r7.01.43 Elastoplastic law with smoothed Mohr-Coulomb criterion

Summary:

This document presents the method for resolving the elastoplastic law not associated with a smoothed Mohr-Coulomb load surface dedicated particularly to granular geo-materials, accessible via the MFront environment. The original Mohr-Coulomb criterion is a pyramid: the edges and the vertex constitute difficulties for the resolution algorithm, cf. [R7.01.28]. Here we adopt the invariant formulation and the smoothing (regularization) solution proposed by Abbo and Sloan in [2], with an implicit integration method direct in time. It is implemented in the MFront environment, cf. [4], using the algorithm developed by [3] within the community `http://www.opengeosys.org`_ < http://www.opengeosys.org/> ``_ < http://www.opengeosys.org/>.

• 1. Introduction
• 2. Theoretical formulation
  • 2.1. State variables, state law
  • 2.2. Criterion (load area) smoothed
  • 2.3. Plastic flow potential
  • 2.4. Energy dissipation by plastic flow
  • 2.5. Behavioral relationship parameters
• 3. Numerical integration of the law of behavior
  • 3.1. Direct implicit integration
  • 3.2. Update at the end of the integration step
  • 3.3. Coherent tangent matrix expression
  • 3.4. Steps MFront
  • 3.5. Local variables MFront
• 4. Internal variables of the law of behavior
• 5. Verification and validation of the law of behavior
• 6. Bibliography