# Contact Module

The interaction of moving bodies is a common occurrence in our world, and therefore modeling such problems is essential to accurately represent the mechanical behavior of the physical world. However, finite element methods do not have an inherent means of modeling contact. Therefore, specific contact algorithms are required. These algorithms enforce constraints between surfaces in the mesh, to prevent penetration and develop contact forces. The MOOSE contact module provides the necessary tools for modeling mechanical contact.

## Theory

Mechanical contact between two deformable bodies is based on three requirements.

That is, the penetration distance (typically referred to as the gap in the contact literature) of one of the body into another must not be positive; the contact force opposing penetration must be positive in the normal direction; and either the penetration distance or the contact force must be zero at all times. In the MOOSE Contact Module, these contact constraints are enforced through the use of either node/face constraints or by using a mortar method.

## Node/Face Mechanical Contact

Contact constraints can be enforced through the use of node/face constraints in a manner similar to that detailed by Heinstein and Laursen (1999)). In this approach, first, a geometric search determines which secondary nodes have penetrated primary faces. For those nodes, the internal force computed by the divergence of stress is moved to the appropriate primary face at the point of contact. Those forces are distributed to primary nodes by employing the finite element shape functions. Additionally, the secondary nodes are constrained to remain on the primary faces, preventing penetration. The module currently supports frictionless, frictional, and glued contact.

## Mortar-Based Mechanical Contact

Models specific for mechanical contact enforcement have been developed based on the MOOSE mortar constraint system, and provide an alternative discretization technique for solving mechanical contact. Results of performance studies using this approach are summarized in MortarPerformance.

## Contact Syntax Block

Setting up a model to use contact enforcement in MOOSE requires the creation of multiple types of MOOSE objects. Using the top-level Contact syntax block, which streamlines the process of setting up these objects, is highly recommended, and supports most available types of contact. The following input file example shows the basic usage of the Contact block:

[Contact]
[./leftright]
secondary = 3
primary = 2
model = frictionless
penalty = 1e+6
normal_smoothing_distance = 0.1
[../]
[]

(modules/contact/test/tests/sliding_block/sliding/frictionless_kinematic.i)

## Objects, Actions, and Syntax

AuxKernels
• Contact App
• ContactPressureAuxComputes the contact pressure from the contact force and nodal area
Constraints
• Contact App
• MechanicalContactConstraintApply non-penetration constraints on the mechanical deformation using a node on face, primary/secondary algorithm, and multiple options for the physical behavior on the interface and the mathematical formulation for constraint enforcement
• NormalMortarLMMechanicalContactEnforces the normal contact complementarity conditions in a mortar discretization
• NormalNodalMechanicalContactApplies the normal contact force to displacement residuals through a Lagrange Multiplier
• RANFSNormalMechanicalContactApplies the Reduced Active Nonlinear Function Set scheme in which the secondary node's non-linear residual function is replaced by the zero penetration constraint equation when the constraint is active
• TangentialNodalLMMechanicalContactImplements the KKT conditions for frictional Coulomb contact using an NCP function. Requires that either the relative tangential velocity is zero or the tangential stress is equal to the friction coefficient times the normal contact pressure.
Contact
• Contact App
• ContactActionSets up all objects needed for mechanical contact enforcement
Dampers
• Contact App
• ContactSlipDamperDamp the iterative solution to minimize oscillations in frictional contact constriants between nonlinear iterations
DiracKernels
• Contact App
• ContactPrimary
• SecondaryConstraint
Postprocessors
• Contact App
• ContactDOFSetSizeOutputs the number of dofs greater than a tolerance threshold indicating mechanical contact
Preconditioning
• Contact App
• ContactSplitSplit-based preconditioner that partitions the domain into DOFs directly involved in contact (on contact surfaces) and those that are not
Problem
UserObjects
• Contact App
• NodalAreaCompute the tributary area for nodes on a surface

## References

1. Martin W. Heinstein and Tod A. Laursen. An algorithm for the matrix-free solution of quasistatic frictional contact problems. International Journal for Numerical Methods in Engineering, 44(9):1205–1226, March 1999.[BibTeX]