v6.03.159 SSNP159 — Elastic energy in large plastic deformations of a bar under tension

Summary:

This quasistatic mechanical test consists in subjecting a bar with a rectangular (\(\mathrm{3D}\)) or cylindrical (\(\mathrm{2D}\) axisymmetric) cross section to simple traction. The object is to validate the calculation of elastic energies in three deformation formalisms: “PETIT”, “GDEF_LOG” and “SIMO_MIEHE”, with the command POST_ELEM.

In addition, the B modeling of this test case proposes to test the keyword factor ETAT_INIT proposed by the STAT_NON_LINE command, with GDEF_LOG. The user wishing to impose an initial state of constraint with the GDEF_LOG formalism will find the necessary information.

The bar is modelled by a volume element (HEXA20, ModelizationA) or quadrangular element (QUAD4, for axisymmetric modeling, modellingB).

The solution is analytical.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
• 2. Benchmark solution
  • 2.1. Generic result to formalisms
  • 2.2. Results for Simo_Miehe
  • 2.3. Results for GDEF_LOG
  • 2.4. Results in small deformations
  • 2.5. Tests carried out
• 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
  • 4.4. GDEF_LOG with ETAT_INIT
• 5. Summary of results