Reference problem ===================== Geometry --------- According to modeling :math:`\mathrm{2D}` or :math:`\mathrm{3D}`, we consider respectively a square or a cube with side 2 :math:`\text{mm}`. 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: .. csv-table:: ":math:`E=30000\text{MPa}` ", "Young's module" ":math:`\nu =0.2` ", "Poisson's ratio" ":math:`{G}_{f}=0.1\text{N/mm}` ", "Cracking energy" ":math:`p=5` ", "Shape parameter" ":math:`{f}_{t}=3\text{MPa}` ", "Traction limit" ":math:`{f}_{c}=15\text{MPa}` ", "Compression limit" ":math:`\tau \mathrm{=}4\text{MPa}` ", "Shear limit" ":math:`D=50\text{mm}` ", "Half-width of the damage band" The internal parameters of the model, as described in paper [:ref:`U4.43.01 `], are obtained by the formulas presented there. They lead to the following results: .. csv-table:: "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", "" 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 :math:`X` is equal to: :math:`u(x)=\varepsilon \cdot x` Initial conditions -------------------- None.