v6.04.150 SSNV150 - Triaxial traction with the BETON_DOUBLE_DP law of behavior

Summary

This validation case is intended to verify the 3D behavior model BETON_DOUBLE_DP formulated in the context of thermoplasticity, for the description of the non-linear behavior of concrete, in tension, and in compression, with the consideration of irreversible variations in the thermal and mechanical characteristics of concrete, which are particularly sensitive to high temperature.

The description of cracking is treated in the context of plasticity, using energy equivalence, by identifying the cracking energy density in \(I\) mode, with the plastic work of an equivalent homogeneous medium, where the plastic deformation is uniformly distributed, in an « elementary » zone. This approach maintains the continuity of the formulation of the model, throughout its behavior, and contributes to the avoidance of possible numerical difficulties when the state of the material changes.

The pathological sensitivity of the numerical solution to spatial discretization (mesh), generated by the introduction of a softening behavior of concrete under tension and compression, is partially resolved by introducing a cracking or breaking energy, depending on a characteristic length \({l}_{c}\), linked to the size of the elements. The resolution of the equations constituting the model is carried out by an implicit diagram.

It is an 8-knot cube subjected to triaxial traction, in imposed displacement. This loading leads to the particular case of a state of hydrostatic stress, resolved by projection at the top of the traction cone, when using an equivalent stress/hydrostatic stress diagram. This is a test case with an analytical solution.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and mechanical loads
• 2. Benchmark solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Calculation of the reference reference solution
  • 2.3. Uncertainty about the solution
  • 2.4. Bibliographical references
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested values
• 4. Summary of results