r5.03.08 Integration of viscoelastoplastic behavior relationships in nonlinear mechanical operators

Summary

This document describes, in the case of nonlinear viscoelastic and viscoelastoplastic behaviors with threshold, built on the basis of Lemaître’s nonlinear viscoelastic model, the ingredients necessary for the implementation of the nonlinear mechanics algorithm, as in STAT_NON_LINE described in [R5.03.01]. The input data for all of these nonlinear viscoelastic behavior relationships embedded in Code_Aster generally have the same shape. Only the way to enter the main data (the viscous deformation rate function) varies: it is presented according to the various keywords that allow the user to choose the desired behavior relationship.

These quantities are calculated by a semi-implicit or implicit integration method. From the initial state, or from the previous calculation instant, the stress field resulting from a deformation increment is calculated.

• 1. Introduction
• 2. Ongoing relationship
• 3. Nature of the g function for each of the behavioral relationships
  • 3.1. Viscoelastic relationship LEMAITRE
  • 3.2. Fluency dependent relationship of LEMAITRE (LEMAITRE_IRRA)
  • 3.3. Relationship LEMA_SEUIL
  • 3.4. Relationship VISC_IRRA_LOG
• 4. Integrating the behavioral relationship
  • 4.1. Establishment of the scalar equation for the implicit schema and with constant elastic coefficients
  • 4.2. Solving the scalar equation: routine principle ZEROF2
  • 4.3. Calculation of the stress at the end of the current time step
  • 4.4. Semi-implicit schema
  • 4.5. Taking into account the variation of elastic coefficients as a function of temperature
• 5. Calculation of the tangent operator
• 6. Bibliography
• 7. Description of document versions