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_FISS_EXP 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
\({G}_{f}=0.1{\text{N/mm}}^{2}\)	Cracking energy
\(p=5\)	Shape parameter
\({f}_{t}=2.986\text{MPa}\)	Traction limit
\({f}_{c}=29.86\text{MPa}\)	Compression limit
\(D=50\text{mm}\)	Half-width of the damage band

The choice of these values of*ft* and fc in connection with François” criterion in ENDO_FISS_EXP corresponds to a confined traction limit of s*c* = 3 MPa. Moreover, the internal parameters of the model that are involved in the analytical solution are equal to:

\(k=1.5\times {10}^{-3}\text{MPa}\); \(m=11.111\); \(\gamma =9.534\times {10}^{3}\)

In the test, they are calculated by the macro command DEFI_MATER_GC.

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: \(u(x)=\epsilon \cdot x\). We start by imposing a uniaxial tensile deformation and then unloading until a compression deformation is imposed in order to verify the effect of the restoration of stiffness under compression.

1.4. Initial conditions

None.