2. Modeling A#

In this modeling, the crack is not meshed, and the mesh is chosen so that the crack bottom is located at the center of the elements containing the bottom.

2.1. Characteristics of the mesh#

The structure is modelled by a regular mesh composed of \(5\mathrm{\times }5\mathrm{\times }5\) HEXA8, respectively along the \(x,y,z\) [Figure 2.1-2.1-a] axes. The crack bottom is therefore located at the center of the elements containing the crack bottom.

_images/1000000000000527000003EB205A42BE711EA864.png

Figure 2.1‑ 2.1-a : mesh such that the background is located at the center of the elements

2.2. Tested features#

We test the application of Dirichlet conditions via the AFFE_CHAR_MECA command on enriched nodes (here, nodes enriched by the Heaviside function and other nodes enriched by the asymptotic functions). This imposition is done as for the nodes using the keyword DDL_IMPO or FACE_IMPO.

2.3. Tested sizes and results#

We test the values of the movements of the nodes on which the conditions have been applied. Post-processing the move with X- FEM requires a specific reconstruction step, which does not preserve node groups. It is therefore necessary to recreate groups of nodes on the « cracked » post-processed mesh. Care must be taken to keep only the old nodes, and to eliminate the new nodes from the group, i.e. those that coincide with the intersection of the crack and the edges of the healthy mesh. This sorting is done using the name of the nodes:

  • \(N\dots\) for the nodes that are classic,

  • \(\mathit{NX}\dots\) for X-FEM knots that are not on the crack,

  • \(\mathit{NM}\dots\) and \(\mathit{NP...}\) For the new X-FEM knots that are on the « minus » lip and the « plus » lip.

So we eliminate nodes whose names start with \(\mathit{NM}\) and \(\mathit{NP}\).

To test all the nodes in the group at once, we test the minimum and maximum values.