1. Reference problem#

1.1. Geometry#

We consider a plate with a height \(h=\mathrm{0,1}m\), a width \(l=\mathrm{0,05}m\) and a thickness \(e=0.005m\). A crack is positioned in the middle of the height of the beam, with a depth of \(\mathrm{0,1}l\) .

Fz y x
_images/Object_1.png
_images/Object_2.png

1.2. Material properties#

We consider the classical properties of a steel:

Young’s module:

\(E={2.10}^{5}\mathrm{MPa}\)

Poisson’s ratio:

\(\nu =0.3\)

Density

\(\rho =7800\mathrm{kg}/{m}^{3}\)

1.3. Boundary conditions and loads#

The plate is:

  1. embedded on surface \({S}_{\mathrm{1 }}\);

  2. subjected to a \(F(t)\) force on the \({S}_{2}\) surface.

The evolution of the \(F(t)\) standard is shown in the figure above. We take \(\tau =\mathrm{0,001}s\). The direction of force \(F(t)\) is as follows:

  1. \(F(t)=f(t)\mathrm{.}{e}_{x}\) for modeling A;

  2. \(F(t)=(a{e}_{x}+b{e}_{y}+c{e}_{z})f(t)\) for B modeling, with \(b=\mathrm{2a}\) and \(c=0.4a\).

For modeling A, we block the movements in the \(z\) direction (plane problem).