r5.03.11 Mono and polycrystalline elastoviscoplastic behaviors

Summary:

The purpose of this document is to describe the integration of mono and polycrystalline behaviors.

Here we treat the integration of these laws of behavior associated with sliding systems corresponding to the usual or user-specified crystal families. This integration can be done explicitly (Runge-Kutta method with precision control and local redistribution of the time step) or implicitly (Newton method with local redistribution of the time step).

These behaviors can be used for the calculation of microstructures (mesh of an aggregate, with geometric representation of each physical monocrystalline grain) or for the calculation of type POLYCRISTAL, a « homogenized » medium possessing at any hardware point (or integration or calculation point) several simultaneous phases, in variable proportions.

We also describe the types of calculations possible with these behaviors as well as the procedure for generating meshes.

• 1. Introduction
• 2. Formulation of mono and polycrystalline behaviors
  • 2.1. Principle of the laws of behavior of single crystals
  • 2.2. Single crystal behavior laws available
  • 2.3. Sliding systems and the overall behavior of the single crystal
  • 2.4. Behaviour of homogenized polycrystal
• 3. Local integration and digital implementation
  • 3.1. System of equations to be solved
  • 3.2. Implicit behavior resolution MONOCRISTAL
  • 3.3. Explicit resolution
• 4. Internal variables
  • 4.1. Single crystal case
  • 4.2. Polycrystal case
• 5. Digital implementation in Code_Aster
• 6. Use
  • 6.1. Single crystal case
  • 6.2. Polycrystal case
  • 6.3. example
• 7. Bibliography
• 8. Document version history