r7.01.19 Modeling the creep/plasticity coupling for concrete

Summary

It is a coupling model between behaviors modeling creep, type GRANGER and plasticity models, either general (Von Mises law with isotropic work hardening), or specific to concrete, of the BETON_DOUBLE_DP type, and implemented in the general resolution algorithm of DYNA/STAT_NON_LINE. The coupling is achieved by chaining the resolution of the equations of the two models during an iterative algorithm, which will take place at each Gauss point, at each iteration. It is therefore a « strong » coupling, since the equations of the law of creep and the law of plasticity are satisfied rigorously at all times.

This chaining makes it possible to avoid the complete development of a true resolution coupled with creep/plasticity, by using existing models, and without intervening in their resolution, but has the disadvantage of a higher calculation cost.

• 1. Introduction
• 2. Principle of creep/plasticity coupling
• 3. Put into equations
  • 3.1. Formulation of Granger creep in Code_Aster (Reminder)
  • 3.2. Formulation of the 1D creep/plasticity coupling
• 4. Algorithm for integrating creep/plasticity coupling
  • 4.1. Gauss point algorithm
  • 4.2. General organization chart
  • 4.3. Treatment of internal variables
  • 4.4. Managing behaviors and taking into account the redistribution of the time step
• 5. Bibliography
• 6. Description of document versions
• 7. ANNEXE: convergence of the coupling method
  • 7.1. Ratings and hypotheses
  • 7.2. Writing the global incremental problem in the form of a minimization
  • 7.3. Algorithm convergence
  • 7.4. Calculation of the tangent operator