v6.03.103 SSNP103 - Calculation of the energy return rate in nonlinear elasticity

Summary:

This test is a test case in nonlinear fracture mechanics.

We consider a rectangular plate that is finished, cracked and subjected to a loading of tension. The law of behavior used is a nonlinear elastic law of the Henky von Mises type.

This test case includes four models in \(\mathrm{2D}\):

• Modeling A, in plane deformations, treats a stressed crack in pure mode 1. Only half of the plate is modelled symmetrically.

• Modeling B, in plane deformations, treats a crack stressed in mixed modes. The complete plate is modelled.

• The C modeling uses the geometry of the A modeling but solves the associated axisymmetric problem. So here it is not a cracked plate but a cracked cylinder.

• Modeling D, reproduces the calculation of modeling B by adding a thermal loading.

• Modeling E, reproduces the calculation of modeling B with HHO linear.

• Modeling F, reproduces the calculation of modeling B with HHO quadratic.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loading
• 2. Benchmark solution
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested sizes and 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 the mesh
  • 5.3. Tested sizes and results
• 6. D modeling
  • 6.1. Characteristics of modeling
  • 6.2. Characteristics of the mesh
  • 6.3. Tested sizes and results
• 7. E modeling
  • 7.1. Characteristics of modeling
  • 7.2. Characteristics of the mesh
  • 7.3. Tested sizes and results
• 8. F modeling
  • 8.1. Characteristics of modeling
  • 8.2. Characteristics of the mesh
  • 8.3. Tested sizes and results
• 9. Summary of results