ComputeWeightedGapLMMechanicalContact

The Karush-Kuhn-Tucker conditions of mechanical contact are:

$var element = document.getElementById("moose-equation-9b73c206-9a4e-403a-a46d-192310520b01");katex.render("\\begin{aligned} g &\\ge 0\\\\ \\lambda &\\ge 0\\\\ g\\lambda &= 0 \\end{aligned}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-39bff0ad-0102-4230-a8b6-e906d699b6f1");katex.render("g", element, {displayMode:false,throwOnError:false});$ is the gap and $var element = document.getElementById("moose-equation-83c6a513-b381-4bbf-a64a-83e342389276");katex.render("\\lambda", element, {displayMode:false,throwOnError:false});$ is the contact pressure, a Lagrange multipler variable living on the secondary face. Per (Wohlmuth, 2011) and (Popp and Wall, 2014), the variationally consistent, discretized version of the KKT conditions are:

$var element = document.getElementById("moose-equation-310ecdf9-96a6-4315-9f46-d722435c59bc");katex.render("\\begin{aligned} (\\tilde{g}_n)_j &\\ge 0\\\\ (\\lambda_n)_j &\\ge 0\\\\ (\\tilde{g}_n)_j (\\lambda_n)_j &= 0 \\end{aligned}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-a14bdfd3-673e-415c-9908-92a18dcb5074");katex.render("n", element, {displayMode:false,throwOnError:false});$ indicates the normal direction, $var element = document.getElementById("moose-equation-8370d238-0ac6-4b69-af8a-033aa982963c");katex.render("j", element, {displayMode:false,throwOnError:false});$ denotes the j'th secondary contact interface node, and $var element = document.getElementById("moose-equation-218df332-0db2-43fb-b2ca-b2ac5e7f5b22");katex.render("(\\tilde{g}_n)_j", element, {displayMode:false,throwOnError:false});$ is the discrete weighted gap, computed by:

$var element = document.getElementById("moose-equation-6b624528-7212-455e-a795-10a1eb825aeb");katex.render("(\\tilde{g}_n)_j = \\int_{\\gamma_c^{(1)}} \\Phi_j g_{n,h} dA", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-e8ddbdb2-2ebf-448b-9db8-ba5addd33c33");katex.render("\\gamma_c^{(1)}", element, {displayMode:false,throwOnError:false});$ denotes the secondary contact interface, $var element = document.getElementById("moose-equation-066a64de-a915-4d56-8bde-48d121fc1d99");katex.render("\\Phi_j", element, {displayMode:false,throwOnError:false});$ is the j'th lagrange multiplier test function, and $var element = document.getElementById("moose-equation-d09faffe-d1a8-4fc3-bd3c-bbfa841cc122");katex.render("g_{n,h}", element, {displayMode:false,throwOnError:false});$ is the discretized version of the gap function.

The ComputeWeightedGapLMMechanicalContact object computes the weighted gap and applies the KKT conditions. The KKT conditions are enforced using a nonlinear complimentarity problem (NCP) function, in this case the most simple such function, $var element = document.getElementById("moose-equation-3901b39f-b671-4908-bbd0-4a13141dfcee");katex.render("min(c(\\tilde{g}_n)_j, (\\lambda_n)_j)", element, {displayMode:false,throwOnError:false});$ , where $var element = document.getElementById("moose-equation-11bddf0a-b30b-4b03-8e00-6d255ec5b609");katex.render("c", element, {displayMode:false,throwOnError:false});$ (implemented with the input parameter c) is used to balance the size of the gap and the normal contact pressure. If the contact pressure is of order 10000, and the gap is of order .01, then c should be set to 1e6 in order to bring components of the NCP function onto the same level and achieve optimal convergence in the non-linear solve.

Computes the weighted gap that will later be used to enforce the zero-penetration mechanical contact conditions

Input Parameters

disp_xThe x displacement variable
C++ Type:std::vector<VariableName>
Options:
Description:The x displacement variable
disp_yThe y displacement variable
C++ Type:std::vector<VariableName>
Options:
Description:The y displacement variable
primary_boundaryThe name of the primary boundary sideset.
C++ Type:BoundaryName
Options:
Description:The name of the primary boundary sideset.
primary_subdomainThe name of the primary subdomain.
C++ Type:SubdomainName
Options:
Description:The name of the primary subdomain.
secondary_boundaryThe name of the secondary boundary sideset.
C++ Type:BoundaryName
Options:
Description:The name of the secondary boundary sideset.
secondary_subdomainThe name of the secondary subdomain.
C++ Type:SubdomainName
Options:
Description:The name of the secondary subdomain.

Required Parameters

c1e+06Parameter for balancing the size of the gap and contact pressure
Default:1e+06
C++ Type:double
Options:
Description:Parameter for balancing the size of the gap and contact pressure
compute_lm_residualsTrueWhether to compute Lagrange Multiplier residuals
Default:True
C++ Type:bool
Options:
Description:Whether to compute Lagrange Multiplier residuals
compute_primal_residualsTrueWhether to compute residuals for the primal variable.
Default:True
C++ Type:bool
Options:
Description:Whether to compute residuals for the primal variable.
interpolate_normalsTrueWhether to interpolate the nodal normals (e.g. classic idea of evaluating field at quadrature points). If this is set to false, then non-interpolated nodal normals will be used, and then the _normals member should be indexed with _i instead of _qp
Default:True
C++ Type:bool
Options:
Description:Whether to interpolate the nodal normals (e.g. classic idea of evaluating field at quadrature points). If this is set to false, then non-interpolated nodal normals will be used, and then the _normals member should be indexed with _i instead of _qp
periodicFalseWhether this constraint is going to be used to enforce a periodic condition. This has the effect of changing the normals vector for projection from outward to inward facing
Default:False
C++ Type:bool
Options:
Description:Whether this constraint is going to be used to enforce a periodic condition. This has the effect of changing the normals vector for projection from outward to inward facing
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Options:
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
variableThe name of the lagrange multiplier variable that this constraint is applied to. This parameter may not be supplied in the case of using penalty methods for example
C++ Type:NonlinearVariableName
Options:
Description:The name of the lagrange multiplier variable that this constraint is applied to. This parameter may not be supplied in the case of using penalty methods for example

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
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.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
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.

Advanced Parameters

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
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<TagName>
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

Tagging Parameters

References

Alexander Popp and WA Wall. Dual mortar methods for computational contact mechanics–overview and recent developments. GAMM-Mitteilungen, 37(1):66–84, 2014.

@article{popp2014dual,
    author = "Popp, Alexander and Wall, WA",
    title = "Dual mortar methods for computational contact mechanics--overview and recent developments",
    journal = "GAMM-Mitteilungen",
    volume = "37",
    number = "1",
    pages = "66--84",
    year = "2014",
    publisher = "Wiley Online Library"
}

Barbara Wohlmuth. Variationally consistent discretization schemes and numerical algorithms for contact problems. Acta Numerica, 20:569–734, 2011.

@article{wohlmuth2011variationally,
    author = "Wohlmuth, Barbara",
    title = "Variationally consistent discretization schemes and numerical algorithms for contact problems",
    journal = "Acta Numerica",
    volume = "20",
    pages = "569--734",
    year = "2011"
}

Input Parameters
References