ComputeFrictionalForceLMMechanicalContact

This class represents a preliminary implementation of frictional mortar contact constraints intended to be used with Lagrange's multiplier interpolation with dual bases. The nonlinear complementarity constraints employed here are based on a primal-dual active set strategy (PDASS), see (Gitterle et al., 2010). These constraints capture nodes in sticking and slipping states on different solution branches, and can be written as:

$var element = document.getElementById("moose-equation-2640fee0-bb6c-4c0a-bbbc-74633093aae4");katex.render("C_{tj}(\\lambda_{j},\\boldsymbol{u}, \\boldsymbol{\\dot{u}}) = \\max({\\mu({pressure} + c_{n}\\tilde{g}_{nj}), abs({\\lambda_{j} + c_t \\tilde{u}_{tj}})) \\lambda_{j} - \\mu \\max({0,({pressure} + c_{n}\\tilde{g}_{nj})}) (\\lambda_{j} + c_t \\tilde{u}_{tj}) }", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-e806f78c-ff5e-499d-883c-4c1f3903ed77");katex.render("\\lambda_{j}", element, {displayMode:false,throwOnError:false});$ is a Lagrange's multiplier that refers to the tangential contact pressure at node $var element = document.getElementById("moose-equation-d1c2d3d8-29a5-4947-b750-a6c0030c1999");katex.render("j", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-2eabe1e2-dbb2-4c5b-a3e2-a7e9d4fda8d5");katex.render("\\tilde{u}_{tj}", element, {displayMode:false,throwOnError:false});$ is the weighted tangential velocity integrated forward in time, $var element = document.getElementById("moose-equation-95e8e837-30c6-472e-892f-5e654719f867");katex.render("\\tilde{g}_n)_j", element, {displayMode:false,throwOnError:false});$ is the weighted normal gap, $var element = document.getElementById("moose-equation-26c41d48-4f7f-4b5c-aff5-ac6cf6487d73");katex.render("c_{n}", element, {displayMode:false,throwOnError:false});$ is a numerical parameter ( $var element = document.getElementById("moose-equation-30cba035-096e-400a-bd9f-98e3a8ad7d52");katex.render("c", element, {displayMode:false,throwOnError:false});$ in ComputeWeightedGapLMMechanicalContact) and $var element = document.getElementById("moose-equation-a1c61853-3254-423f-be8d-25469ffcc70b");katex.render("c_{t}", element, {displayMode:false,throwOnError:false});$ is a numerical parameter that can determine convergence properties but has no effect on the results.

The nodal, weighted tangential velocity is computed as $var element = document.getElementById("moose-equation-33824154-871b-4e66-839d-467369a0aa0d");katex.render("\\tilde{v}_{tj} = \\int_{\\gamma_c^{(1)}} \\Phi_j v_{t,h} dA", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-1f8d5bda-52f4-4c8a-825b-d53e4ca27e2d");katex.render("\\gamma_c^{(1)}", element, {displayMode:false,throwOnError:false});$ denotes the secondary contact interface, $var element = document.getElementById("moose-equation-e3a754cd-9792-41f4-85d2-6500ecf44604");katex.render("\\Phi_j", element, {displayMode:false,throwOnError:false});$ is the j'th lagrange multiplier test function, and $var element = document.getElementById("moose-equation-20c6a949-18f0-47eb-b69a-ac3ce3f3e21a");katex.render("v_{t,h}", element, {displayMode:false,throwOnError:false});$ is the discretized version of the tangential velocity function.

This object automatically enforces normal contact constraints by making calls to its parent class ComputeWeightedGapLMMechanicalContact, see ComputeWeightedGapLMMechanicalContact for input parameters and details.

The preliminary recommendation is to select c to be on the order of the moduli of elasticity of the bodies into contact, and c_t to be a few orders of magnitude less than c. This selection of these purely numerical parameters can represent an initial difficulty when running new models, but they can be held constant once good convergence behavior has been attained.

Computes the tangential frictional forces

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
friction_lmThe frictional Lagrange's multiplier
C++ Type:std::vector<VariableName>
Options:
Description:The frictional Lagrange's multiplier
muThe friction coefficient for the Coulomb friction law
C++ Type:double
Options:
Description:The friction coefficient for the Coulomb friction law
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
c_t1Numerical parameter for tangential constraints
Default:1
C++ Type:double
Options:
Description:Numerical parameter for tangential constraints
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.
epsilon1e-07Minimum value of contact pressure that will trigger frictional enforcement
Default:1e-07
C++ Type:double
Options:
Description:Minimum value of contact pressure that will trigger frictional enforcement
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

Markus Gitterle, Alexander Popp, Michael W Gee, and Wolfgang A Wall. Finite deformation frictional mortar contact using a semi-smooth newton method with consistent linearization. International Journal for Numerical Methods in Engineering, 84(5):543–571, 2010.

@article{gitterle2010finite,
    author = "Gitterle, Markus and Popp, Alexander and Gee, Michael W and Wall, Wolfgang A",
    title = "Finite deformation frictional mortar contact using a semi-smooth Newton method with consistent linearization",
    journal = "International Journal for Numerical Methods in Engineering",
    volume = "84",
    number = "5",
    pages = "543--571",
    year = "2010",
    publisher = "Wiley Online Library"
}

Input Parameters
References