r7.01.24 Law of viscoplastic behavior LETK

Summary:

The L&K law describes the elasto-visco-plastic behavior of rocks. Elastoplasticity is characterized by positive work-hardening in the pre-peak and a softening behavior beyond the strength. Viscoplasticity reflects the effect of time on behavior. It is described by a power law of Perzyna.

The initiation of elastoplastic or viscoplastic phenomena is triggered as soon as the corresponding threshold is crossed. The behavior associated with each phase is described by the evolution of these various thresholds. This evolution is governed by plastic or viscoplastic work hardening functions.

For the elastoplastic mechanism, a load surface evolves through various thresholds:

• A damage threshold that is confused with the initial viscosity threshold,

• A macroscopic peak threshold, defined from laboratory tests,

• An intermediate threshold, qualified as a cleavage limit, determined analytically,

• A characteristic threshold defined as the envelope of the damage threshold and the cleavage limit, also called the contract/expansion limit (this limit is confused with the maximum viscoplasticity threshold),

• A residual resistance threshold.

For the viscous mechanism, a viscoplastic surface evolves through:

• An initial threshold confused with the damage threshold

• A maximum viscosity threshold considered to be confused with the contractan/dilatance limit

• 1. Ratings
  • 1.1. Generalities
  • 1.2. Sign convention
  • 1.3. Model parameters
• 2. Introduction
• 3. L&K model equations
  • 3.1. Simplifying the model
  • 3.2. Description of the mechanisms
  • 3.3. Deformation tensor decomposition
  • 3.4. Criteria expressions
  • 3.5. Work hardening functions
  • 3.6. Laws of dilatance
  • 3.7. Derivatives of the criterion
• 4. Code_Aster integration
  • 4.1. Internal variables
  • 4.2. Explicit integration diagram (SPECIFIQUE)
  • 4.3. Implicit integration diagram
• 5. References
• 6. Features and verification
• 7. Description of document versions
• 8. Appendices: Jacobian matrix terms