=}0.64\mathit{mm}\)

(keyword: HPEN)

stiffness module:

\({G}_{\mathit{lia}}\mathrm{=}{\mathrm{6.65x10}}^{3}\mathit{MPa}\)

(keyword: GTT)

  • Tangential damage parameters:

elastic deformation threshold:

\({\varepsilon }_{\gamma }^{0}\mathrm{=}5\mathrm{\times }{10}^{\mathrm{-}4}\)

(key word: GAMD0)

damage coefficient region 1:

\({\mathit{Ad}}_{1}\mathrm{=}1.0\)

(keyword: AD1)

damage coefficient region 1:

\({\mathit{Bd}}_{1}\mathrm{=}0.5\)

(keyword: BD1)

threshold of major landslides:

\({\varepsilon }_{\gamma }^{2}\mathrm{=}9.6\mathrm{\times }{10}^{\mathrm{-}1}\)

(keyword: GAMD2)

damage coefficient region 2:

\({\mathit{Ad}}_{2}\mathrm{=}4\mathrm{\times }{10}^{\mathrm{-}5}{\mathit{MPa}}^{\mathrm{-}1}\)

(keyword: AD2)

damage coefficient region 2:

\({\mathit{Bd}}_{2}\mathrm{=}1.0\)

(keyword: BD2)

  • Parameters for crack friction and confinement:

material coefficient by friction:

\(\gamma \mathrm{=}10.0\mathit{MPa}\)

(keyword: VIFROT)

coefficient by kinematic work hardening:

\(\alpha \mathrm{=}4\mathrm{\times }{10}^{\mathrm{-}1}{\mathit{MPa}}^{\mathrm{-}1}\)

(keyword: FA)

confinement coefficient:

\(c\mathrm{=}1.0\)

(keyword: FC)

  • Normal damage parameters:

critical normal deformation (opening):

\({\varepsilon }_{N}^{0}\mathrm{=}9\mathrm{\times }{10}^{\mathrm{-}1}\)

(keyword: EPSTR0)

normal damage coefficient:

\({\mathit{Ad}}_{N}\mathrm{=}1\mathrm{\times }{10}^{\mathrm{-}9}{\mathit{MPa}}^{\mathrm{-}1}\)

(keyword: ADN)

normal damage coefficient:

\({\mathit{Bd}}_{N}\mathrm{=}1.5\)

(keyword: BDN)

1.3. Boundary conditions and loads#

Zero imposed displacements (embedment) on the lateral face of the concrete elements.

The axis of rotation is fixed in the middle of the steel bar.

Monotonous mechanical loading is applied in the form of movements imposed on the end of the steel bar in two stages:

  • 20 increments of \(0.005\mathit{mm}\), for \(U\mathrm{=}\mathrm{\{}0\text{à}0.1\mathit{mm}\mathrm{\}}\)

  • 118 increments of \(0.05\mathrm{mm}\), for \(U\mathrm{=}\mathrm{\{}0.1\text{à}6\mathit{mm}\mathrm{\}}\)