v2.04.123 SDLV123 - Calculation of elastodynamic G in an infinite medium for a plane crack of finite length

Summary

This is a problem of fracture mechanics in a medium in a state of plane deformation under transient elastodynamic regime. We consider a crack of length \(\mathrm{2a}\) immersed in a medium that is supposed to be infinite. Uniform pressure is imposed on the lips of the crack, which reaches a plateau in a period of 1 microsecond (shock). This test makes it possible to calculate the \(G\) energy return rate over time, taking into account inertia terms.

The interest of the test is the stability of \(G\) according to different crowns and the comparison to an exact analytical solution up to time \(t\mathrm{=}\mathrm{2a}\mathrm{/}{V}_{C}\), where \({V}_{C}\) represents the speed of the longitudinal waves.

This test contains plane deformation modeling and three-dimensional modeling. Absorbent boundary conditions on the borders of the solid make it possible to avoid wave feedback and therefore to simulate an infinite medium.

The differences in the calculation of \(G\) on various crowns compared to the reference solution do not exceed 1.4%.

• 1. Reference problem
  • 1.1. Geometry and modeling
  • 1.2. Material properties
  • 1.3. Loads
• 2. Benchmark solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Benchmark result
  • 2.3. Bibliographical reference
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Boundary conditions
  • 3.4. Results
• 4. Summary of results