r5.03.21 Elasto (visco) plastic modeling with isotropic work hardening in large deformations

Summary

Here we describe a relationship of thermoelastoplastic behavior with isotropic work hardening written in large deformations and proposed by Simo and Miehe. This model is available in the STAT_NON_LINE command using the RELATION keyword: “VMIS_ISOT_TRAC”, “VMIS_ISOT_PUIS”, or “VMIS_ISOT_LINE” under the key keyword COMPORTEMENT and with the keyword DEFORMATION: “SIMO_MIEHE”. A viscous version of this model is also available: “VISC_ISOT_TRAC” and “VISC_ISOT_LINE”.

This model is implemented for three-dimensional (3D), axisymmetric (AXIS) and plane deformation (D_ PLAN) models.

The writing and numerical treatment of this law, as well as the associated variational formulation, are presented. It is an Eulerian variational formulation, with an update of the geometry and which takes into account the rigidity of behavior and the geometric rigidity.

• 1. Introduction
• 2. Notations
• 3. Reminders on major deformations
  • 3.1. Cinematics
  • 3.2. Constraints
  • 3.3. Objectivity
• 4. Presentation of the behavior model
  • 4.1. Kinematic aspect
  • 4.2. Behavioral relationships
  • 4.3. Correction of elastic energy in the presence of thermal
  • 4.4. Choice of the work hardening function
  • 4.5. Constraints and internal variables
  • 4.6. Field of use
  • 4.7. Integrating the law of behavior
• 5. Variational formulation
  • 5.1. Case of the continuous medium
  • 5.2. Finite element discretization
  • 5.3. Expression of the tangent matrix of behavior
• 6. Bibliography
• 7. Description of document versions