r5.03.50 Discreet formulation of contact friction

Summary:

This document describes the numerical methods used to treat touch/friction problems during large movements in the STAT_NON_LINEou DYNA_NON_LINEà operator using a discrete formulation. The available algorithms make it possible to treat the problem exactly (in contact) or in an approximate manner (in contact and in friction), without restrictive choices on the underlying mechanical problem (kinematics or laws of non-linear behavior).

This document also contains theoretical elements to describe the resolution of general unilateral problems (without pairing such as oozing for example) usable by the keyword FORMULATION =” LIAISON_UNIL “.

Table of contents

• 1. Introduction
• 2. Contact and friction mechanics
  • 2.1. Problem definition and ratings
  • 2.2. Signorini contact conditions
  • 2.3. Formulation of the friction problem
  • 2.4. Formulation by differential inclusions
  • 2.5. Solving the balance problem
  • 2.6. Variational formulation
  • 2.7. Steps for solving the touch-friction problem
• 3. Geometric pairing problem
  • 3.1. Introduction
  • 3.2. Definition of potential contact areas
  • 3.3. Orientation of the normals
  • 3.4. Matching algorithm
  • 3.5. Kinematic relationships
  • 3.6. Introduction of a fictional game
  • 3.7. Geometric update
• 4. Mechanical touch/friction problem
  • 4.1. Mechanical problem without touch/friction
  • 4.2. Modification of the equilibrium equation with contact/friction
  • 4.3. Contact/friction laws
• 5. Algorithmic resolution — Frictionless contact
  • 5.1. Contact links
  • 5.2. Dualized methods in contact
  • 5.3. The penalized method in contact — ALGO_CONT =” PENALISATION “
• 6. Algorithmic resolution — Contact with friction
  • 6.1. Friction bonds
  • 6.2. Cinematics and tangent play
  • 6.3. The method penalized in contact and friction
• 7. Theoretical convergence results
  • 7.1. Redistribution of the time step
  • 7.2. Compatibility with Dirichlet boundary conditions
• 8. Conclusion
• 9. Bibliography