r5.03.01 Quasi-static nonlinear algorithm (STAT_NON_LINE)

Summary:

In the case of a quasi-static load, the operator STAT_NON_LINE [U4.51.03] allows the integration of various types of non-linearities resulting from the behavior of the material, large geometric transformations or contact/friction conditions. The global resolution algorithm used is described here.

The integration of behavioral relationships proper is described in documents [R5.03….] and [R7.01….], (for example [R5.03.02] for elasto-plasticity), which can be referred to for more details.

For calculations in large geometric transformations, one can consult for example the document [R5.03.20] on nonlinear elasticity in large displacements, or the documents [R5.03.21], [R5.03.22] on thermoelastoplasticity with isotropic work hardening.

For friction contact, there are three documents: [R5.03.50] on the discrete formulation of touch/friction, [R5.03.52] for the hybrid formulation with contact/friction elements.

For everything concerning piloting, refer to the document [R5.03.80].

• 1. Presentation
  • 1.1. Generalities
  • 1.2. Types of nonlinearities
  • 1.3. Position of the nonlinear quasistatic problem
• 2. Newton’s method
  • 2.1. Principle of the method
  • 2.2. Adapting Newton’s method to the problem posed
  • 2.3. Euler prediction phase
  • 2.4. Newton correction phase
  • 2.5. Convergence criteria
  • 2.6. Use of a tangent-secant evolutionary matrix
  • 2.7. Newton-Krylov method
• 3. Limit conditions and loads
  • 3.1. Classification
  • 3.2. Follower loads
  • 3.3. Dualized boundary conditions — Linear case
  • 3.4. Dualized boundary conditions — Nonlinear case
• 4. Linear search
  • 4.1. Principle
  • 4.2. Minimization of a functional
  • 4.3. Minimization method
  • 4.4. Application to the minimization of energy
  • 4.5. Determining the progress step
  • 4.6. Calculation of the linear search coefficient
• 5. Piloting
• 6. Viscoelastic regularization REGU_VISC
• 7. Bibliography
• 8. Document version history