v3.02.320 SSLP320 - Propagation of an X-FEM through crack solicited in Mode I

Summary

The purpose of this test is to validate the calculation of the stress intensity factors (\({K}_{I}\) and \({K}_{\mathrm{II}}\)) and the crack propagation path with X- FEM in 2D, in the context of linear elasticity.

This test involves a rectangular plate with an through crack, and subjected to a loading of traction on the lower and upper edges of the plate.

Three methods for managing the propagation of an X- FEM crack are available. Each of them is the subject of modeling.

Three models are considered:

• modeling A: mesh method,

• B modeling: simplex method,

• C modeling: upwind method,

• D modeling: geometric method,

The relevance of the results is evaluated by comparing the stress intensity factors with the analytical values.

We find a theoretical difference between \({K}_{I}\) and \({K}_{I}\) of less than 1.13% for the mesh method, 1.12% for the simplex method, 1.13% for the upwind method, 1.1% for the geometric method and 1.1% for the upwind & FMM method.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
• 2. Benchmark solution
  • 2.1. Calculation method
  • 2.2. Reference quantities and results
  • 2.3. Uncertainties about the solution
  • 2.4. Bibliographical references
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested sizes and results
  • 3.4. Additional results
• 4. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
• 5. C modeling
  • 5.1. Characteristics of modeling
  • 5.2. Characteristics of modeling
  • 5.3. Tested sizes and results
• 6. D modeling
  • 6.1. Characteristics of modeling
  • 6.2. Characteristics of modeling
  • 6.3. Tested sizes and results
• 7. Summaries of results