r7.01.38 Iwan’s law for the cyclic behavior of granular materials

Summary:

Iwan’s behavior model [1], [2] is a classical multi-mechanism elastoplastic model for describing the cyclic deviatoric behavior of materials and particularly geomaterials. Work hardening is linear kinematic for each mechanism and the flow rule in question is associated. By construction, the model automatically verifies the Masing rules.

The model allows an easy description of the behavior via parameters directly obtained from the curves of variation of the secant shear modulus. The user simply needs to provide the parameters of a hyperbolic function describing the variation of the secant modulus as a function of shear deformation.

It is implemented in environment MFront, making it easy to implement and maintain the model.

• 1. Theoretical formulation
  • 1.1. 1D vision of the behavior of the Iwan model
  • 1.2. 3D formulation of the Iwan model
• 2. Numerical integration of the law of behavior
  • 2.1. Prediction stage
  • 2.2. Newton algorithm correction step
  • 2.3. Update stage
  • 2.4. Calculating the terms of the Jacobian matrix
• 3. Implementation in code_aster
  • 3.1. Internal variables
  • 3.2. Model description under MFront
• 4. Features and verification
• 5. Bibliography