v6.03.110 SSNP110 - Edge crack in a rectangular plate finished in elastoplasticity

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 an elastoplastic law of Von Mises.

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

• modeling A, in plane stresses, under the hypothesis of small deformations (DEFORMATION = “PETIT” in the STAT_NON_LINE operator);

• the B modeling, removed in V15, made it possible, under plane constraints, to study the influence of taking into account the second-order terms of the deformations (DEFORMATION = “GREEN” in the operator STAT_NON_LINE) on the calculation of the energy restoration rate \(G\);

• the C and D models, in plane stresses, aim to test the X- FEM method (non-meshed crack) in non-linear elasticity and in elastoplasticity for the calculation of the field of displacement;

• the E modeling, in plane deformations, validates the calculation of \(G\) for the various methods of defining the work hardening curve;

• F modeling is identical to C with quadratic elements.

• 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. C modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
• 5. D modeling
  • 5.1. Characteristics of modeling
  • 5.2. Characteristics of the mesh
  • 5.3. Tested sizes and results
• 6. E modeling
  • 6.1. Characteristics of modeling
  • 6.2. Characteristics of the mesh
  • 6.3. Tested sizes and results
• 7. F modeling
  • 7.1. Characteristics of modeling
  • 7.2. Characteristics of the mesh
  • 7.3. Tested sizes and results
• 8. Summary of results