r5.03.05 Taheri viscoplastic behavior relationship

Summary

This document presents the implementation of the viscoplastic Taheri behavior relationship, available for all isoparametric elements (2D and 3D continuous medium) with the exception of plane stresses. After a presentation of the evolution equations of this law, the system obtained by implicit discretization is described; in particular, it is shown that it always admits a solution.

This model is well suited to describe the response of austenitic steels under cyclic stresses, and in particular the phenomenon of progressive deformation. On the other hand, because of its complexity (two load surfaces, semi-discrete internal variable), it does not seem desirable to use it for different applications (monotonous loading path, for example).

• 1. Model description
  • 1.1. Plastic behavior
  • 1.2. Taking viscosity into account
  • 1.3. Description of the internal variables calculated by Code_Aster
• 2. Numerical formulation of the behavioral relationship
  • 2.1. Implicit discretization of behavioral equations
  • 2.2. Taking into account viscous terms
  • 2.3. Discretization of coherence conditions
  • 2.4. Coaching solutions
• 3. Numerical resolution methods
  • 3.1. Scalar equation: secant method
  • 3.2. Nonlinear systems: Newton method and linear search
  • 3.3. Stop criteria
  • 3.4. Tangent matrix
  • 3.5. Plane stresses
• 4. Bibliography
• 5. Description of document versions