ExplicitDynamicsContactConstraint

Apply non-penetration constraints on the mechanical deformation in explicit dynamics using a node on face formulation by solving uncoupled momentum-balance equations.

This object implements node-face constraints for the enforcement of normal mechanical contact in explicit dynamics. Surrogate balance-momentum equations are solved at each node on the secondary surface.

This method MUST be used with the ExplicitMixedOrder time integrator found in the Solid Mechanics module.

Following the work of (Heinstein et al., 2000), the contact is constrained as such,

$var element = document.getElementById("moose-equation-da8e719d-8ad8-45fb-9be3-2573dd0040e9");katex.render(" \\begin{aligned} \\mathbf{a_n} &= \\mathbf{M}^{-1}(\\mathbf{F}^\\text{ext}-\\mathbf{F}^{\\text{int}}(\\mathbf{u}_n)-\\mathbf{G}^T_n\\lambda_n)\\\\ \\end{aligned}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-52e9acaf-a7d0-4200-b860-eb4bb5a75680");katex.render("\\lambda_n", element, {displayMode:false,throwOnError:false});$ is the contact force, and $var element = document.getElementById("moose-equation-6f81adb0-7329-426e-a29c-c77b508e4299");katex.render("\\mathbf{G_n}", element, {displayMode:false,throwOnError:false});$ is the Jacobian of the contact constraints. $var element = document.getElementById("moose-equation-b4e79c97-2b62-4d33-94b1-40bc4b81e284");katex.render("\\lambda_n", element, {displayMode:false,throwOnError:false});$ is calculated with the following iteration, $var element = document.getElementById("moose-equation-9c5e37f1-9d97-492b-9874-4ca2abfe0020");katex.render(" \\begin{aligned} \\mathbf{v}^{0}_{n+\\frac{1}{2}} &= \\mathbf{M}^{-1}(\\mathbf{F}^\\text{ext}-\\mathbf{F}^{\\text{int}}(\\mathbf{u}_n)),\\\\ \\mathbf{v}^{j+1}_{n+\\frac{1}{2}} &= \\mathbf{v}^j_{n+\\frac{1}{2}}-\\Delta t \\mathbf{M}^{-1}\\mathbf{G_n}(\\lambda^{j+1}_n-\\lambda^{j}_n),\\\\ j & \\leftarrow j+1, \\text{next } j, \\end{aligned}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-4d6550f1-d4a0-4f3d-9702-7ad3f3cbbf54");katex.render("\\mathbf{v}^0_{n+\\frac{1}{2}}", element, {displayMode:false,throwOnError:false});$ is the initial guess for the midstep velocity.

$var element = document.getElementById("moose-equation-7e0d1282-be64-4ae4-9dcf-a94c34881d41");katex.render("\\lambda_n", element, {displayMode:false,throwOnError:false});$ is calculated at each node as a function of the wave speed and density of the primary and secondary material, the gap rate $var element = document.getElementById("moose-equation-d3de3e16-c33c-4e9a-b68a-d9f8d0dd3781");katex.render("\\mathbf{\\dot g}", element, {displayMode:false,throwOnError:false});$ , and tributary area $var element = document.getElementById("moose-equation-5ddace36-0830-4865-924e-3c2390e8943a");katex.render("\\Delta A", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-265a6e28-45ee-4fa3-97c5-ba4247b2848a");katex.render(" \\begin{aligned} \\lambda_{n_q} = \\frac{\\rho^{(1)}\\rho^{(2)}c^{(1)}c^{(2)}}{\\rho^{(1)}c^{(1)}+\\rho^{(2)}c^{(2)}}\\mathbf{\\dot g}_{n+\\frac{1}{2}}\\mid_q \\Delta A_q, \\end{aligned}", element, {displayMode:true,throwOnError:false});$

where the subscript $var element = document.getElementById("moose-equation-71e3279d-983d-4dab-b619-7a40bdd7b086");katex.render("_q", element, {displayMode:false,throwOnError:false});$ is a nodal index. With this formulation, the constraint force will be calculated within a few iterations.

Input Parameters

boundaryThe primary boundary
C++ Type:BoundaryName
Controllable:No
Description:The primary boundary
componentAn integer corresponding to the direction the variable this constraint acts on. (0 for x, 1 for y, 2 for z)
C++ Type:unsigned int
Controllable:No
Description:An integer corresponding to the direction the variable this constraint acts on. (0 for x, 1 for y, 2 for z)
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

displacementsThe displacements appropriate for the simulation geometry and coordinate system
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements appropriate for the simulation geometry and coordinate system
friction_coefficient0The friction coefficient
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The friction coefficient
gap_rateGap rate for output.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Gap rate for output.
mapped_primary_gap_offsetoffset to the gap distance mapped from primary side
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:offset to the gap distance mapped from primary side
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
modelfrictionlessThe contact model to use
Default:frictionless
C++ Type:MooseEnum
Options:frictionless, frictionless_balance
Controllable:No
Description:The contact model to use
normal_smoothing_distanceDistance from edge in parametric coordinates over which to smooth contact normal
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Distance from edge in parametric coordinates over which to smooth contact normal
normal_smoothing_methodMethod to use to smooth normals (edge_based|nodal_normal_based)
C++ Type:std::string
Controllable:No
Description:Method to use to smooth normals (edge_based|nodal_normal_based)
orderFIRSTThe finite element order used for projections
Default:FIRST
C++ Type:MooseEnum
Options:FIRST, SECOND, THIRD, FOURTH
Controllable:No
Description:The finite element order used for projections
penalty1e+08The penalty to apply. Its optimal value can vary depending on the stiffness of the materials
Default:1e+08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The penalty to apply. Its optimal value can vary depending on the stiffness of the materials
primaryThe boundary ID associated with the primary side
C++ Type:BoundaryName
Controllable:No
Description:The boundary ID associated with the primary side
primary_variableThe variable on the primary side of the domain
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
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
Controllable:No
Description:Whether to print the number of nodes in contact.
secondaryThe secondary boundary
C++ Type:BoundaryName
Controllable:No
Description:The secondary boundary
secondary_gap_offsetoffset to the gap distance from secondary side
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:offset to the gap distance from secondary side
tangential_toleranceTangential distance to extend edges of contact surfaces
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Tangential distance to extend edges of contact surfaces
vel_xx-component of velocity.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:x-component of velocity.
vel_yy-component of velocity.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:y-component of velocity.
vel_zz-component of velocity.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:z-component of velocity.

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
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>
Controllable:No
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
Controllable:No
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
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
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
Controllable:No
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
Controllable:No
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
Controllable:No
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

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
Unit:(no unit assumed)
Controllable:No
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.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

References

Martin W Heinstein, Frank J Mello, Stephen W Attaway, and Tod A Laursen. Contact—impact modeling in explicit transient dynamics. Computer Methods in Applied Mechanics and Engineering, 187(3-4):621–640, 2000.

@article{heinstein2000contact,
    author = "Heinstein, Martin W and Mello, Frank J and Attaway, Stephen W and Laursen, Tod A",
    title = "Contact—impact modeling in explicit transient dynamics",
    journal = "Computer Methods in Applied Mechanics and Engineering",
    volume = "187",
    number = "3-4",
    pages = "621--640",
    year = "2000",
    publisher = "Elsevier"
}

Input Parameters
References