Models - Functions

compute_models(datamanager::Module, block_nodes::Dict{Int64,Vector{Int64}}, dt::Float64, time::Float64, options::Vector{String}, synchronise_field, to::TimerOutput)

Computes the models models

Arguments

• datamanager::Module: The datamanager
• block_nodes::Dict{Int64,Vector{Int64}}: The block nodes
• dt::Float64: The time step
• time::Float64: The current time of the solver
• options::Vector{String}: The options
• synchronise_field: The synchronise field
• to::TimerOutput: The timer output

Returns

• datamanager: The datamanager

get_block_model_definition(params::Dict, block_id::Int64, prop_keys::Vector{String}, properties)

Get block model definition.

Special case for pre calculation. It is set to all blocks, if no block definition is defined, but pre calculation is.

Arguments

• params::Dict: Parameters.
• blocks::Vector{Int64}: List of block id's.
• prop_keys::Vector{String}: Property keys.
• properties: Properties function.

Returns

• properties: Properties function.

init_models(params::Dict, datamanager::Module, block_nodes::Dict{Int64,Vector{Int64}}, solver_options::Dict)

Initialize models

Arguments

• params::Dict: Parameters.
• datamanager::Module: Datamanager.
• block_nodes::Dict{Int64,Vector{Int64}}: block nodes.
• solver_options::Dict: Solver options.

Returns

• datamanager::Data_manager: Datamanager.

read_properties(params::Dict, datamanager::Module, material_model::Bool)

Read properties of material.

Arguments

• params::Dict: Parameters.
• datamanager::Data_manager: Datamanager.
• material_model::Bool: Material model.

Returns

• datamanager::Data_manager: Datamanager.

set_heat_capacity(params::Dict, block_nodes::Dict, heat_capacity::SubArray)

Sets the heat capacity of the nodes in the dictionary.

Arguments

• params::Dict: The parameters
• block_nodes::Dict: The block nodes
• heat_capacity::SubArray: The heat capacity array

Returns

• heat_capacity::SubArray: The heat capacity array

additive_name()

Gives the additive name. It is needed for comparison with the yaml input deck.

Arguments

Returns

• name::String: The name of the additive model.

Example:

println(additive_name())
"additive Template"

compute_model(
datamanager::Module,
nodes::Union{SubArray,Vector{Int64}},
additive_parameter::Dict,
block::Int64,
time::Float64,
dt::Float64,

)

Calculates the force densities of the additive. This template has to be copied, the file renamed and edited by the user to create a new additive. Additional files can be called from here using include and import .any_module or using .any_module. Make sure that you return the datamanager.

Arguments

• datamanager::Data_manager: Datamanager.
• nodes::Union{SubArray,Vector{Int64}}: List of block nodes.
• additive parameter::Dict(String, Any): Dictionary with additive parameter.
• time::Float64: The current time.
• dt::Float64: The current time step.

Returns

• datamanager::Data_manager: Datamanager.

Example:

damage_name()

Gives the damage name. It is needed for comparison with the yaml input deck.

Arguments

Returns

• name::String: The name of the damage.

Example:

println(damage_name())
"Damage Template"

c omputedamage(datamanager, nodes, damageparameter, block, time, dt)

Calculates the damage criterion of each bond. This template has to be copied, the file renamed and edited by the user to create a new material. Additional files can be called from here using include and import .any_module or using .any_module. Make sure that you return the datamanager.

Arguments

• datamanager::Data_manager: Datamanager.
• nodes::Union{SubArray,Vector{Int64}}: List of block nodes.
• damage_parameter::Dict(String, Any): Dictionary with material parameter.
• block::Int64: Block number
• time::Float64: The current time.
• dt::Float64: The current time step.

Returns

• datamanager::Data_manager: Datamanager.

Example:

damage_index(datamanager,::Union{SubArray, Vector{Int64})

Function calculates the damage index related to the neighborhood volume for a set of corresponding nodes. The damage index is defined as damaged volume in relation the neighborhood volume. damageIndex = sumi (brokenBondsi * volume_i) / volumeNeighborhood

Arguments

• datamanager::Data_manager: all model data
• nodes::Union{SubArray, Vector{Int64}}: corresponding nodes to this model

set_bond_damage(datamanager::Module, nodes::Union{SubArray,Vector{Int64}})

Set the bond damage field to the bond damage field

Arguments

• datamanager::Module: The datamanager
• nodes::Union{SubArray,Vector{Int64}}: The nodes

Returns

• datamanager::Module: The datamanager

init_interface_crit_values(datamanager::Module, params::Dict, block_id::Int64)

Initialize the critical values

Arguments

• datamanager::Module: The datamanager
• params::Dict: The parameters
• block_id::Int64: current block

Returns

• datamanager::Module: The datamanager

init_aniso_crit_values(datamanager::Module, params::Dict, block_id::Int64)

Initialize the anisotropic critical values

Arguments

• datamanager::Module: The datamanager
• params::Dict: The parameters
• block_id::Int64: current block

Returns

• datamanager::Module: The datamanager

get_quad_horizon(horizon::Float64, dof::Int64)

Get the quadric of the horizon.

Arguments

• horizon::Float64: The horizon of the block.
• dof::Int64: The degree of freedom.
• thickness::Float64: The thickness of the block.

Returns

• quad_horizon::Float64: The quadric of the horizon.

initmodel(datamanager::Module, nodes::Union{SubArray,Vector{Int64}}, materialparameter::Dict)

Initializes the material model.

Arguments

• datamanager::Data_manager: Datamanager.
• nodes::Union{SubArray,Vector{Int64}}: List of block nodes.
• material_parameter::Dict(String, Any): Dictionary with material parameter.

Returns

• datamanager::Data_manager: Datamanager.

material_name()

Gives the material name. It is needed for comparison with the yaml input deck.

Arguments

Returns

• name::String: The name of the material.

Example:

println(material_name())
"Material Template"

compute_model(datamanager, nodes, material_parameter, time, dt, to::TimerOutput)

Calculates the force densities of the material. This template has to be copied, the file renamed and edited by the user to create a new material. Additional files can be called from here using include and import .any_module or using .any_module. Make sure that you return the datamanager.

Arguments

• datamanager::Data_manager: Datamanager.
• nodes::Union{SubArray,Vector{Int64}}: List of block nodes.
• material_parameter::Dict(String, Any): Dictionary with material parameter.
• time::Float64: The current time.
• dt::Float64: The current time step.

Returns

• datamanager::Data_manager: Datamanager.

Example:

determine_isotropic_parameter(datamanager::Module, prop::Dict)

Determine the isotropic parameter.

Arguments

• prop::Dict: The material property.

Returns

• prop::Dict: The material property.

check_material_symmetry(dof::Int64, prop::Dict)

Check the symmetry of the material.

Arguments

• dof::Int64: The degree of freedom.
• prop::Dict: The material property.

Returns

• prop::Dict: The material property.

distribute_force_densities(datamanager::Module, nodes::Union{SubArray,Vector{Int64}})

Distribute the force densities.

Arguments

• datamanager::Data_manager: Datamanager.
• nodes::Union{SubArray,Vector{Int64}}: The nodes.

Returns

• datamanager::Data_manager: Datamanager.

get_all_elastic_moduli(datamanager::Module, parameter::Union{Dict{Any,Any},Dict{String,Any}})

Returns the elastic moduli of the material.

Arguments

• parameter::Union{Dict{Any,Any},Dict{String,Any}}: The material parameter.

get_Hooke_matrix(parameter::Dict, symmetry::String, dof::Int64, ID::Int64=1)

Returns the Hooke matrix of the material.

Arguments

• parameter::Union{Dict{Any,Any},Dict{String,Any}}: The material parameter.
• symmetry::String: The symmetry of the material.
• dof::Int64: The degree of freedom.
• ID::Int64=1: ID of the point. Needed for point wise defined material properties.

Returns

• matrix::Matrix{Float64}: The Hooke matrix.

distribute_forces(nodes::Union{SubArray,Vector{Int64}}, nlist::SubArray, nlist_filtered_ids::SubArray, bond_force::SubArray, volume::SubArray, bond_damage::SubArray, displacements::SubArray, bond_norm::SubArray, force_densities::SubArray)

Distribute the forces on the nodes

Arguments

• nodes::Union{SubArray,Vector{Int64}}: The nodes.
• nlist::SubArray: The neighbor list.
• nlist_filtered_ids::SubArray: The filtered neighbor list.
• bond_force::SubArray: The bond forces.
• volume::SubArray: The volumes.
• bond_damage::SubArray: The bond damage.
• displacements::SubArray: The displacements.
• bond_norm::SubArray: The pre defined bond normal.
• force_densities::SubArray: The force densities.

Returns

• force_densities::SubArray: The force densities.

distribute_forces(nodes::Union{SubArray,Vector{Int64}}, nlist::SubArray, bond_force::SubArray, volume::SubArray, bond_damage::SubArray, force_densities::SubArray)

Distribute the forces on the nodes

Arguments

• nodes::Union{SubArray,Vector{Int64}}: The nodes.
• nlist::SubArray: The neighbor list.
• bond_force::SubArray: The bond forces.
• volume::SubArray: The volumes.
• bond_damage::SubArray: The bond damage.
• force_densities::SubArray: The force densities.

Returns

• force_densities::SubArray: The force densities.

matrix_to_voigt(matrix)

Convert a 2x2 or 3x3 matrix to Voigt notation (6x1 vector)

Arguments

• matrix::Matrix{Float64}: The matrix.

Returns

• voigt::Vector{Float64}: The Voigt notation.

voigt_to_matrix(voigt::Union{Vector{Float64},Vector{Int64}})

Convert a Voigt notation (6x1 or 3x1 vector) to a 2x2 or 3x3 matrix

Arguments

• voigt::Vector{Float64}: The Voigt notation.

Returns

• matrix::Matrix{Float64}: The matrix.

check_symmetry(prop::Dict, dof::Int64)

Check if the symmetry information is present in the material dictionary.

Arguments

• prop::Dict: A dictionary containing material information.
• dof::Int64: The number of degrees of freedom.

Returns

• true: If the symmetry information is present.

get_symmetry(material::Dict)

Return the symmetry information from the given material dictionary.

Arguments

• material::Dict: A dictionary containing material information.

Returns

• If the key "Symmetry" is present in the dictionary, the corresponding value is returned.
• If the key is not present, the default value "3D" is returned.

Example

```julia materialdict = Dict("Symmetry" => "Cubic", "Color" => "Red") symmetry = getsym(material_dict)

get_von_mises_stress(von_Mises_stress::Float64, dof::Int64, stress_NP1::Matrix{Float64})

Arguments

• von_Mises_stress::Float64: Von Mises stress
• dof::Int64: Degree of freedom.
• stress_NP1::Matrix{Float64}: Stress.

returns

• spherical_stress_NP1::Float64: Spherical stress
• deviatoric_stress_NP1::Matrix{Float64}: Deviatoric stress

elastic(nodes, dof, undeformed_bond, deformed_bond, bond_damage, theta, weighted_volume, omega, material, bond_force)

Calculate the elastic bond force for each node.

$F = \omega \cdot \theta \cdot (\frac{3K}{V} - \frac{\frac{15B}{V}}{3} \cdot \zeta + \alpha \cdot stretch)$ [4] for 3D, plane stress and plane strain it is refered to [1] page 152; Eq. (6.12); after (6.21) and after (6.23)

Arguments

• nodes: array of node IDs
• dof: number of degrees of freedom
• undeformed_bond: dictionary of bond geometries for each node
• deformed_bond: dictionary of deformed bond geometries for each node
• bond_damage: dictionary of bond damages for each node
• theta: dictionary of theta values for each node
• weighted_volume: dictionary of weighted volumes for each node
• omega: dictionary of omega values for each node
• material: dictionary of material properties
• bond_force: dictionary to store the calculated bond forces for each node

Returns

• bond_force: dictionary of calculated bond forces for each node

calculate_symmetry_params(symmetry::String, shear_modulus::Float64, bulk_modulus::Float64)

Calculate the symmetry parameters based on the given material symmetry. These parameters are defined in [1] Section 6.3, 6.3.1.1 and 6.3.1.2.

Arguments

• symmetry::String: Symmetry of the material.
• shear_modulus::Float64: Shear modulus.
• bulk_modulus::Float64: Bulk modulus.

Returns

• alpha::Float64: Alpha parameter.
• gamma::Float64: Gamma parameter.
• kappa::Float64: Kappa parameter.

compute_weighted_volume(nodes::Union{SubArray,Vector{Int64}},
                        nlist::SubArray,
                        undeformed_bond_length::SubArray,
                        bond_damage::SubArray,
                        omega::SubArray,
                        volume::SubArray)

Compute the weighted volume for each node, [9]. Taken from Peridigm -> but adding the bond_damage; this is missing in Peridigm, but should be there.

Arguments

• nodes::Union{SubArray,Vector{Int64}}: Vector of node indices or a subarray representing the indices of the nodes.
• nlist::SubArray: Subarray representing the neighbor list for each node.
• undeformed_bond_length::SubArray: Subarray representing the undeformed bonds.
• bond_damage::SubArray: Subarray representing the bond damage.
• omega::SubArray: Subarray representing the weights for each bond.
• volume::SubArray: Subarray representing the volume for each node.

Returns

• weighted_volume::Vector{Float64}: Vector containing the computed weighted volume for each node.

compute_dilatation(nodes::Union{SubArray,Vector{Int64}}, nneighbors::SubArray, nlist::SubArray, undeformed_bond::SubArray, deformed_bond::SubArray, bond_damage::SubArray, volume::SubArray, weighted_volume::Vector{Float64}, omega::SubArray, theta::SubArray)

Calculate the dilatation for each node, [9].

Arguments

• nodes::Union{SubArray,Vector{Int64}}: Nodes.
• nneighbors::SubArray: Number of neighbors.
• nlist::SubArray: Neighbor list.
• undeformed_bond_length::SubArray: Bond geometry.
• deformed_bond_length::SubArray: Deformed bond geometry.
• bond_damage::SubArray: Bond damage.
• volume::SubArray: Volume.
• weighted_volume::SubArray: Weighted volume.
• omega::SubArray: Influence function.
• theta::SubArray: Dilatation.

Returns

• theta::Vector{Float64}: Dilatation.

zero_energy_mode_compensation(datamanager::Module, nodes::Union{SubArray,Vector{Int64}}, material_parameter::Dict, time::Float64, dt::Float64)

Global - J. Wan et al., "Improved method for zero-energy mode suppression in peridynamic correspondence model in Acta Mechanica Sinica https://doi.org/10.1007/s10409-019-00873-y

Arguments

• datamanager::Data_manager: Datamanager.
• nodes::Union{SubArray,Vector{Int64}}: List of block nodes.
• material_parameter::Dict(String, Any): Dictionary with material parameter.
• time::Float64: The current time.
• dt::Float64: The current time step.

Returns

• datamanager::Data_manager: Datamanager.

calculate_bond_force(nodes::Union{SubArray,Vector{Int64}}, deformation_gradient::SubArray, undeformed_bond::SubArray, bond_damage::SubArray, inverse_shape_tensor::SubArray, stress_NP1::SubArray, bond_force::SubArray)

Calculate bond forces for specified nodes based on deformation gradients.

Arguments

• nodes::Union{SubArray,Vector{Int64}}: List of block nodes.
• deformation_gradient::SubArray: Deformation gradient.
• undeformed_bond::SubArray: Undeformed bond geometry.
• bond_damage::SubArray: Bond damage.
• inverse_shape_tensor::SubArray: Inverse shape tensor.
• stress_NP1::SubArray: Stress at time step n+1.
• bond_force::SubArray: Bond force.

Returns

• bond_force::SubArray: Bond force.

compute_stresses(datamanager::Module, iID:Int64, dof::Int64, material_parameter::Dict, time::Float64, dt::Float64, strain_increment::SubArray, stress_N::SubArray, stress_NP1::SubArray)

Calculates the stresses of the material. This template has to be copied, the file renamed and edited by the user to create a new material. Additional files can be called from here using include and import .any_module or using .any_module. Make sure that you return the datamanager.

Arguments

• datamanager::Data_manager: Datamanager.
• iID::Int64: Node ID.
• dof::Int64: Degrees of freedom
• material_parameter::Dict(String, Any): Dictionary with material parameter.
• time::Float64: The current time.
• dt::Float64: The current time step.
• strainInc::Union{Array{Float64,3},Array{Float64,6}}: Strain increment.
• stress_N::SubArray: Stress of step N.
• stress_NP1::SubArray: Stress of step N+1.
• `iIDjIDnID::Tuple=(): (optional) are the index and node id information. The tuple is ordered iID as index of the point, jID the index of the bond of iID and nID the neighborID.

Returns

• datamanager::Data_manager: Datamanager.
• stress_NP1::SubArray: updated stresses

Example:

compute_stresses(datamanager::Module, dof::Int64, material_parameter::Dict, time::Float64, dt::Float64, strain_increment::SubArray, stress_N::SubArray, stress_NP1::SubArray)

Calculates the stresses of a single node. Needed for FEM. This template has to be copied, the file renamed and edited by the user to create a new material. Additional files can be called from here using include and import .any_module or using .any_module. Make sure that you return the datamanager.

Arguments

• datamanager::Data_manager: Datamanager.
• dof::Int64: Degrees of freedom
• material_parameter::Dict(String, Any): Dictionary with material parameter.
• time::Float64: The current time.
• dt::Float64: The current time step.
• strainInc::Union{Array{Float64,3},Array{Float64,6}}: Strain increment.
• stress_N::SubArray: Stress of step N.
• stress_NP1::SubArray: Stress of step N+1.

Returns

• datamanager::Data_manager: Datamanager.
• stress_NP1::SubArray: updated stresses

Example:

correspondence_name()

Gives the material name. It is needed for comparison with the yaml input deck.

Arguments

Returns

• name::String: The name of the material.

Example:

println(material_name())
"Material Template"

control_name()

Returns the name of the zero energy control

compute_control(datamanager::Module, nodes::Union{SubArray,Vector{Int64}}, material_parameter::Dict, time::Float64, dt::Float64)

Computes the zero energy control

Arguments

• datamanager::Module: The datamanager
• nodes::Union{SubArray,Vector{Int64}}: The nodes
• material_parameter::Dict: The material parameter
• time::Float64: The current time
• dt::Float64: The current time step

Returns

• datamanager::Module: The datamanager

get_zero_energy_mode_force(nodes::Union{SubArray,Vector{Int64}}, zStiff::SubArray, deformation_gradient::SubArray, undeformed_bond::SubArray, deformed_bond::SubArray, bond_force::SubArray)

Computes the zero energy mode force

Arguments

• nodes::Union{SubArray,Vector{Int64}}: The nodes
• zStiff::SubArray: The zero energy stiffness
• deformation_gradient::SubArray: The deformation gradient
• undeformed_bond::SubArray: The bond geometry
• deformed_bond::SubArray: The bond geometry at the next time step
• bond_force::SubArray: The bond force

Returns

• bond_force::SubArray: The bond force

create_zero_energy_mode_stiffness(nodes::Union{SubArray,Vector{Int64}}, dof::Int64, CVoigt::Union{MMatrix,Matrix{Float64}}, angles::Vector{Float64}, Kinv::SubArray, zStiff::SubArray, rotation::Bool)

Creates the zero energy mode stiffness

Arguments

• nodes::Union{SubArray,Vector{Int64}}: The nodes
• dof::Int64: The degree of freedom
• CVoigt::Union{MMatrix, Matrix{Float64}}: The Voigt matrix
• angles::Vector{Float64}: The angles
• Kinv::SubArray: The inverse shape tensor
• zStiff::SubArray: The zero energy stiffness
• rotation::Bool: The rotation

Returns

• zStiff::SubArray: The zero energy stiffness

create_zero_energy_mode_stiffness(nodes::Union{SubArray,Vector{Int64}}, dof::Int64, CVoigt, Kinv, zStiff)

Creates the zero energy mode stiffness

Arguments

• nodes::Union{SubArray,Vector{Int64}}: The nodes
• dof::Int64: The degree of freedom
• CVoigt::Union{MMatrix, Matrix{Float64}}: The Voigt matrix
• Kinv::SubArray: The inverse shape tensor
• zStiff::SubArray: The zero energy stiffness

Returns

• zStiff::SubArray: The zero energy stiffness

create_zero_energy_mode_stiffness(nodes::Union{SubArray,Vector{Int64}}, dof::Int64, CVoigt::Union{MMatrix,Matrix{Float64}}, angles::SubArray, Kinv::SubArray, zStiff::SubArray)

Creates the zero energy mode stiffness

Arguments

• nodes::Union{SubArray,Vector{Int64}}: The nodes
• dof::Int64: The degree of freedom
• CVoigt::Union{MMatrix, Matrix{Float64}}: The Voigt matrix
• angles::SubArray: The angles
• Kinv::SubArray: The inverse shape tensor
• zStiff::SubArray: The zero energy stiffness

Returns

• zStiff::SubArray: The zero energy stiffness

rotate_fourth_order_tensor(angles::Union{Vector{Float64},Vector{Int64}}, C::Array{Float64,4}, dof::Int64, back::Bool)

Rotates the fourth order tensor

Arguments

• angles::Union{Vector{Float64},Vector{Int64}}: The angles
• C::Array{Float64,4}: The fourth order tensor
• dof::Int64: The degree of freedom
• back::Bool: The back

Returns

• C::Array{Float64,4}: The fourth order tensor

thermal_model_name()

Gives the thermal model name. It is needed for comparison with the yaml input deck.

Arguments

Returns

• name::String: The name of the thermal flow model.

Example:

println(flow_name())
"Thermal Template"

compute_model(datamanager, nodes, thermal_parameter, time, dt)

Calculates the thermal behavior of the material. This template has to be copied, the file renamed and edited by the user to create a new flow. Additional files can be called from here using include and import .any_module or using .any_module. Make sure that you return the datamanager.

Arguments

• datamanager::Data_manager: Datamanager.
• nodes::Union{SubArray,Vector{Int64}}: List of block nodes.
• flow parameter::Dict(String, Any): Dictionary with flow parameter.
• time::Float64: The current time.
• dt::Float64: The current time step.

Returns

• datamanager::Data_manager: Datamanager.

Example:

distribute_heat_flows(datamanager::Module, nodes::Union{SubArray,Vector{Int64}})

Distribute the heat flow Note: is included, because also additional heat flow influences can be included as well here and it might be important for bond-associated formulations.

Arguments

• datamanager::Module: The datamanager
• nodes::Union{SubArray,Vector{Int64}}: The nodes

Returns

• datamanager::Module: The datamanager

calculatespecificvolume(nodes::Int64, nlist::SubArray, coordinates::Union{SubArray,Vector{Float64}}, volume::SubArray, surface_nodes::Union{SubArray,Vector{Bool}})

Calculates the specific volume.

Arguments

• iID::Int64: The index of the node.
• nlist::SubArray: The neighbor list.
• coordinates::Union{SubArray,Vector{Float64}}: The coordinates of the nodes.
• volume::SubArray: The volume of the nodes.
• surface_nodes::Union{SubArray,Vector{Bool}}: The surface nodes.

Returns

• specific_volume::Union{SubArray,Vector{Bool}}: The surface nodes.

thermal_deformation(nodes, alpha, temperature, undeformed_bond, thermal_deformation)

Calculate thermal deformation for a set of nodes.

This function calculates thermal deformation for a specified set of nodes based on the given inputs, including the nodes, thermal expansion coefficient (alpha), nodal temperatures, undeformed bond information, and the resulting thermal deformation.

Arguments

• nodes::Union{SubArray, Vector{Int64}}: A collection of node indices where thermal deformation is to be calculated.

• alpha::Union{Matrix{Float64},Matrix{Int64}}: The thermal expansion matrix, representing the material's response to temperature changes.

• temperature::SubArray: A SubArray containing nodal temperatures for the specified nodes.

• undeformed_bond::SubArray: A SubArray containing information about the undeformed bond geometry.

• thermal_deformation::SubArray: A SubArray to store the calculated thermal deformation for each node.

Returns

• thermal_deformation::SubArray: A SubArray containing the calculated thermal deformation for the specified nodes.

Notes

• The thermal deformation is calculated based on the formula: thermal_deformation[iID] = alpha * temperature[iID] * undeformed_bond[iID].

Example

```julia nodes = [1, 2, 3] alpha = [1.3 0.0; 0.0 1.3] # Example thermal expansion coefficient temperature = SubArray(...) # Provide temperature data undeformedbond = SubArray(...) # Provide undeformed bond geometry data thermaldeformation = SubArray(zeros(3, 3)) # Initialize thermal_deformation with zeros

result = thermaldeformation(nodes, alpha, temperature, undeformedbond, thermal_deformation)

[12] is a prototype with some errors

compute_heat_flow_state_bond_based(nodes::Union{SubArray,Vector{Int64}}, dof::Int64, nlist::SubArray,
  lambda::Union{Float64, Int64}, bond_damage::SubArray, undeformed_bond::SubArray, horizon::SubArray,
  temperature::SubArray, heat_flow::SubArray)

Calculate heat flow based on a bond-based model for thermal analysis.

Arguments

• nodes::Union{SubArray,Vector{Int64}}: An array of node indices for which heat flow should be computed.
• dof::Int64: The degree of freedom, either 2 or 3, indicating whether the analysis is 2D or 3D.
• nlist::SubArray: A SubArray representing the neighbor list for each node.
• lambda::Union{Float64, Int64}: The thermal conductivity.
• apply_print_bed::Bool: A boolean indicating whether the print bed should be applied to the thermal conductivity.
• t_bed::Float64: The thickness of the print bed.
• lambda_bed::Float64: The thermal conductivity of the print bed.
• bond_damage::SubArray: A SubArray representing the damage state of bonds between nodes.
• undeformed_bond::SubArray: A SubArray representing the geometry of the bonds.
• undeformed_bond_length::SubArray: A SubArray representing the undeformed bond length for each bond.
• horizon::SubArray: A SubArray representing the horizon for each node.
• temperature::SubArray: A SubArray representing the temperature at each node.
• heat_flow::SubArray: A SubArray where the computed heat flow values will be stored.

Returns

• heat_flow: updated bond heat flow values will be stored.

Description

This function calculates the heat flow between neighboring nodes based on a bond-based model for thermal analysis [7]. It considers various parameters, including thermal conductivity, damage state of bonds, geometry of bonds, horizons, temperature, and volume. The calculated bond heat flow values are stored in the heat_flow array.