r4.04.03 Law of elasto (visco) plastic behavior in large deformations with metallurgical transformations

Summary

This document presents a model of thermo-elasto- (visco) plastic behavior with isotropic work hardening with the effects of metallurgical transformations written in large deformations. This model can be used for three-dimensional, axisymmetric and plane deformation models.

The writing of this model and its numerical processing are presented.

To understand this document, it is practically essential to read the two notes [R5.03.21] and [R4.04.02] devoted to behavior models written, respectively, in large deformations without metallurgical effects and in small deformations with metallurgical effects.

• 1. Introduction
• 2. Notations
• 3. Reminders of the metallurgical model and the large deformation model
  • 3.1. Model with metallurgical transformations
  • 3.2. Model written in large deformations
• 4. Extension of the large deformations model
  • 4.1. Thermodynamic aspect
  • 4.2. Extension
  • 4.3. Behavioral relationships
  • 4.4. The different relationships
  • 4.5. Constraints and internal variables
• 5. Numerical formulation
  • 5.1. Integration of different behavioral relationships
  • 5.2. Tangent matrix expression
• 6. Bibliography
• 7. Description of document versions