r7.01.17 Barcelona model

Summary:

This document presents the formulation and numerical integration of the behavior model. elastoplastic from Barcelona [bib2] __, designed to describe the mechanical behavior of non saturated, especially clays. This model is an extension of the modified Cam-Clay model [bia1] __ taking into account, schematically, the effects of capillary pressure on the elasticity, the reversibility range, and the work-hardening mechanisms observed experimentally on unsaturated soils. The Barcelona model has a total of sixteen settings. Behavioral equations are solved using an integration method implicit in time, implemented in the tool MFront [bib5] __. The use of the model is necessarily linked to the environment HHM [r7.01.11].

• 1. Notations
• 2. Introduction to the Barcelona model: behavior under isotropic loading
  • 2.1. At constant capillary pressure
  • 2.2. At constant net pressure
  • 2.3. General behavior under isotropic loading
• 3. Three-dimensional formulation of the model
  • 3.1. Elastic behavior
  • 3.2. Range of elasticity
  • 3.3. Work hardening functions
  • 3.4. Flow rules
  • 3.5. Critical state equations
• 4. Settings
• 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
• 7. Bibliography
• 8. Appendix: Expression of the Jacobian matrix
  • 8.1. First line
  • 8.2. Second line
  • 8.3. Third line