1. Reference problem

1.1. Geometry

The structure is a healthy rectangle in which four horizontal cracks are introduced, shown in red in Figure 1.1.a. The dimensions of the structure as well as the position of the cracks are given in this figure in meters.

Figure 1.1-a: Structure geometry and crack positioning.

1.2. Material properties

Young’s module: \(100\text{MPa}\)

Poisson’s ratio: 0.0

1.3. Boundary conditions and loads

In the case with contact (models A to F), component \(\text{X}\) of the movement is blocked on the right part of the structure. The \(\text{Y}\) component of the movement is blocked on its lower part. A loading of pressure according to \(\text{X}\) constant per piece is applied to the left part, so as to obtain a staircase. This load is represented in FIG. 1.3-b. The contact is active on the cracks, a constant pressure is applied to the upper part, so as to activate contact forces at the level of the cracks.

In the non-contact case (models G to I), the components \(\text{X}\) and \(\text{Y}\) of the movement are blocked on the right part of the structure and a loading in pressure according to \(\text{X}\) constant by piece is applied to the left part, so as to obtain a staircase. This load is represented in FIG. 1.3-b. The contact is not active on the cracks, so there is no pressure applied according to \(\text{Y}\).

Figure 1.3-a: Illustration of boundary conditions and loads, contact cases.

Figure 1.3-b: Pressure imposed through \(Y\) on the left edge (in \(\mathit{MPa}\) ) .

Figure 1.3- c : Illustration of boundary conditions and loads, non-contact cases .