1. Reference problem

1.1. Geometry

The cube is in space \([0.\mathrm{,1}\mathrm{.}]\times [0.\mathrm{,1}\mathrm{.}]\times [0.\mathrm{,1}\mathrm{.}]\).

Coordinates of points \((m)\):

\(A:(0.,0.,0.)\)

\(G:(1.,1.,1.)\)

Cube geometry

\(L=1\)

1.2. Material properties

• • • Elastic

      • \(E=200.0\times {10}^{3}\mathrm{Pa}\) Young’s module

      • \(\nu =0.3\) Poisson’s ratio

    • Lemaitre (modeling A)

      • \(n=10.8\); \(\frac{1}{K}=6.9\times {10}^{-4}\); \(\frac{1}{m}=0.102\)

• • • Taheri (B modeling)

      • \({R}_{0}=0.001\)

      • \(\alpha =0.\)

      • \(m=1.\)

      • \(A=0.\)

      • \(b=0.\)

      • \({C}_{1}=0.\)

      • \({C}_{\infty }=0.\)

      • \(S=900.\)

• • • Taheri (C modeling)

      • \({R}_{0}=72.\)

      • \(\mathrm{\alpha }=0.3\)

      • \(m=0.1\)

      • \(A=312.\)

      • \(b=30.\)

      • \({C}_{1}=0.\)

      • \({C}_{\mathrm{\infty }}=0.065\)

      • \(S=450.\)

1.3. Boundary conditions and loads

1.3.1. A and B models

Imposed displacement \((m)\):

• side \(\mathit{ABCD}\): \(\mathit{DZ}=0\)

• side \(\mathit{AEHD}\): \(\mathit{DY}=0\)

• side \(\mathit{BFGC}\): \(\mathit{DY}=0.5\)

• side \(\mathit{ABFE}\): \(\mathit{DX}=0\)

The displacement \(\mathit{DY}\) imposed on face \(\mathit{BFGC}\) varies progressively according to the function shown in the figure below.

1.3.2. C modeling

Imposed displacement \((m)\):

• side \(\mathit{ABCD}\): \(\mathit{DZ}=0\)

• side \(\mathit{AEHD}\): \(\mathit{DY}=0\)

• side \(\mathit{ABFE}\): \(\mathit{DX}=0\)

Pressure imposed \((\mathit{Pa})\):

• side \(\mathit{BFGC}\): \(\mathit{PRES}=-520\)

The multiplier function of the pressure imposed on face \(\mathit{BFGC}\) as a function of time is represented in the figure below.