r7.01.48 Behavior Model MCC

Summary:

This document presents the formulation and numerical integration of the modified Cam-Clay elastoplastic behavior model within the framework of Generalized Standard Materials. This model is dedicated to qualitatively representing the phenomenology of granular soils, taking into account the effects of dilatance/contraction, softening/hardening, as well as the critical state. The parameters of the model The total number of behaviors is seven. Three define isotropic nonlinear elastic behavior; three represent the initial reversibility domain. Combined kinematic-isotropic work hardening carried out by volume plastic deformation is controlled by a last parameter.

The behavioral equations are solved according to a variational principle for which the conditions of optimality are equivalent to a system of non-linear equations governing the equations of incremental evolution of the internal variables. These are resolved by using a direct time implicit integration method in MFront.

User Documentation

• 1. Introduction
• 2. Formulation of the model
  • 2.1. State laws
  • 2.2. Laws of evolution
  • 2.3. Critical state equations
• 3. Incremental formulation
  • 3.1. Principle of incremental minimization
  • 3.2. Optimality equations
• 4. Settings
  • 4.1. Classification
  • 4.2. Equivalence to parameters [r7.01.14]
• 5. Digital integration
  • 5.1. Implicit solving behavior equations in MFront
  • 5.2. Calculation of the algorithmic tangent operator
  • 5.3. Internal variables
• 6. Verification and validation
  • 6.1. Test cases
  • 6.2. Examples of answers to the material point
• 7. Bibliography
• 8. Appendix: Expression of the Jacobian matrix
  • 8.1. First line
  • 8.2. Second line
  • 8.3. Third line