Helper - Functions

check_inf_or_nan(array, msg)

Checks if the sum of the array is finite. If not, an error is raised.

Arguments

• array: The array to check.
• msg: The error message to raise.

Returns

• Bool: true if the sum of the array is finite, false otherwise.

compute_surface_nodes_and_connections(points::Union{Matrix{Float64},Matrix{Int64}},
                                           poly, free_surfaces::Vector{Int64})

Computes the points which are connected free surfaces (()). This function is used for contact search purposes. The free surface nodes are used to compute the nearest neighbors. The connections and underlying points are needed for the contact algorithm. They are a subset of the surface points to create the polyhedron and the only ones which can be in contact.

Arguments

• points::Union{Matrix{Float64},Matrix{Int64}}: Points which form the polyhedron.
• poly: Polyhedron object.
• free_surfaces::Vector{Int64}: List of the free surfaces of the polyhedron.

Returns

• connections: Tthe connections to the free surfaces. There can be more surface points than connections.

create_centroid_and_search_radius(coor::Union{Matrix{Float64},Matrix{Int64}},
                                  el_topology::Matrix{Int64},
                                  dof::Int64,
                                  fu)

Computes the centroid and Contact Radius for each element in a given mesh.

Arguments

• coor::Union{Matrix{Float64}, Matrix{Int64}}: A matrix of size (N x dof), where each row represents the coordinates of a point in the space.
• el_topology::Matrix{Int64}: A matrix of size (M x num_nodes), where each row contains the indices of points that define an element.
• dof::Int64: The number of spatial dimensions (degrees of freedom), e.g., 2 for 2D and 3 for 3D.
• fu: A function of four point 2D surface or eight point 3D volume.

Returns

• el_centroid::Matrix{Float64}: A matrix of size (M × dof), where each row represents the centroid of an element.
• search_radius::Vector{Float64}: A vector of size M, where each entry is the maximum distance from the element centroid to any of its nodes.

find_files_with_ending(folder_path::AbstractString, file_ending::AbstractString)

Returns a list of files in folder_path that end with file_ending.

Arguments

• folder_path::AbstractString: The path to the folder.
• file_ending::AbstractString: The ending of the files.

Returns

• file_list::Vector{String}: The list of files that end with file_ending.

find_indices(vector, what)

Returns the indices of vector that are equal to what.

Arguments

• vector::Vector: The vector to search in.
• what: The value to search for.

Returns

• indices::Vector: The indices of vector that are equal to what.

find_inverse_bond_id(nlist::Vector{Vector{Int64}})

Finds the inverse of the bond id in the nlist.

Arguments

• nlist::Vector{Vector{Int64}}: The nlist to find the inverse of.

Returns

• inverse_nlist::Vector{Dict{Int64,Int64}}: The inverse nlist.

get_active_update_nodes(active::Vector{Bool}, update_list::Vector{Bool}, nodes::Vector{Int64}, index::Vector{Int64})

Returns the active nodes and the update nodes.

Arguments

• active::Vector{Bool}: The active vector.
• update_list::Vector{Bool}: The update vector.
• nodes::Vector{Int64}: The vector of nodes.
• index::Vector{Int64}: Pre allocated Vector.

Returns

• update_nodes::Vector{Int64}: The nodes of update that are true.

get_block_nodes(block_ids, nnodes)

Returns a dictionary mapping block IDs to collections of nodes.

Arguments

• block_ids::Vector{Int64}: A vector of block IDs
• nnodes::Int64: The number of nodes

Returns

• block_nodes::Dict{Int64,Vector{Int64}}: A dictionary mapping block IDs to collections of nodes

get_fourth_order(CVoigt, dof)

Constructs a symmetric fourth-order tensor from a Voigt notation vector. It uses Tensors.jl package.

This function takes a Voigt notation vector CVoigt and the degree of freedom dof to create a symmetric fourth-order tensor. The CVoigt vector contains components that represent the tensor in Voigt notation, and dof specifies the dimension of the tensor.

Arguments

• CVoigt::Matrix{Float64}: A vector containing components of the tensor in Voigt notation.
• dof::Int64: The dimension of the resulting symmetric fourth-order tensor.

Returns

• SymmetricFourthOrderTensor{dof}: A symmetric fourth-order tensor of dimension dof.

Example

```julia CVoigt = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0] dof = 3 result = getfourthorder(CVoigt, dof)

get_hexagon(coor::Union{Matrix{Float64},Matrix{Int64}}, topo::Vector{Int64})

Description

This function gives the hexahedron model back to compute centroids of this surface and check if a point lies inside. The el_topology has to be transformed from PeriLab notation, to avoid overlapping.

Arguments

• coor::Union{Matrix{Float64},Matrix{Int64}}: Coordinates.
• topo::Vector{Int64}: el_topology of an element.

Returns

• Hexahedron: eight point hexahedron.

get_ring(coor::Union{Matrix{Float64},Matrix{Int64}}, topo::Vector{Int64})

Description

This function gives the ring model back to compute centroids of this surface and check if a point lies inside. The el_topology has to be transformed from PeriLab notation, to avoid overlapping.

Arguments

• coor::Union{Matrix{Float64},Matrix{Int64}}: Coordinates.
• topo::Vector{Int64}: el_topology of an element.

Returns

• Ring: four point closed surface.

invert(A::Union{Matrix{Float64},Matrix{Int64}}, error_message::String="Matrix is singular")

Invert a n x n matrix. Throws an error if A is singular.

Arguments

• A::Union{Matrix{Float64},Matrix{Int64}}: A n x n matrix.
• error_message::String="Matrix is singular": The error message returned if A is singular.

Returns

• inverted matrix or nothing if not inverable.

matrix_style(A)

Include a scalar or an array and reshape it to style needed for LinearAlgebra package

Arguments

• A: The array or scalar to reshape

Returns

• Array: The reshaped array

 matrix_to_vector(mat::Union{Matrix{Float64},Matrix{Int64}})

Transforming a matrix representation in a Vector{Vector} representation.

Arguments

• mat::Union{Matrix{Float64},Matrix{Int64}}: Points which form the polyhedron.

Returns

• ``: transformed data

progress_bar(rank::Int64, nsteps::Int64, silent::Bool)

Create a progress bar if the rank is 0. The progress bar ranges from 1 to nsteps + 1.

Arguments

• rank::Int64: An integer to determine if the progress bar should be created.
• nsteps::Int64: The total number of steps in the progress bar.
• silent::Bool: de/activates the progress bar

Returns

• ProgressBar or UnitRange: If rank is 0, a ProgressBar object is returned. Otherwise, a range from 1 to nsteps + 1 is returned.

qdim(order::Int64, dof::Int64)

Calculate the number of terms in a polynomial expansion up to a specified accuracy order. Simplied first complex loop in Peridigm correspondence::computeLagrangianGradientWeights. In the unit test this values where tested.

Arguments

• order::Int64: The accuracy order of the polynomial expansion.

Returns

• Int64: The total number of terms in the polynomial expansion.

Description

This function calculates the number of terms in a polynomial expansion up to the specified accuracy order using an analytical formula derived from combinatorial considerations. The function iterates over each order from 1 to the specified order and calculates the sum of binomial coefficients according to the formula: qdim(order) = Σ(i=1 to order) [(i+2)! / (2! * i!)]

rotate(nodes::Union{SubArray,Vector{Int64}}, dof::Int64, matrix::Union{SubArray,Array{Float64,3}}, angles::SubArray, back::Bool)

Rotates the matrix.

Arguments

• nodes::Union{SubArray,Vector{Int64}}: List of block nodes.
• matrix::Union{SubArray,Array{Float64,3}}: Matrix.
• rot::SubArray: Rotation tensor.
• back::Bool: Back.

Returns

• matrix::SubArray: Matrix.

rotate_second_order_tensor(angles::Union{Vector{Float64},Vector{Int64}}, tensor::Matrix{Float64}, dof::Int64, back::Bool)

Rotates the second order tensor.

Arguments

• angles::Union{Vector{Float64},Vector{Int64}}: Angles.
• tensor::Matrix{Float64}: Second order tensor.
• dof::Int64: Degree of freedom.
• back::Bool: Back.

Returns

• tensor::Matrix{Float64}: Second order tensor.