r7.01.16 Integration of elasto-plastic mechanical behaviors of Drucker-Prager, associated (DRUCK_PRAGER) and non-associated (DRUCK_PRAG_N_A) and post-treatments

Summary:

This document describes the principles of several developments concerning the Drucker-Prager law of elastoplastic behavior in associated (DRUCK_PRAGER) and non-associated (DRUCK_PRAG_N_A) versions.

We are first interested in the integration itself of the law then, this law being softening, in a Rice location indicator and finally in the calculation of sensitivity by direct differentiation for this law.

To integrate the law, an implicit schema is used.

Table of Contents

• 1. Introduction
• 2. Integration of the Drucker-Prager law of behavior
  • 2.1. Ratings
  • 2.2. Formulation in associated version
  • 2.3. Formulation in an unassociated version
  • 2.4. Internal variables of the associated and unassociated Drucker-Prager laws
• 3. Rice location indicator for the Drucker-Prager law
  • 3.1. The different ways to study location
  • 3.2. Theoretical approach
• 4. Sensitivity calculations
  • 4.1. Sensitivity to material data
  • 4.2. Load sensitivity
• 5. Features and verification
• 6. Bibliography