r5.03.09 1D nonlinear behavioral relationships

Summary:

This document describes the quantities calculated by the operator STAT_NON_LINE necessary for the implementation of the quasistatic nonlinear algorithm described in [R5.03.01] in the case of one-dimensional elastoplastic or viscoplastic behaviors. These behaviors, unless otherwise specified, are applicable to the elements of BARRE, to the elements of beams and multifibre beams (axial directions only) and to the elements of concrete reinforcement (modeling GRILLE).

The behaviors described in this document are:

• the Von Mises behavior with linear isotropic work hardening: VMIS_ISOT_LINE, and any VMIS_ISOT_TRAC,

• the Von Mises behavior with linear kinematic work hardening: VMIS_CINE_LINE,

• the Von Mises behavior at linear, non-symmetric work hardening under tension and compression: with restoration of the center of the elastic domain: VMIS_ASYM_LINE. The latter was developed to model the action of the ground on gas-insulated cables,

• the behavior of PINTO - MENEGOTTO which makes it possible to represent the uniaxial elasto-plastic behavior of reinforced concrete reinforcements. This model reflects the non-linearity of bar work hardening under cyclic loading and takes into account the Bauschinger effect. It also makes it possible to simulate the buckling of reinforcements under compression. This relationship is available in the*Code_Aster* for bar items and grid items,

• viscoplastic behaviors with the effect of irradiation: VISC_IRRA_LOG, GRAN_IRRA_LOG.

• the behavior of MAZARS in its \(\mathrm{1D}\) version. Version \(\mathrm{1D}\) of the Mazars model makes it possible to report on the restoration of stiffness in the event of cracks being closed.

• the behavior to model the relaxation of pre-stressed cables.

The resolution is made case by an implicit integration method. Unless otherwise stated, from the previous calculation moment, the stress field resulting from a deformation increment is calculated, and the tangent behavior that makes it possible to build the tangent matrices are calculated.

Finally, a method is described, similar to the method due to R.deborst [R5.03.03], making it possible to use all the behaviors available in 3D in the 1D elements.

• 1. Using 1D behavioral relationships
  • 1.1. 1D behavior relationships in Code_Aster
  • 1.2. General ratings
  • 1.3. Change of variables
• 2. Von-Mises behavior with linear isotropic work hardening: VMIS_ISOT_LINE or VMIS_ISOT_TRAC
  • 2.1. Model VMIS_ISOT_LINE equations
  • 2.2. Integrating the relationship VMIS_ISOT_LINE
  • 2.3. Internal variables
• 3. Von Mises behavior, 1D linear kinematic work hardening: VMIS_CINE_LINE
  • 3.1. Model equation VMIS_CINE_LINE
  • 3.2. Relationship integration VMIS_CINE_LINE
  • 3.3. Internal variables
• 4. Von Mises behavior, 1D linear kinematic work hardening: vmis_ CINE_gc
  • 4.1. Model equation VMIS_CINE_GC
  • 4.2. Relationship integration VMIS_CINE_GC
  • 4.3. Internal variables
• 5. Von Mises behavior at asymmetric linear work hardening: VMIS_ASYM_LINE
  • 5.1. Model VMIS_ASYM_LINE equations
  • 5.2. Behaviour integration VMIS_ASYM_LINE
  • 5.3. Internal variables
• 6. PINTO_MENEGOTTO model
  • 6.1. Formulation of the model
  • 6.2. Implementation in Code_Aster
  • 6.3. Internal variables
• 7. Behaviors VISC_IRRA_LOG and GRAN_IRRA_LOG
  • 7.1. Formulation of the model
  • 7.2. Internal variables
  • 7.3. Implicit integration
• 8. MAZARS model in 1D
  • 8.1. Model equations
  • 8.2. Internal variables
• 9. Law of behavior RELAX_ACIER
  • 9.1. Formulation of the model
  • 9.2. Internal variables
  • 9.3. Explicit integration
  • 9.4. Identifying parameters
  • 9.5. Result of an identification
  • 9.6. Usage in code_aster
• 10. Method for using all 3D behaviors in 1D
• 11. Bibliography