v1.01.361 ZZZZ361 - Degenerate cutting cases for XFEM quadratic 3D elements

Summary:

In this test case, it is proposed to check the correct progress of particular volume cutting cases in the quadratic XFEM frame. In three-dimensional XFEM, the « parent » finite elements crossed by the crack are cut into « child » tetrahedra, which are then cut back into sub-tetrahedra to conform to the discontinuity.

There are a total of five configurations for cutting « child » tetrahedra into sub-tetrahedra (cf. [R7.02.12]), distinguished according to the number of vertex nodes of the child tetrahedron for which the lsn is cancelled (npts) and the number of intersection points between the lsn =0 surface and the edges of the child tetrahedron (npts) and the number of intersection points between the lsn =0 surface and the edges of the child tetrahedron. However, degenerate « grazing » configurations exist. These degenerate configurations can easily be reduced to conventional cutting configurations.

We are interested here in the six degenerate configurations (models A to F) for which the surface lsn=0 shaves the surface of the child tetrahedron, and which only occur in quadratic XFEM. These situations occur when one or more edges of the child tetrahedron have exactly 2 points such as*lsn=0* (necessarily one end and the middle node according to the adjustment of level set in the quadratic case). Finally, in G modeling, we study the case of non-degenerate cutting for which the lsn=0 surface shaves one of the edges of the tetrahedron.

• 1. Reference problem
  • 1.1. Geometry of the problem
• 2. Modeling A
  • 2.1. Characteristics of modeling A
  • 2.2. Characteristics of the mesh
  • 2.3. Tested sizes and results
• 3. B modeling
  • 3.1. Characteristics of B modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested sizes and results
• 4. C modeling
  • 4.1. Characteristics of C modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
• 5. D modeling
  • 5.1. Characteristics of modeling D
  • 5.2. Characteristics of the mesh
  • 5.3. Tested sizes and results
• 6. E modeling
  • 6.1. Characteristics of modeling E
  • 6.2. Characteristics of the mesh
  • 6.3. Tested sizes and results
• 7. F modeling
  • 7.1. Characteristics of F modeling
  • 7.2. Characteristics of the mesh
  • 7.3. Tested sizes and results
• 8. G modeling
  • 8.1. Characteristics of G modeling
  • 8.2. Characteristics of the mesh
  • 8.3. Tested sizes and results
• 9. Summary of results