v1.01.346 ZZZZ346 — Bifurcation of a straight XFEM interface with quadratic 2D elements

Summary

The purpose of this test is to validate the sub-division algorithm XFEM, with quadratic 2D elements. The general subdivision algorithm is described in the reference material [R7.02.12]. Moreover, sub-division occurs mainly when calling the operator MODI_MODELE_XFEM [U4.41.11].

In this test, we are interested in a particular cutting situation: the bifurcation of an interface along an edge, within an element itself. Depending on the position of the bifurcation point on the edge, we have two cutting configurations [R7.02.12]. These configurations correspond to two regularizations of the shape of the level-set.

We are considering 4 models:

1. modeling \(A\): \(\text{X-FEM}\mathrm{2D}\) with TRIA6 elements, the interface bifurcates before the midpoint on the bifurcation edge.

2. modeling \(B\): \(\text{X-FEM}\mathrm{2D}\) with QUAD8 elements, the interface bifurcates before the midpoint on the bifurcation edge.

3. Modeling \(C\): \(\text{X-FEM}\mathrm{2D}\) with TRIA6 elements, the interface bifurcates after the midpoint on the bifurcation edge.

4. modeling \(D\): \(\text{X-FEM}\mathrm{2D}\) with QUAD8 elements, the interface bifurcates after the midpoint on the bifurcation edge.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
  • 1.4. Benchmark solution
  • 1.5. Bibliographical references
• 2. Modeling A
  • 2.1. Characteristics of the mesh
  • 2.2. Tested sizes and results
  • 2.3. Additional results
• 3. B modeling
  • 3.1. Characteristics of the mesh
  • 3.2. Tested sizes and results
• 4. C modeling
  • 4.1. Characteristics of the mesh
  • 4.2. Tested sizes and results
  • 4.3. Additional results
• 5. D modeling
  • 5.1. Characteristics of the mesh
  • 5.2. Tested sizes and results
• 6. Summaries of results