1. Reference problem#

1.1. Geometry#

_images/100002000000061500000800E410EB20C594714E.png

We assign any value to the inclination, \(\beta \mathrm{=}37\mathit{degrés}\).

We choose \(a=1.E-3m\).

1.2. Material properties#

The material is isotropic linear elastic, with a Young’s modulus \(E=2.E11\mathrm{Pa}\) and a Poisson’s ratio \(\nu =0.3\).

The traction curve is defined as:

  • the slope is equal to 3.

  • the elastic limit is equal to \(1.88\mathrm{GPa}\).

The hypothesis of plane constraints is applied.

1.3. Boundary conditions and loads#

  • Arbitrary mesh domain limits:

\(-{x}_{\mathrm{max}}\le x\le {x}_{\mathrm{max}}\) with \({x}_{\mathrm{max}}=\mathrm{10a}\)

\(-{y}_{\mathrm{max}}\le y\le {y}_{\mathrm{max}}\) with \({y}_{\mathrm{max}}=\mathrm{20a}\)

  • Boundary conditions:

In order to exclusively block the 3 rigid plane modes.

\(\mathrm{UX}=\mathrm{UY}=0\) at the bottom left corner of the full model.

\(\mathrm{UY}=0\) at the bottom right corner of the full model.

On the bottom edge, we impose \(\mathrm{UY}=0\)

  • Charging: uniform tension \({\sigma }_{\mathrm{yy}}={\sigma }_{0}\) on the top edge:

The value of \({\sigma }_{0}\) is \(\mathrm{100MPa}\), in plane constraints.