1. Reference problem#

The purpose of this test is to validate the damage part of behavior model BETON_RAG.

1.1. Geometry#

The test is based on a unit cubic finite element (1 m x 1 m).

1.2. Property of the law of behavior#

Young’s module: \(E=32000\mathrm{MPa}\)

Poisson’s ratio: \(\mathrm{\nu }=0.2\)

Parameter of fragility of concrete under tension: \(\mathit{MT}=\mathrm{1,7}\)

Parameter of fragility of concrete under compression: \(\mathit{MC}=\mathrm{1,5}\)

Equivalent tensile stress of concrete: \({\mathrm{\sigma }}_{\mathit{ft}}=5.66\mathit{MPa}\)

Equivalent stress of concrete in compression: \({\mathrm{\sigma }}_{\mathit{fc}}=38.3\mathit{MPa}\)

Angle of the Drucker Prager criterion: \(\mathrm{\alpha }=\mathrm{0,15}\mathit{rad}\)

1.3. Boundary conditions and loads#

The loading, applied to the nodes of the X=1m plane, consists in the application of two load cycles in tension and then of two load cycles in compression:

Control while moving

1.pull \({\epsilon }_{\mathit{xx}}\mathrm{=}\mathrm{1,4}{.10}^{\mathrm{-}4}\) 2.release to \({\sigma }_{\mathit{xx}}\mathrm{=}0\) 3.pull \({\epsilon }_{\mathit{xx}}\mathrm{=}\mathrm{1,0}{.10}^{\mathrm{-}3}\) 4.compression \({\epsilon }_{\mathit{xx}}\mathrm{=}\mathrm{-}\mathrm{4,0}{.10}^{\mathrm{-}3}\) 5.release to \({\sigma }_{\mathit{xx}}\mathrm{=}0\) 6.compression \({\epsilon }_{\mathit{xx}}\mathrm{=}\mathrm{-}\mathrm{5,0}{.10}^{\mathrm{-}3}\) 7.pull 7.pull \({\epsilon }_{\mathit{xx}}\mathrm{=}0\)

 _images/100000000000042D000002CFF363EC8A8A5E3BC0.png

The following boundary conditions apply:

  • for the nodes in the plane X=0 → DX = 0

  • for node N1 (0, 0, 0) → DX = DY = DZ = 0

  • for node N5 (0, 0, 1) → DY = 0