3. Modeling A#

3.1. Characteristics of modeling#

We consider damage modeling GRAD_VARI, which is a mixed Lagrangian formulation of damages regulated by the damage gradient. In addition to the degrees of freedom of movement and damage to the nodes, it takes into account the Lagrange coefficients.

3.2. Characteristics of the mesh#

The mesh contains 1034 TRIA6 elements and 462 QUAD8 elements. The mesh at the center of the test piece is oriented out of symmetry.

_images/10000000000001F9000003044A9724E6DB505A33.png

Figure 2: Representation of the mesh

3.3. Law of damage: material ENDO_SCALAIRE#

Standard characteristics of concrete are defined above.

Characteristics related to the law of non-local damage:

\(c=1.875\text{N};p=1.5;m=10\) which corresponds to damage zone \(\mathrm{1D}\) equal to \(D=0.5\text{dm}\)

The correspondence with the physical parameters is as follows:

\(c=3/8D{G}_{f};m=\frac{3E{G}_{f}}{2D\cdot {\mathit{SY}}^{2}};p=m/4-1;\)

3.4. Boundary conditions and loads#

Loading:

A normal speed of movement of \(-5\mathit{SY}/E=-5E-04\) is imposed on the upper part and \(+5\mathit{SY}/E=5e-04\) on the lower part of the notched test piece so that the specimen works under compression.

Imposed on-the-go loading is applied during \(1.2\mathit{sec}\).

3.5. Tested sizes and results#

This test case is only validated in non-regression:

  • Non-regression test on the movement at point \(\text{P\_HAUT}\).

  • Non-regression test on the stress field at the Gauss point 1 of mesh \(\mathit{M160}\).

  • Non-regression test on the stress field at the Gauss point 1 of cell \(\mathit{M1324}\).

  • Non-regression test on the maximum stress in the specimen.

  • Non-regression test on the nodal reaction at point \(\text{P\_HAUT}\).