r5.04.01 Non-local modeling with gradients of internal variables GRAD_VARI

Summary

Here we present the non-local gradient modeling of internal variables entitled GRAD_VARI in Code_Aster. This modeling is the result of the work of E. Lorentz [Bib 1]. However, the algorithm for solving the equilibrium and regularization equations has been modified compared to the initial version of the model.

Non-local models of type GRAD_VARI are available in 3D (3D_ GRAD_VARI), axisymmetric (AXIS_GRAD_VARI), and plane deformations (D_ PLAN_GRAD_VARI).

Unlike the old version, the use of GRAD_VARI is relatively simple, since it is sufficient to specify the X_ GRAD_VARI modeling in AFFE_MODELE, to specify a characteristic length under the keyword NON_LOCAL in DEFI_MATERIAU, and to check that the law of behavior that one wishes to use is indeed available in a non-local version.

The writing and numerical processing of this model are presented.

• 1. Reminder on the theory of gradient models
  • 1.1. Construction of gradient models
  • 1.2. Dualization and discretization in time
  • 1.3. Spatial discretization by finite elements
  • 1.4. Integration of the law of behavior at Gauss points
  • 1.5. Calculation of internal forces
• 2. Choice of finite elements
• 3. Available models
• 4. Behavioral laws available with GRAD_VARI models
• 5. Advice/Procedure for the implementation of a new law of behavior with gradients of internal variables
• 6. Bibliography
• 7. Description of document versions