Some insight into algorithms available in different software for "contact
analysis"..
In an FE solution wherein contacts have been defined – all “contact algorithms” do one thing fundamentally- they maintain “contact compatibility” i.e. prevent inter-penetration between the contacting bodies because physical contacting bodies do not “inter-penetrate”
These algorithms being;
Penalty based contact formulation :
This uses the concept of “contact stiffness” between the contacting bodies.
Higher the contact stiffness, lower is the penetration. It is important, therefore, that the contact stiffness be large enough so that the resulting penetration is negligibly small but the contact stiffness cannot be so large so as to cause instability and non-convergence.
It might be therefore a good try to reduce the contact stiffness in issues of non-convergence / instability.
Augmented Lagrangian method:
This method is most attractive because there is an automated parameter within the constraint equation corresponding to this method which adds to the “contact stiffness” thus this method is less sensitive to the magnitude of the contact stiffness. This method is the default algorithm in many software’s because of this attractive feature
MPC algorithm:
MPC, or Multi-Point Constraint, internally adds constraint equations to “tie” [some software’s use the terminology “glued”] the displacements between surfaces. The DOF of the contact surface are eliminated and set to be dependent on those of the target surface through constraint equations. This approach is not penalty- or Lagrange multiplier-based. No contact stiffness is required;No extra DOF are added to the system
Lagrange algorithm:
When Lagrange algorithm is selected, “normal penalty stiffness” is replaced with “Allowable tensile contact pressure”, a chatter control parameter used to activate bisections based on surface pressure generated at contact interface. Works similar to traditional normal stiffness, except with the inverse effect (higher values reduce sensitivity and converge more easily)
In an FE solution wherein contacts have been defined – all “contact algorithms” do one thing fundamentally- they maintain “contact compatibility” i.e. prevent inter-penetration between the contacting bodies because physical contacting bodies do not “inter-penetrate”
These algorithms being;
Penalty based contact formulation :
This uses the concept of “contact stiffness” between the contacting bodies.
Higher the contact stiffness, lower is the penetration. It is important, therefore, that the contact stiffness be large enough so that the resulting penetration is negligibly small but the contact stiffness cannot be so large so as to cause instability and non-convergence.
It might be therefore a good try to reduce the contact stiffness in issues of non-convergence / instability.
Augmented Lagrangian method:
This method is most attractive because there is an automated parameter within the constraint equation corresponding to this method which adds to the “contact stiffness” thus this method is less sensitive to the magnitude of the contact stiffness. This method is the default algorithm in many software’s because of this attractive feature
MPC algorithm:
MPC, or Multi-Point Constraint, internally adds constraint equations to “tie” [some software’s use the terminology “glued”] the displacements between surfaces. The DOF of the contact surface are eliminated and set to be dependent on those of the target surface through constraint equations. This approach is not penalty- or Lagrange multiplier-based. No contact stiffness is required;No extra DOF are added to the system
Lagrange algorithm:
When Lagrange algorithm is selected, “normal penalty stiffness” is replaced with “Allowable tensile contact pressure”, a chatter control parameter used to activate bisections based on surface pressure generated at contact interface. Works similar to traditional normal stiffness, except with the inverse effect (higher values reduce sensitivity and converge more easily)
How about Nitsche's Algorithm? I am guessing that is the improved version of Augmented Lagrangian.
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