Constraints System

MortarConstraints

Overview

An excellent overview of the conservative mortar constraint implementation in MOOSE is given in Peterson (2018). We have verified that the MOOSE mortar implementation satisfies a priori error estimates (see discussion and plots on this github issue):

Primal FE Type	Lagrange Multiplier (LM) FE Type	Primal L2 Convergence Rate	LM L2 Convergence Rate
Second order Lagrange	First order Lagrange	3	2.5
Second order Lagrange	Constant monomial	3	1
First order Lagrange	First order Lagrange	2	1.5
First order Lagrange	Constant monomial	2	1.5

Parameters

There are four required parameters the user will always have to supply for a constraint derived from MortarConstraint:

primary_boundary: the boundary name or ID assigned to the primary side of the mortar interface
secondary_boundary: the boundary name or ID assigned to the secondary side of the mortar interface
primary_subdomain: the subdomain name or ID assigned to the lower-dimesional block on the primary side of the mortar interface
secondary_boundary: the subdomain name or ID assigned to the lower-dimensional block on the secondary side of the mortar interface

As suggested by the above required parameters, the user must do some mesh work before they can use a MortarConstraint object. The easiest way to prepare the mesh is to assign boundary IDs to the secondary and primary sides of the interface when creating the mesh in their 3rd-party meshing software (e.g. Cubit or Gmsh). If these boundary IDs exist, then the lower dimensional blocks can be generated automatically using the LowerDBlockFromSidesetGenerator mesh generator as shown in the below input file snippet:


[Mesh]
  [./primary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = '20'
  [../]
  [./secondary]
    type = LowerDBlockFromSidesetGenerator
    sidesets = '1'
    new_block_id = '10'
  [../]
[]

There are also some optional parameters that can be supplied to MortarConstraints. They are:

variable: Corresponds to a Lagrange Multipler variable that lives on the lower dimensional block on the secondary face
secondary_variable: Primal variable on the secondary side of the mortar interface (lives on the interior elements)
primary_variable: Primal variable on the primary side of the mortar interface (lives on the interior elements). Most often secondary_variable and primary_variable will correspond to the same variable
compute_lm_residuals: Whether to compute Lagrange Multiplier residuals. This will automatically be set to false if a variable parameter is not supplied. Other cases where the user may want to set this to false is when a different geometric algorithm is used for computing residuals for the LM and primal variables. For example, in mechanical contact the Karush-Kuhn-Tucker conditions may be enforced at nodes (through perhaps a NodeFaceConstraint) whereas the contact forces may be applied to the displacement residuals through MortarConstraint
compute_primal_residuals: Whether to compute residuals for the primal variables. Again this may be a useful parameter to use when applying different geometric algorithms for computing residuals for LM variables and primal variables.
periodic: Whether this constraint is going to be used to enforce a periodic condition. This has the effect of changing the normals vector, for mortar projection, from outward to inward facing.

At present, either the secondary_variable or primary_variable parameter must be supplied.

Limitations

Unfortunately the mortar system does not currently work in three dimensions. It is on the to-do list, but it will require a significant amount of work to get all the projections correct.

Available Objects

Moose App
CoupledTiedValueConstraintRequires the value of a variable to be the consistent on both sides of an interface.
EqualGradientConstraintEqualGradientConstraint enforces continuity of a gradient component between secondary and primary sides of a mortar interface using lagrange multipliers
EqualValueBoundaryConstraintConstraint for enforcing that variables on each side of a boundary are equivalent.
EqualValueConstraintEqualValueConstraint enforces solution continuity between secondary and primary sides of a mortar interface using lagrange multipliers
EqualValueEmbeddedConstraintThis is a constraint enforcing overlapping portions of two blocks to have the same variable value
LinearNodalConstraintConstrains secondary node to move as a linear combination of primary nodes.
OldEqualValueConstraintOldEqualValueConstraint enforces solution continuity between secondary and primary sides of a mortar interface using lagrange multipliers
TiedValueConstraintConstraint that forces the value of a variable to be the same on both sides of an interface.
XFEMApp
XFEMEqualValueAtInterfaceEnforce that the solution have the same value on opposing sides of an XFEM interface.
XFEMSingleVariableConstraintEnforce constraints on the value or flux associated with a variable at an XFEM interface.
Heat Conduction App
GapConductanceConstraintComputes the residual and Jacobian contributions for the 'Lagrange Multiplier' implementation of the thermal contact problem. For more information, see the detailed description here: http://tinyurl.com/gmmhbe9
Contact App
ApplyPenetrationConstraintLMMechanicalContactImplements the KKT conditions for normal contact using an NCP function, in this case just the min function. This function enforces that either the gap distance or the normal contact pressure (represented by the value of variable) is zero.
ComputeWeightedGapLMMechanicalContactComputes the weighted gap that will later be used to enforce the zero-penetration mechanical contact conditions
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
NormalMortarMechanicalContactThis class is used to apply normal contact forces using lagrange multipliers
NormalNodalLMMechanicalContactImplements the KKT conditions for normal contact using an NCP function. Requires that either the gap distance or the normal contact pressure (represented by the value of variable) is zero. The LM variable must be of the same order as the mesh
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
TangentialMortarLMMechanicalContactEnsures that the Karush-Kuhn-Tucker conditions of Coulomb frictional contact are satisfied
TangentialMortarMechanicalContactUsed to apply tangential stresses from frictional contact using lagrange multipliers
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.
Tensor Mechanics App
NodalFrictionalConstraintFrictional nodal constraint for contact
NodalStickConstraintSticky nodal constraint for contact

Available Actions

Moose App
AddConstraintActionAdd a Constraint object to the simulation.

References

John W. Peterson. Progress toward a new implementation of the mortar finite element method in moose. 2 2018. doi:10.2172/1468630.

@article{osti_1468630,
    author = "Peterson, John W.",
    title = "Progress toward a new implementation of the mortar finite element method in MOOSE",
    abstractNote = {The mortar finite element method has been used for many years in a variety of applications, including the enforcement of continuity conditions across decomposed domains, the implementation of Dirichlet boundary conditions, obtaining improved estimates of surface fluxes, and for solving large deformation contact mechanics problems. There is a currently great deal of interest in developing more robust mechanical and thermal contact solution strategies in the MOOSE framework and physics modules, and schemes based on the mortar finite element approach appear to be a promising avenue of development. There are a number of challenges associated with the development of a robust Lagrange multiplier based formulation of the mortar finite element method which can be tackled using the relatively simple framework of thermal contact problems, before tackling more complicated applications such as thermomechanical contact. In this report, we describe several aspects of our mortar finite element method implementation for solving thermal contact problems. The approach and notation used are based primarily based on the work of Bin Yang et al. ("Two dimensional mortar contact methods for large deformation frictional sliding," International Journal for Numerical Methods in Engineering 62(9), 2005).},
    doi = "10.2172/1468630",
    journal = "",
    place = "United States",
    year = "2018",
    month = "2"
}

MortarConstraints
Available Objects
Available Actions
References

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