r5.03.24 Large deformation model GDEF_LOG

Summary:

This paper presents a hypoelastic formulation of large deformations for von Mises-type laws of behavior called GDEF_LOG in Code_Aster.

This model, due to C.Miehe, N.Apel and M.Lambrecht [13] is a model of large deformations based on a logarithmic measurement, with a particular duality stress tensor. It is valid regardless of the behavior in small deformations and has the advantage of providing a symmetric tangent matrix. No modification of kinematic internal variables is necessary. It allows for an incrementally objective integration of laws of behavior (like model SIMO_MIEHE). However, like all hypoelastic laws, the laws of behavior are, from a decreasing point of view, limited to slight elastic deformations.

This document illustrates the capabilities of this model and the advantages compared to approximation PETIT_REAC.

• 1. Introduction
• 2. Writing and hypotheses
  • 2.1. Kinematic elements
  • 2.2. Hypo-elastoplastic laws of behavior
  • 2.3. Deformation and stress tensors
• 3. Algorithm
  • 3.1. Pre-treatment
  • 3.2. Connection to the law of behavior HPP
  • 3.3. Post-treatment
• 4. Validity of large deformation models
  • 4.1. Identifying parameters
• 5. Comparison with PETIT_REAC
  • 5.1. Approximation of large deformations by PETIT_REAC
  • 5.2. Comparison on an example
• 6. Bibliography
• 7. Description of document versions
• 8. Appendix 1: Calculation of logarithmic deformations
  • 8.1. Ratings:
  • 8.2. Expression of constraints in Lagrangian configuration
  • 8.3. Expression of the tangent operator in Lagrangian configuration
  • 8.4. Effective calculation of logarithmic deformations