v7.02.100 HPLP100 - Calculation of the energy return rate of a cracked plate in thermoelasticity

Summary

It is a thermo-elasticity test for a two-dimensional problem. We consider a rectangular plate that is cracked and the hypothesis of plane deformations is assumed.

In modeling A, the energy return rate is calculated during post-treatment by two different methods:

• classical calculation using the theta method,

• calculation by the IRWIN formula using the stress intensity coefficient \(\mathit{KI}\).

These two calculations are carried out on 4 different integration rings. Their interest is to compare the values of \(G\), \(G(\mathrm{IRWIN})\) and \(\mathit{KI}\) with respect to the reference solution and to test the invariance of the calculations with respect to the various integration crowns.

In the B modeling, the energy return rate is calculated by post-processing a classical calculation by the theta method. This calculation is carried out for several crowns of different integrations, in a formalism of large transformations.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. 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
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Test values and modeling results A
  • 3.4. notes
• 4. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Test values and B modeling results
• 5. Summaries of results