1. Reference problem#

1.1. Geometry#

We consider a notched plate with a height of \(10\mathit{dm}\). With a width \(3\mathit{dm}\) and a notch radius \(1\mathit{dm}\).

Figure 1: Representation of the problem

The material in question is assimilated to concrete (we work on a decimeter scale):

Elastic characteristics:

\(E\mathrm{=}3.E10\text{Pa}\mathrm{=}3.E8{\text{N/dm}}^{2}\)

\(\nu =0.2\)

Tensile elasticity limit of the law of damage:

\(\mathit{SY}\mathrm{=}3.E4{\text{N/dm}}^{2}\mathrm{=}3.E6\text{Pa}\)

Energy release rate per crack surface (Griffith constant):

\({G}_{f}\mathrm{=}10\text{N/dm}\mathrm{=}100{\text{J/m}}^{2}\)

Block: \(\mathrm{DX}=0\) on a group of nodes located in the middle of the axis (\(x=0.\)), in order to ensure the maintenance of the structure.

Load: Imposed or controlled displacement (varies according to the modeling) in the direction of traction.