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

ENDO_SCALAIRE

NON_LOCAL

E=3.E4

K=31.5E-3

C_ GRAD_VARI = 1.875

NU = 0.2

M = 10

P=5

C_ VOLU = 3.68

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.