# MechanicalContactConstraint

Apply 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

## Description

The MechanicalContactConstraint class enforces mechanical contact of different types. Three contact models are available. These are glued, frictionless, and coulomb. Here we have where denote the total traction, is the normal traction, represents the tangential traction, and are the normal and tangential unit vectors, respectively. The normal contact constraint is the same for these three contact types and are detailed in contact module description. The differences among these contact types lie in the constraint equations for the tangential contact, which is described in the following section.

### Contact Models

The glued contact does not allow slip between the nodes once they come into contact, i.e., , where is the tangential relative velocity. Due to the no-slip condition, the glued contact is often used to model bonded connections between adjacent bodies that may have mismatching meshes in solid mechanics.

In contrast to the glued contact, the frictionless contact allows slip between the nodes that are in contact. No tangential traction is assumed, i.e., and . The frictionless contact is often utilized when the contact surface is pretty smooth thus tangential fraction along the interface can be omitted.

Different from the above two contact models, the coulomb model accounts for the friction along the interface caused by the relative motion between nodes. This is modeled using the Coulomb law, which computes a tangential traction that is proportional to the normal traction via a slip condition: where is the friction coefficient.

### Contact Formulations

To enforce the contact constraints, three types of formulations are available. These are kinematic, penalty, and mortar. The kinematic and penalty formulations have been developed for some time and turn out to be robust for many mechanical contact problems. Recent efforts have been put in developing a mortar-based contact formulation. In this documentation, however, we focus on kinematic and penalty formulations. For readers who are interested in mortar-based mechanical contact, please go to mortar constraint system for more information.

The overall workflow of imposing a mechanical constraint is as follows: 1) Determine whether penetration occurs. If so, constrain displacement; 2) In the normal direction, eliminate the penetration; 3) In the tangential direction, slip must satisfy friction model, no slip is allowed for the glued model, no constraint is applied for the frictionless model, Kuhn-Tucker conditions must be satisfied in the tangential direction for the coulomb model. The mechanical contact enforcement steps for the glued and frictionless models are summarized below:

For penalty:

GluedFrictionless

For kinematic:

GluedFrictionless

Note that the kinematic method uses penalty parameter only to enforce the condition that the secondary node has the desired position on the primary face, so the errors are very small in the converged solution. Unlike in penalty formulations, penalty compliance is not introduced on the contact surface. Therefore, the converged solution has no error due to penalty compliance.

For the frictional contact (coulomb model), the penalty method calculates normal force and tangential predictor force using penalty stiffness and check for frictional capacity. While using the kinematic method, the deformation of surrounding material serves the role of the penalty parameter.

### Contact gap offset

Gap offset can be provided to the current mechanical contact constraint. It can be either secondary_gap_offset (gap offset from secondary side) or mapped_primary_gap_offset (gap offset from primary side but mapped to secondary side). Use of these gap offset parameters treats the surfaces as if they were virtually extended (positive offset value) or narrowed (negative offset value) by the specified amount, so that the surfaces are treated as if they are closer or further away than they actually are. There is no deformation within the material in this gap offset region.

## Input Parameters

• boundaryThe primary boundary

C++ Type:BoundaryName

Options:

Description:The primary boundary

• componentAn integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)

C++ Type:unsigned int

Options:

Description:An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)

• nodal_areaThe nodal area

C++ Type:std::vector

Options:

Description:The nodal area

• variableThe name of the variable that this constraint is applied to.

C++ Type:NonlinearVariableName

Options:

Description:The name of the variable that this constraint is applied to.

### Required Parameters

• al_frictional_force_toleranceThe tolerance of the frictional force for augmented Lagrangian method.

C++ Type:double

Options:

Description:The tolerance of the frictional force for augmented Lagrangian method.

• al_incremental_slip_toleranceThe tolerance of the incremental slip for augmented Lagrangian method.

C++ Type:double

Options:

Description:The tolerance of the incremental slip for augmented Lagrangian method.

• al_penetration_toleranceThe tolerance of the penetration for augmented Lagrangian method.

C++ Type:double

Options:

Description:The tolerance of the penetration for augmented Lagrangian method.

• capture_tolerance0Normal distance from surface within which nodes are captured

Default:0

C++ Type:double

Options:

Description:Normal distance from surface within which nodes are captured

• connected_secondary_nodes_jacobianTrueWhether to include jacobian entries coupling nodes connected to secondary nodes.

Default:True

C++ Type:bool

Options:

Description:Whether to include jacobian entries coupling nodes connected to secondary nodes.

• disp_xThe x displacement

C++ Type:std::vector

Options:

Description:The x displacement

• disp_yThe y displacement

C++ Type:std::vector

Options:

Description:The y displacement

• disp_zThe z displacement

C++ Type:std::vector

Options:

Description:The z displacement

• displacementsThe displacements appropriate for the simulation geometry and coordinate system

C++ Type:std::vector

Options:

Description:The displacements appropriate for the simulation geometry and coordinate system

• execute_onLINEARThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.

Default:LINEAR

C++ Type:ExecFlagEnum

Options:NONE INITIAL LINEAR NONLINEAR TIMESTEP_END TIMESTEP_BEGIN FINAL CUSTOM

Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.

• formulationkinematicThe contact formulation

Default:kinematic

C++ Type:MooseEnum

Options:ranfs kinematic penalty augmented_lagrange tangential_penalty mortar

Description:The contact formulation

• friction_coefficient0The friction coefficient

Default:0

C++ Type:double

Options:

Description:The friction coefficient

• mapped_primary_gap_offsetoffset to the gap distance mapped from primary side

C++ Type:std::vector

Options:

Description:offset to the gap distance mapped from primary side

• modelfrictionlessThe contact model to use

Default:frictionless

C++ Type:MooseEnum

Options:frictionless glued coulomb

Description:The contact model to use

• non_displacement_variables_jacobianTrueWhether to include jacobian entries coupling with variables that are not displacement variables.

Default:True

C++ Type:bool

Options:

Description:Whether to include jacobian entries coupling with variables that are not displacement variables.

• normal_smoothing_distanceDistance from edge in parametric coordinates over which to smooth contact normal

C++ Type:double

Options:

Description:Distance from edge in parametric coordinates over which to smooth contact normal

• normal_smoothing_methodMethod to use to smooth normals

C++ Type:MooseEnum

Options:edge_based nodal_normal_based

Description:Method to use to smooth normals

• normalize_penaltyFalseWhether to normalize the penalty parameter with the nodal area for penalty contact.

Default:False

C++ Type:bool

Options:

Description:Whether to normalize the penalty parameter with the nodal area for penalty contact.

• orderFIRSTThe finite element order: FIRST, SECOND, etc.

Default:FIRST

C++ Type:MooseEnum

Options:CONSTANT FIRST SECOND THIRD FOURTH

Description:The finite element order: FIRST, SECOND, etc.

• penalty1e+08The penalty to apply. This can vary depending on the stiffness of your materials

Default:1e+08

C++ Type:double

Options:

Description:The penalty to apply. This can vary depending on the stiffness of your materials

• primaryThe boundary ID associated with the primary side

C++ Type:BoundaryName

Options:

Description:The boundary ID associated with the primary side

• primary_secondary_jacobianTrueWhether to include jacobian entries coupling primary and secondary nodes.

Default:True

C++ Type:bool

Options:

Description:Whether to include jacobian entries coupling primary and secondary nodes.

• primary_variableThe variable on the primary side of the domain

C++ Type:std::vector

Options:

Description:The variable on the primary side of the domain

• print_contact_nodesFalseWhether to print the number of nodes in contact.

Default:False

C++ Type:bool

Options:

Description:Whether to print the number of nodes in contact.

• secondaryThe secondary boundary

C++ Type:BoundaryName

Options:

Description:The secondary boundary

• secondary_gap_offsetoffset to the gap distance from secondary side

C++ Type:std::vector

Options:

Description:offset to the gap distance from secondary side

• stick_lock_iterations4294967295Number of times permitted to switch between sticking and slipping in a solution before locking node in a sticked state.

Default:4294967295

C++ Type:unsigned int

Options:

Description:Number of times permitted to switch between sticking and slipping in a solution before locking node in a sticked state.

• stick_unlock_factor1.5Factor by which frictional capacity must be exceeded to permit stick-locked node to slip again.

Default:1.5

C++ Type:double

Options:

Description:Factor by which frictional capacity must be exceeded to permit stick-locked node to slip again.

• tangential_toleranceTangential distance to extend edges of contact surfaces

C++ Type:double

Options:

Description:Tangential distance to extend edges of contact surfaces

• tension_release0Tension release threshold. A node in contact will not be released if its tensile load is below this value. No tension release if negative.

Default:0

C++ Type:double

Options:

Description:Tension release threshold. A node in contact will not be released if its tensile load is below this value. No tension release if negative.

### Optional Parameters

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Options:

Description:Adds user-defined labels for accessing object parameters via control logic.

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Options:

Description:Set the enabled status of the MooseObject.

• use_displaced_meshTrueWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Default:True

C++ Type:bool

Options:

Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

• extra_matrix_tagsThe extra tags for the matrices this Kernel should fill

C++ Type:std::vector

Options:

Description:The extra tags for the matrices this Kernel should fill

• extra_vector_tagsThe extra tags for the vectors this Kernel should fill

C++ Type:std::vector

Options:

Description:The extra tags for the vectors this Kernel should fill

• matrix_tagssystemThe tag for the matrices this Kernel should fill

Default:system

C++ Type:MultiMooseEnum

Options:nontime system

Description:The tag for the matrices this Kernel should fill

• vector_tagsnontimeThe tag for the vectors this Kernel should fill

Default:nontime

C++ Type:MultiMooseEnum

Options:nontime time

Description:The tag for the vectors this Kernel should fill