Description: A penalty method is available in ABAQUS/Standard for enforcing contact constraints in the normal direction. The penalty method typically does not generate additional degrees of freedom, unlike the contact constraint options in previous versions, which would always generate Lagrange multiplier degrees of freedom. The penalty method can significantly reduce solver cost (in terms of CPU time and memory) for models with a significant fraction of nodes involved in contact. Furthermore, the numerical softening associated with the penalty method can be helpful for improving robustness for difficult to resolve contact situations and for situations involving overconstraints. The penalty method is used by default for the new finite-sliding, surface-to-surface formulation (see “Finite-sliding, surface-to-surface contact,” Section 11.2).

A variation of the penalty method that does make use of Lagrange multipliers to avoid ill-conditioning issues for high-penalty stiffness (at some computational expense) is also provided in ABAQUS/Standard. ABAQUS/Standard automatically chooses whether to make use of Lagrange multipliers with the penalty method based on the ratio of the penalty stiffness to the underlying element stiffness; Lagrange multipliers are not used with the default penalty stiffness.

You can directly specify whether or not ABAQUS/Standard uses Lagrange multipliers for both the penalty and the preexisting augmented Lagrange constraint enforcement methods. In the past the augmented Lagrange method in ABAQUS/Standard always used Lagrange multipliers. See “Contact formulation for ABAQUS/Standard contact pairs,” Section 29.2.2 of the ABAQUS Analysis User's Manual, for more detailed discussion of the contact constraint enforcement methods.

Interaction module: 
   Contact property editor: MechanicalNormal Behavior: 
   Constraint enforcement method: Penalty (Standard) 
   ABAQUS/Standard contact controls editor: Enforce using Lagrange multipliers: Off or On