v3.04.155 SSLV155 — Lens crack under traction

Summary:

The purpose of this test is to validate the calculation of stress intensity factors (SIFs) along the bottom of a non-planar 3D crack, in the context of linear elasticity.

This test involves a cube with a crack in the form of a lens, subjected to hydrostatic tension.

This test contains 3 models:

• Modeling A: the crack is meshed in 2D-axI (FEM);

• B modeling: the crack is not meshed, it is represented by level sets (X- FEM) in 2D-axI;

• C modeling: the crack is not meshed, it is represented by level sets (X- FEM) in 3D;

• D modeling: the crack is not meshed, it is represented by level sets (X- FEM) in 2D-axI and a structured mesh is used;

• E-modeling: the crack is not meshed, it is represented by 2D-axI level sets (X- FEM) with quadratic elements;

• F modeling: the crack is not meshed, it is represented by 2D-axI level sets (X- FEM) with quadratic elements and a structured mesh is used;

There is no FEM modeling in 3D because creating the mesh is extremely difficult.

For each model, the SIFs are evaluated by the commands POST_K1_K2_K3 and CALC_G (FEM)/CALC_G_XFEM (X- FEM).

Numerical values are compared to analytical values.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. The characteristic equation of the crack background is:
  • 1.3. Material properties
  • 1.4. Boundary conditions and loads
• 2. Benchmark solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Benchmark results
  • 2.3. Bibliographical references
• 3. Modeling A: Modeling FEM 2d-AXI
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Boundary conditions and loads
  • 3.4. Tested sizes and results
• 4. Modeling B: Modeling X- FEM 2d-AXI
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Boundary conditions and loads
  • 4.4. Tested sizes and results
• 5. C modeling: X- FEM 3D modeling
  • 5.1. Characteristics of modeling
  • 5.2. Characteristics of the mesh
  • 5.3. Boundary conditions and loads
  • 5.4. Tested sizes and results
• 6. D modeling: X-FEM 2d-AXi modeling with structured mesh
  • 6.1. Characteristics of modeling
  • 6.2. Characteristics of the mesh
  • 6.3. Boundary conditions and loads
  • 6.4. Tested sizes and results
• 7. E modeling: X-FEM 2d-Axi modeling with quadratic elements
  • 7.1. Characteristics of modeling
  • 7.2. Characteristics of the mesh
  • 7.3. Boundary conditions and loads
  • 7.4. Tested sizes and results
• 8. F modeling: X-FEM 2d-AXI modeling with quadratic elements and structured mesh
  • 8.1. Characteristics of modeling
  • 8.2. Characteristics of the mesh
  • 8.3. Boundary conditions and loads
  • 8.4. Tested sizes and results
• 9. Summary of results