1. Reference problem#
1.1. Geometry#
According to modeling \(\mathrm{2D}\) or \(\mathrm{3D}\), we consider respectively a square or a cube with side 2 \(\text{mm}\).
1.2. Material properties#
The material obeys the law of brittle elastic behavior ENDO_SCALAIRE with a damage gradient (D_ PLAN_GRAD_VARI and 3D_ GRAD_VARI). The macroscopic data correspond to:
\(E=30000\text{MPa}\) |
Young’s module |
\(\nu =0.2\) |
Poisson’s ratio |
\({G}_{f}=0.1\text{N/mm}\) |
Cracking energy |
\(p=5\) |
Shape parameter |
\({f}_{t}=3\text{MPa}\) |
Traction limit |
\({f}_{c}=15\text{MPa}\) |
Compression limit |
\(\tau \mathrm{=}4\text{MPa}\) |
Shear limit |
\(D=50\text{mm}\) |
Half-width of the damage band |
The internal parameters of the model, as described in paper [U4.43.01], are obtained by the formulas presented there. They lead to the following results:
Keyword: ELAS |
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E=3.E4 |
K=31.5E-3 |
C_ GRAD_VARI = 1.875 |
NU = 0.2 |
M = 10 |
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P=5 |
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C_ VOLU = 3.68 |
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C_ COMP = 1.847520861 |
1.3. Boundary conditions and loads#
The displacements are imposed at all the nodes of the structure, so as to correspond to the desired homogeneous deformation. More precisely, the displacement in a node with coordinates \(X\) is equal to: \(u(x)=\varepsilon \cdot x\)
1.4. Initial conditions#
None.