Peridynamics.jl public API

BBMaterial()
BBMaterial{Correction}()

A material type used to assign the material of a Body with the standard bond-based formulation of peridynamics.

Possible correction methods are:

• NoCorrection: No correction is applied. (default)
• EnergySurfaceCorrection: The energy based surface correction method of Le and Bobaru (2018) is applied.

Examples

julia> mat = BBMaterial()
BBMaterial{NoCorrection}()

julia> mat = BBMaterial{EnergySurfaceCorrection}()
BBMaterial{EnergySurfaceCorrection}()

BBMaterial{Correction}

Material type for the bond-based peridynamics formulation.

Type Parameters

• Correction: A correction algorithm type. See the constructor docs for more informations.

Allowed material parameters

When using material! on a Body with BBMaterial, then the following parameters are allowed:

• horizon::Float64: Radius of point interactions
• rho::Float64: Density
• E::Float64: Young's modulus
• Gc::Float64: Critical energy release rate
• epsilon_c::Float64: Critical strain

Allowed export fields

When specifying the fields keyword of Job for a Body with BBMaterial, the following fields are allowed:

• position::Matrix{Float64}: Position of each point
• displacement::Matrix{Float64}: Displacement of each point
• velocity::Matrix{Float64}: Velocity of each point
• velocity_half::Matrix{Float64}: Velocity parameter for Verlet time solver
• acceleration::Matrix{Float64}: Acceleration of each point
• b_int::Matrix{Float64}: Internal force density of each point
• b_ext::Matrix{Float64}: External force density of each point
• damage::Vector{Float64}: Damage of each point
• n_active_bonds::Vector{Int}: Number of intact bonds of each point

OSBMaterial()
OSBMaterial{Correction}()

A material type used to assign the material of a Body with the ordinary state-based formulation of peridynamics.

Possible correction methods are:

• NoCorrection: No correction is applied (default)
• EnergySurfaceCorrection: The energy based surface correction method of Le and Bobaru (2018) is applied

Examples

julia> mat = OSBMaterial()
OSBMaterial{NoCorrection}()

julia> mat = OSBMaterial{EnergySurfaceCorrection}()
OSBMaterial{EnergySurfaceCorrection}()

OSBMaterial{Correction}

Material type for the ordinary state-based peridynamics formulation.

Type Parameters

• Correction: A correction algorithm type. See the constructor docs for more informations.

Allowed material parameters

When using material! on a Body with OSBMaterial, then the following parameters are allowed:

• horizon::Float64: Radius of point interactions
• rho::Float64: Density
• E::Float64: Young's modulus
• nu::Float64: Poisson's ratio
• Gc::Float64: Critical energy release rate
• epsilon_c::Float64: Critical strain

Allowed export fields

When specifying the fields keyword of Job for a Body with OSBMaterial, the following fields are allowed:

• position::Matrix{Float64}: Position of each point
• displacement::Matrix{Float64}: Displacement of each point
• velocity::Matrix{Float64}: Velocity of each point
• velocity_half::Matrix{Float64}: Velocity parameter for Verlet time solver
• acceleration::Matrix{Float64}: Acceleration of each point
• b_int::Matrix{Float64}: Internal force density of each point
• b_ext::Matrix{Float64}: External force density of each point
• damage::Vector{Float64}: Damage of each point
• n_active_bonds::Vector{Int}: Number of intact bonds of each point

NOSBMaterial(; maxdmg, maxjacobi, corr)

A material type used to assign the material of a Body with the local continuum consistent (correspondence) formulation of non-ordinary state-based peridynamics.

Keywords

• maxdmg::Float64: Maximum value of damage a point is allowed to obtain. If this value is exceeded, all bonds of that point are broken because the deformation gradient would then possibly contain NaN values. (default: 0.95)
• maxjacobi::Float64: Maximum value of the Jacobi determinant. If this value is exceeded, all bonds of that point are broken. (default: 1.03)
• corr::Float64: Correction factor used for zero-energy mode stabilization. The stabilization algorithm of Silling (2017) is used. (default: 100.0)

Examples

julia> mat = NOSBMaterial()
NOSBMaterial(maxdmg=0.95, maxjacobi=1.03, corr=100.0)

NOSBMaterial

Material type for the local continuum consistent (correspondence) formulation of non-ordinary state-based peridynamics.

Fields

• maxdmg::Float64: Maximum value of damage a point is allowed to obtain. See the constructor docs for more informations.
• maxjacobi::Float64: Maximum value of the Jacobi determinant. See the constructor docs for more informations.
• corr::Float64: Correction factor used for zero-energy mode stabilization. See the constructor docs for more informations.

Allowed material parameters

When using material! on a Body with NOSBMaterial, then the following parameters are allowed:

• horizon::Float64: Radius of point interactions
• rho::Float64: Density
• E::Float64: Young's modulus
• nu::Float64: Poisson's ratio
• Gc::Float64: Critical energy release rate
• epsilon_c::Float64: Critical strain

Allowed export fields

When specifying the fields keyword of Job for a Body with NOSBMaterial, the following fields are allowed:

• position::Matrix{Float64}: Position of each point
• displacement::Matrix{Float64}: Displacement of each point
• velocity::Matrix{Float64}: Velocity of each point
• velocity_half::Matrix{Float64}: Velocity parameter for Verlet time solver
• acceleration::Matrix{Float64}: Acceleration of each point
• b_int::Matrix{Float64}: Internal force density of each point
• b_ext::Matrix{Float64}: External force density of each point
• damage::Vector{Float64}: Damage of each point
• n_active_bonds::Vector{Int}: Number of intact bonds of each point

CKIMaterial()

A material type used to assign the material of a Body with the continuum-kinematics-inspired peridynamics fomulation.

Examples

julia> mat = CKIMaterial()
CKIMaterial()

CKIMaterial

Material type for the continuum-kinematics-inspired peridynamics framework.

Allowed material parameters

When using material! on a Body with CKIMaterial, then the following parameters are allowed:

• horizon::Float64: Radius of point interactions
• rho::Float64: Density
• E::Float64: Young's modulus
• nu::Float64: Poisson's ratio
• Gc::Float64: Critical energy release rate
• epsilon_c::Float64: Critical strain
• C1::Float64: One-neighbor interaction parameter (default: 0.0)
• C2::Float64: Two-neighbor interaction parameter (default: 0.0)
• C3::Float64: Two-neighbor interaction parameter (default: 0.0)

Allowed export fields

When specifying the fields keyword of Job for a Body with CKIMaterial, the following fields are allowed:

• position::Matrix{Float64}: Position of each point
• displacement::Matrix{Float64}: Displacement of each point
• velocity::Matrix{Float64}: Velocity of each point
• velocity_half::Matrix{Float64}: Velocity parameter for Verlet time solver
• acceleration::Matrix{Float64}: Acceleration of each point
• b_int::Matrix{Float64}: Internal force density of each point
• b_ext::Matrix{Float64}: External force density of each point
• damage::Vector{Float64}: Damage of each point
• n_active_one_nis::Vector{Int}: Number of intact one-neighbor interactions of each point

NoCorrection

A correction handler for materials that use the bond system. If NoCorrection is used, then no correction will be applied.

See also BBMaterial, OSBMaterial for further information on how to use the correction type.

EnergySurfaceCorrection

A correction handler for materials that use the bond system. If EnergySurfaceCorrection is used, then the energy based surface correction method of Le and Bobaru (2018) is used.

See also BBMaterial, OSBMaterial for further information on how to use the correction type.

Body(material, position, volume)
Body(material, inp_file)

Constructs a Body for a peridynamics simulation.

Arguments

• material::AbstractMaterial: The material which is defined for the whole body.
• position::AbstractMatrix: A 3×n matrix with the point position of the n points.
• volume::AbstractVector: A vector with the volume of each point.
• inp_file::AbstractString: An Abaqus input file containing meshes, imported with read_inp.

Throws

• Errors if the number of points is not larger than zero
• Errors if position is not a 3×n matrix and has the same length as volume
• Errors if position or volume contain NaN values

Example

julia> Body(BBMaterial(), rand(3, 10), rand(10))
10-point Body{BBMaterial{NoCorrection}}:
  1 point set(s):
    10-point set `all_points`

Body{Material,PointParameters}

Type Parameters

• Material <: AbstractMaterial: Type of the specified material model
• PointParameters <: AbstractPointParameters: Type of the point parameters

Fields

• mat::Material: The material formulation.
• n_points::Int: The number of points that in the body.
• position::Matrix{Float64}: A 3×n_points matrix with the position of the points.
• volume::Vector{Float64}: A vector with the volume of each point.
• fail_permit::Vector{Bool}: A vector that describes if failure is allowed for each point.
• point_sets::Dict{Symbol,Vector{Int}}: A dictionary containing point sets.
• point_params::Vector{PointParameters}: A vector containing all point parameters.
• params_map::Vector{Int}: A vector that maps parameters in point_params to each point.
• single_dim_bcs::Vector{SingleDimBC}: A vector with boundary conditions on a single dimension.
• posdep_single_dim_bcs::Vector{PosDepSingleDimBC}: A vector with position dependent boundary conditions on a single dimension.
• single_dim_ics::Vector{SingleDimIC}: A vector with initial conditions on a single dimension.
• posdep_single_dim_ics::Vector{PosDepSingleDimIC}: A vector with position dependent initial conditions on a single dimension.
• point_sets_precracks::Vector{PointSetsPreCrack}: A vector with predefined point set cracks.

MultibodySetup(body_pairs...)

Setup for a peridynamic simulation with multiple bodies.

Arguments

• body_pairs::Pair{Symbol,<:AbstractBody}: Pairs of :body_name => body_object. The name of the body has to be specified as a Symbol.

Throws

• Errors if less than 2 bodies are defined

Examples

julia> sphere = Body(BBMaterial(), pos_sphere, vol_sphere)
280-point Body{BBMaterial{NoCorrection}}:
  1 point set(s):
    280-point set `all_points`

julia> plate = Body(BBMaterial(), pos_plate, vol_plate)
25600-point Body{BBMaterial{NoCorrection}}:
  1 point set(s):
    25600-point set `all_points`

julia> ms = MultibodySetup(:sphere => sphere, :plate => plate)
25880-point MultibodySetup:
  280-point Body{BBMaterial{NoCorrection}} with name `sphere`
  25600-point Body{BBMaterial{NoCorrection}} with name `plate`

MultibodySetup{Bodies}

Type Parameters

• Bodies <: Tuple: All types of the different bodies in the multibody setup.

Fields

• bodies::Bodies: A Tuple containing all the bodies.
• body_names::Vector{Symbol}: All body names.
• body_idxs::Dict{Symbol,Int}: A Dict to get the body index with the body name.
• srf_contacts::Vector{ShortRangeForceContact}: All short range force contacts.

point_set!(body, set_name, points)
point_set!(fun, body, set_name)

Add a point set to a Body. The points of the set can be either specified directly with the points::AbstractVector argument, or as the result of the filter function fun. By default, a body already contains a point set with the name :all_points, containg a set with all points.

Arguments

• body::AbstractBody: Body where the set will be added.
• set_name::Symbol: Name of the point set.
• points::AbstractVector: Some vector containing the point indices of the set. The indices have to be in bounds with the position and volume of body.
• fun::Function: Function for filtering points. This function accepts only one positional argument and will be used in a findall call. Depending on the argument name, a different input will be processed:
  • x: The function will receive the x-coordinate of each point in position of body:

    points = findall(fun, @view(position[1, :]))

  • y: The function will receive the y-coordinate of each point in position of body:

    points = findall(fun, @view(position[2, :]))

  • z: The function will receive the z-coordinate of each point in position of body:

    points = findall(fun, @view(position[3, :]))

  • p: The function will receive the a vector containing each dimension of each point in position of body:

    points = findall(fun, eachcol(position))

Throws

• Errors if a point set with the same set_name already exists.
• Errors if points are not in bounds with position and volume of the body.

Examples

Add a point set to body with all points that have a x-corrdinate larger than zero:

julia> point_set!(x -> x > 0, body, :larger_than_zero)

julia> point_sets(body)
Dict{Symbol, Vector{Int64}} with 2 entries:
  :larger_than_zero => [6, 7, 8, 9, 10, 16, 17, 18, 19, 20  …  9…
  :all_points       => [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  991, 9…

Add a point set to body with all points that are positioned inside a sphere with radius r around the center. Note that the do-syntax can be used, as fun is the first argument of point_set!:

julia> point_set!(body, :inside_sphere) do p
           sqrt(p[1]^2 + p[2]^2 + p[3]^2) ≤ r
       end

julia> point_sets(body)
Dict{Symbol, Vector{Int64}} with 2 entries:
  :larger_than_zero => [6, 7, 8, 9, 10, 16, 17, 18, 19, 20  …  9…
  :inside_sphere    => [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  991, 9…

point_sets(body)

Returns all point sets of body.

Arguments

• body::AbstractBody: Body.

Example

julia> body = Body(BBMaterial(), rand(3,100), rand(100))
100-point Body{BBMaterial{NoCorrection}}:
  100-point set `all_points`

julia> point_set!(body, :set_a, 1:10) # first ten points

julia> Peridynamics.point_sets(body)
Dict{Symbol, Vector{Int64}} with 2 entries:
  :all_points => [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  91, 92, 93, 94, 95, 96, 97, 98, 9…
  :set_a      => [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

failure_permit!(body, fail_permit)
failure_permit!(body, set_name, fail_permit)

Set the failure permission for points of a body. By default, failure is allowed for all points. If no set_name is specified, then the permission fail_permit is set for all points of the body.

Arguments

• body::AbstractBody: Body where the failure permission will be set.
• set_name::Symbol: The name of a point set of this body.
• fail_permit::Bool: If true, failure is allowed, and if false then no bonds of this point are allowed to break during the simulation.

Throws

• Errors if the body does not contain a set with set_name.

Examples

julia> failure_permit!(body, false)

julia> body
1000-point Body{BBMaterial{NoCorrection}}:
  1 point set(s):
    1000-point set `all_points`
  1000 points with no failure permission

material!(body, set_name; kwargs...)
material!(body; kwargs...)

Assign material point parameters to points of body. If no set_name is specified, then the parameters will be set for all points of the body.

Arguments

• body::AbstractBody: Body.
• set_name::Symbol: The name of a point set of this body.

Keywords

Allowed keywords depend on the selected material model. Please look at the documentation of the material you specified when creating the body. The default material keywords are:

• horizon::Float64: Radius of point interactions
• rho::Float64: Density
• E::Float64: Young's modulus
• nu::Float64: Poisson's ratio
• Gc::Float64: Critical energy release rate
• epsilon_c::Float64: Critical strain

Throws

• Errors if a kwarg is not eligible for specification with the body material.

Example

julia> material!(body; horizon=3.0, E=2.1e5, rho=8e-6, Gc=2.7)

julia> body
1000-point Body{BBMaterial{NoCorrection}}:
  1 point set(s):
    1000-point set `all_points`
  1 point parameter(s):
    Parameters BBMaterial: δ=3.0, E=210000.0, nu=0.25, rho=8.0e-6, Gc=2.7

velocity_bc!(fun, body, set_name, dim)

Specifies velocity boundary conditions for points of the set set_name in body. The value of the boundary condition is calculated with the function fun at every time step.

Arguments

• fun::Function: Condition function for the calculation of a value, should return a Float64. If the condition function returns a NaN, then this value is ignored, which can be used to turn conditions off after a specified period of time. This function accepts one ore two positional arguments and is aware of the argument names. Possible arguments and names:
  • fun(t): The function will receive the current time t at every time step. This makes it possible to specify conditions that change over time.
  • fun(p, t): This function will be processed for every point of set_name and receives the reference position of a point as SVector{3} and the current time t at every time step. This makes it possible to specify conditions that also depend on the position of a point.
• body::AbstractBody: Body the condition is specified on.
• set_name::Symbol: The name of a point set of this body.
• dim::Union{Integer,Symbol}: Direction of the condition, either specified as Symbol or integer.
  • x-direction: :x or 1
  • y-direction: :y or 2
  • z-direction: :z or 3

Throws

• Errors if the body does not contain a set with set_name.
• Errors if the direction is not correctly specified.
• Errors if function is not suitable as condition function and has the wrong arguments.

Example

julia> velocity_bc!(t -> 2.0, body, :all_points, 1)

julia> velocity_bc!((p,t) -> p[1] * t, body, :all_points, :y)

julia> velocity_bc!(t -> t > 0.00001 ? 1.0 : NaN, body, :all_points, :z)

julia> body
1000-point Body{BBMaterial{NoCorrection}}:
  1 point set(s):
    1000-point set `all_points`
  3 boundary condition(s):
    BC on velocity: point_set=all_points, dim=1
    BC on velocity: point_set=all_points, dim=3
    Pos.-dep. BC on velocity: point_set=all_points, dim=2

velocity_ic!(body, set_name, dim, value)
velocity_ic!(fun, body, set_name, dim)

Specifies velocity initial conditions for points of the set set_name in body. The value of the initial condition is specified before time integration. If a function fun is specified, then the value is with that function.

Arguments

• body::AbstractBody: Body the condition is specified on.
• set_name::Symbol: The name of a point set of this body.
• dim::Union{Integer,Symbol}: Direction of the condition, either specified as Symbol or integer.
  • x-direction: :x or 1
  • y-direction: :y or 2
  • z-direction: :z or 3
• value::Real: Value that is specified before time integration.
• fun::Function: Condition function for the calculation of a value, should return a Float64. If the condition function returns a NaN, then this value is ignored, which can be used to turn off the condition for a specified position. This function accepts one ore two positional arguments and is aware of the argument names. Possible arguments and names:
  • fun(p): The function will receive the reference position p of a point as SVector{3}.

Throws

• Errors if the body does not contain a set with set_name.
• Errors if the direction is not correctly specified.
• Errors if function is not suitable as condition function and has the wrong arguments.

Example

julia> velocity_ic!(body, :all_points, :x, -100.0)

julia> body
1000-point Body{BBMaterial{NoCorrection}}:
  1 point set(s):
    1000-point set `all_points`
  1 initial condition(s):
    IC on velocity: point_set=all_points, dim=1

forcedensity_bc!(fun, body, set, dim)

Specifies force density boundary conditions for points of the set set_name in body. The value of the boundary condition is calculated with the function fun at every time step.

Arguments

• fun::Function: Condition function for the calculation of a value, should return a Float64. If the condition function returns a NaN, then this value is ignored, which can be used to turn conditions off after a specified period of time. This function accepts one ore two positional arguments and is aware of the argument names. Possible arguments and names:
  • fun(t): The function will receive the current time t at every time step. This makes it possible to specify conditions that change over time.
  • fun(p, t): This function will be processed for every point of set_name and receives the reference position of a point as SVector{3} and the current time t at every time step. This makes it possible to specify conditions that also depend on the position of a point.
• body::AbstractBody: Body the condition is specified on.
• set_name::Symbol: The name of a point set of this body.
• dim::Union{Integer,Symbol}: Direction of the condition, either specified as Symbol or integer.
  • x-direction: :x or 1
  • y-direction: :y or 2
  • z-direction: :z or 3

Throws

• Errors if the body does not contain a set with set_name.
• Errors if the direction is not correctly specified.
• Errors if function is not suitable as condition function and has the wrong arguments.

Example

julia> forcedensity_bc!(t -> 8000.0, body, :all_points, :x)

julia> forcedensity_bc!((p,t) -> p[1] * t, body, :all_points, :y)

julia> forcedensity_bc!(t -> t > 0.00001 ? 8000.0 : NaN, body, :all_points, :z)

julia> body
1000-point Body{BBMaterial{NoCorrection}}:
  1 point set(s):
    1000-point set `all_points`
  3 boundary condition(s):
    BC on force density: point_set=all_points, dim=1
    BC on force density: point_set=all_points, dim=3
    Pos.-dep. BC on force density: point_set=all_points, dim=2

precrack!(body, set_a, set_b; update_dmg=true)

Creates a crack between two point sets by prohibiting interaction between points of different point sets. The points in set_a are not allowed to interact with points in set_b.

Arguments

• body::AbstractBody: Body.
• set_a::Symbol: The name of a point set of this body.
• set_b::Symbol: The name of a point set of this body.

Keywords

• update_dmg::Bool: If true, the material points involved in the predefined crack are initially damaged. If false, the bonds involved are deleted and the material points involved with the predefined crack are not damaged in the reference results. (default: true)

Throws

• Errors if the body does not contain sets with name set_a and set_b.
• Errors if the point sets intersect and a point is included in both sets.

Example

julia> point_set!(body, :a, 1:2)

julia> point_set!(body, :b, 3:4)

julia> precrack!(body, :a, :b)

julia> body
1000-point Body{BBMaterial{NoCorrection}}:
  3 point set(s):
    1000-point set `all_points`
    2-point set `a`
    2-point set `b`
  1 predefined crack(s)

contact!(multibody_setup, name_body_a, name_body_b; kwargs...)

Defines a short range force contact between body name_body_a and name_body_b in the MultibodySetup multibody_setup.

Arguments

• multibody_setup::MultibodySetup: MultibodySetup.
• name_body_a::Symbol: The name of a body in this multibody setup.
• name_body_b::Symbol: The name of a body in this multibody setup.

Keywords

• radius::Float64: Contact search radius. If a the distance of a point in body name_body_a and a point in body name_body_b is lower than this radius, a contact force is calculated. This radius should be in the order of the point spacing of a point cloud.
• penalty_factor::Float64: Penalty factor for the short range force contact algorithm. (default: 1e12)

Throws

• Errors if multibody_setup does not contain bodies with name name_body_a and name_body_b.
• Errors if the keyword radius is not specified or radius ≤ 0.
• Errors if penalty_factor ≤ 0.

Examples

julia> ms = MultibodySetup(:a => body_a, :b => body_b)
2000-point MultibodySetup:
  1000-point Body{BBMaterial{NoCorrection}} with name `b`
  1000-point Body{BBMaterial{NoCorrection}} with name `b`

julia> contact!(ms, :a, :b; radius=0.001)

julia> ms
2000-point MultibodySetup:
  1000-point Body{BBMaterial{NoCorrection}} with name `b`
  1000-point Body{BBMaterial{NoCorrection}} with name `b`
  2 short range force contact(s)

uniform_box(lx, ly, lz, ΔX0; kwargs...)

Creates a grid of uniformly distributed points in a cuboid with lengths lx, ly and lz and point spacing ΔX0.

Arguments

• lx::Real: Length in x-dimension.
• ly::Real: Length in y-dimension.
• lz::Real: Length in z-dimension.
• ΔX0::Real: Spacing of the points.

Keywords

• center: The coordinates of the center of the cuboid. Default: (0, 0, 0)

Returns

• position::Matrix{Float64}: A 3×n_points matrix with the position of the points.
• volume::Vector{Float64}: A vector with the volume of each point.

Examples

julia> position, volume = uniform_box(10, 10, 10, 2);

julia> position
3×125 Matrix{Float64}:
 -4.0  -2.0   0.0   2.0   4.0  -4.0  -2.0  …  0.0  2.0  4.0  -4.0  -2.0  0.0  2.0  4.0
 -4.0  -4.0  -4.0  -4.0  -4.0  -2.0  -2.0     2.0  2.0  2.0   4.0   4.0  4.0  4.0  4.0
 -4.0  -4.0  -4.0  -4.0  -4.0  -4.0  -4.0     4.0  4.0  4.0   4.0   4.0  4.0  4.0  4.0

julia> volume
125-element Vector{Int64}:
 8
 8
 8
 8
 ⋮
 8
 8
 8
 8

uniform_sphere(diameter, ΔX0; kwargs...)

Creates a grid of uniformly distributed points in a sphere with a specific diameter and the point spacing ΔX0. Due to the uniform point spacings, edges on the surface of the sphere can occur.

Arguments

• diameter::Real: Diameter of the sphere.
• ΔX0::Real: Spacing of the points.

Keywords

• center: The coordinates of the center of the sphere. Default: (0, 0, 0)

Returns

• position::Matrix{Float64}: A 3×n_points matrix with the position of the points.
• volume::Vector{Float64}: A vector with the volume of each point.

Examples

julia> position, volume = uniform_sphere(10, 2);

julia> position
3×81 Matrix{Float64}:
 -2.0   0.0   2.0  -2.0   0.0   2.0  -2.0  …   0.0   2.0  -2.0  0.0  2.0  -2.0  0.0  2.0
 -2.0  -2.0  -2.0   0.0   0.0   0.0   2.0     -2.0  -2.0   0.0  0.0  0.0   2.0  2.0  2.0
 -4.0  -4.0  -4.0  -4.0  -4.0  -4.0  -4.0      4.0   4.0   4.0  4.0  4.0   4.0  4.0  4.0

julia> volume
81-element Vector{Int64}:
 8
 8
 8
 8
 8
 ⋮
 8
 8
 8
 8
 8

uniform_cylinder(diameter::Real, height::Real, ΔX0::Real; kwargs...)

Creates a grid of uniformly distributed points in a cylindrical shape with a specific height in z-dimension, a diameter and the point spacing ΔX0. Due to the uniform point spacings, edges on the surface of the cylinder can occur.

Arguments

• diameter::Real: Diameter of the cylinder.
• height::Real: Height of the cylinder.
• ΔX0::Real: Spacing of the points.

Keywords

• center: The coordinates of the center of the cylinder. Default: (0, 0, 0)

Returns

• position::Matrix{Float64}: A 3×n_points matrix with the position of the points.
• volume::Vector{Float64}: A vector with the volume of each point.

Examples

julia> position, volume = uniform_cylinder(5, 10, 2);

julia> position
3×20 Matrix{Float64}:
 -1.0   1.0  -1.0   1.0  -1.0   1.0  -1.0  …   1.0  -1.0  1.0  -1.0   1.0  -1.0  1.0
 -1.0  -1.0   1.0   1.0  -1.0  -1.0   1.0     -1.0   1.0  1.0  -1.0  -1.0   1.0  1.0
 -4.0  -4.0  -4.0  -4.0  -2.0  -2.0  -2.0      2.0   2.0  2.0   4.0   4.0   4.0  4.0

julia> volume
20-element Vector{Int64}:
 8
 8
 8
 8
 8
 ⋮
 8
 8
 8
 8
 8

round_sphere(diameter, ΔX0; kwargs...)

Creates a grid of points distributed in a smooth sphere without edges on the surface with a specific diameter and the point spacing ΔX0. Internally, some parts of TrixiParticles.jl were copied and adapted for this function.

Arguments

• diameter::Real: Diameter of the sphere.
• ΔX0::Real: Spacing of the points.

Keywords

• center: The coordinates of the center of the sphere. Default: (0, 0, 0)

Returns

• position::Matrix{Float64}: A 3×n_points matrix with the position of the points.
• volume::Vector{Float64}: A vector with the volume of each point.

Examples

julia> position, volume = round_sphere(10, 2);

julia> position
3×63 Matrix{Float64}:
 0.0  1.74586  0.539501  -1.41243  -1.41243  …  -1.95518   -0.48289   1.35303   0.0
 0.0  0.0      1.66041    1.02619  -1.02619     -0.941566  -2.11568  -1.69664   0.0
 2.0  0.97569  0.97569    0.97569   0.97569     -3.36017   -3.36017  -3.36017  -4.0

julia> volume
63-element Vector{Float64}:
 8.311091676163475
 8.311091676163475
 8.311091676163475
 8.311091676163475
 8.311091676163475
 ⋮
 8.311091676163475
 8.311091676163475
 8.311091676163475
 8.311091676163475

round_cylinder(diameter::Real, height::Real, ΔX0::Real; kwargs...)

Creates a grid of points distributed in a cylindrical shape with a specific height in z-dimension, a diameter and the point spacing ΔX0. Due to a concentric point distribution in the x-y-plane, there are no sharp edges that appear on the surface of the cylinder.

Arguments

• diameter::Real: Diameter of the cylinder.
• height::Real: Height of the cylinder.
• ΔX0::Real: Spacing of the points.

Keywords

• center: The coordinates of the center of the cylinder. Default: (0, 0, 0)

Returns

• position::Matrix{Float64}: A 3×n_points matrix with the position of the points.
• volume::Vector{Float64}: A vector with the volume of each point.

Examples

julia> position, volume = round_cylinder(5, 10, 2);

julia> position
3×30 Matrix{Float64}:
  1.5   0.463525  -1.21353   -1.21353   …  -1.21353   -1.21353    0.463525
  0.0   1.42658    0.881678  -0.881678      0.881678  -0.881678  -1.42658
 -5.0  -5.0       -5.0       -5.0           5.0        5.0        5.0

julia> volume
30-element Vector{Int64}:
 13.089969389957473
 13.089969389957473
 13.089969389957473
 13.089969389957473
 13.089969389957473
  ⋮
 13.089969389957473
 13.089969389957473
 13.089969389957473
 13.089969389957473

n_points(body)

Returns the total number of points in a body.

Arguments

• body::Body: Body.

Returns

• n_points::Int: The number of points in the body.

Examples

julia> body = Body(BBMaterial(), pos, vol)
1000-point Body{BBMaterial{NoCorrection}}:
  1 point set(s):
    1000-point set `all_points`

julia> n_points(body)
1000

n_points(multibody_setup)

Returns the total number of points in a multibody setup.

Arguments

• multibody_setup::MultibodySetup: MultibodySetup.

Returns

• n_points::Int: The sum of all points from all bodies in the multibody setup.

Examples

julia> ms = MultibodySetup(:a => body_a, :b => body_b)
2000-point MultibodySetup:
  1000-point Body{BBMaterial{NoCorrection}} with name `a`
  1000-point Body{BBMaterial{NoCorrection}} with name `b`

julia> n_points(ms)
2000

read_inp(file::String)

Read Abaqus .inp-file and convert meshes to a point cloud with the help of the AbaqusReader.jl package. Every element is converted to a point. The center of the element becomes the position of the point and the element volume becomes the point volume. Element sets defined in Abaqus are converted to corresponding point sets.

Currently supported mesh elements: [:Tet4, :Hex8]

Arguments

• file::String: Path to Abaqus .inp-file

Returns

• position::Matrix{Float64}: Point position (midpoint of every element)
• volume::Vector{Float64}: Point volume (volume of every element)
• point_sets: Element sets defined in the .inp-file

mpi_isroot()

Helper function that returns a bool indicating if a process is the MPI root process. It can be safely used even for multithreading simulations, as it is always true if the package is started in a normal Julia environment which is not started by MPI.

force_mpi_run!()

Helper function to force the usage of the MPI backend. After this function is called, all following simulations will use MPI.

force_threads_run!()

Helper function to force the usage of the multithreading backend. After this function is called, all following simulations will use multithreading.

enable_mpi_timers!()

Helper function to enable timers defined with the TimerOutputs for simulations with the MPI backend. The results of the timers then will be exported into the specified path of a Job. By default, not timers will be used with MPI simulations. It can be safely used with multithreading.

See also disable_mpi_timers!.

disable_mpi_timers!()

Helper function to disable timers defined with the TimerOutputs for simulations with the MPI backend. It is mainly used to reset the behaviour after a call of enable_mpi_timers!. It can be safely used with multithreading.

enable_mpi_progress_bars!()

Helper function to enable progress bars with MPI simulations on a personal computer. After this function is called, progress bars are beeing shown with MPI simulations like with multithreading simulations. This behavior can be reset to default with reset_mpi_progress_bars!.

reset_mpi_progress_bars!()

After this function is called, progress bars are again disabled on MPI simulations (standard setting). This will reset the behavior after a call of enable_mpi_progress_bars!.

@mpitime expression

Time the expression if the mpi rank is zero. Lowers to:

if mpi_isroot()
    @time expression
else
    expression
end

See also: mpi_isroot.

@mpiroot [option] expression

Run the code if the mpi rank is zero. Lowers to something similar as:

if mpi_isroot()
    expression
end

Options

• :wait: All MPI ranks will wait until the root rank finishes evaluating expression.

See also: mpi_isroot.

VelocityVerlet(; kwargs...)

Time integration solver for the Velocity Verlet algorithm. Specify either the number of steps or the time the simulation should cover.

Keywords

• time::Real: The total time the simulation will cover. If this keyword is specified, the keyword steps is no longer allowed. (optional)
• steps::Int: Number of calculated time steps. If this keyword is specified, the keyword time is no longer allowed. (optional)
• stepsize::Real: Manually specify the size of the time step. (optional)
• safety_factor::Real: Safety factor for step size to ensure stability. (default: 0.7)

Throws

• Errors if both time and steps are specified as keywords.
• Errors if neither time nor steps are specified as keywords.
• Errors if safety_factor < 0 or safety_factor > 1.

Example

julia> VelocityVerlet(steps=2000)
VelocityVerlet:
  n_steps        2000
  safety_factor  0.7

julia> VelocityVerlet(time=0.001)
VelocityVerlet:
  end_time       0.001
  safety_factor  0.7

julia> VelocityVerlet(steps=2000, stepsize=0.0001)
┌ Warning: stepsize specified! Please be sure that the CFD-condition holds!
└ @ Peridynamics ~/Code/Peridynamics.jl/src/time_solvers/velocity_verlet.jl:66
VelocityVerlet:
  n_steps        2000
  Δt             0.0001
  safety_factor  0.7

DynamicRelaxation(; kwargs...)

Time integration solver for the adaptive dynamic relaxation algorithm used for quasi-static simulations.

Keywords

• steps::Int: Number of calculated time steps. If this keyword is specified, the keyword time is no longer allowed.
• stepsize::Real: Manually specify the size of the time step. (default: 1.0)
• damping_factor::Real: Damping factor to increase the value in the mass matrix. (default: 1.0)

Throws

• Errors if steps < 0.
• Errors if stepsize < 0.
• Errors if damping_factor < 0.

Example

julia> DynamicRelaxation(steps=1000)
DynamicRelaxation:
  n_steps  1000
  Δt       1
  Λ        1

julia> DynamicRelaxation(steps=1000, damping_factor=2)
DynamicRelaxation:
  n_steps  1000
  Δt       1
  Λ        2

Job(spatial_setup, time_solver; kwargs...)

A type that contains all the information necessary for a peridynamic simulation. You can submit a Job to start the simulation.

Arguments

• spatial_setup: A Body or MultibodySetup.
• time_solver: VelocityVerlet or DynamicRelaxation.

Keywords

• path::String: Path to store results. If it does not exist yet it will be created during the simulation. (optional)

• freq::Int: Output frequency of result files. A output file will be written every freq-th time step. (default: 10)

• fields: Fields that should be exported to output files. Allowed keywords depend on the selected material model. Please look at the documentation of the material you specified when creating the body. (default: (:displacement, :damage))

  If spatial_setup is a Body, the fields keyword can be of the form:

  • fields::Symbol: A symbol specifying a single output field.
  • fields::NTuple{N,Symbol} where N: A Tuple specifying multiple output fields.
  • fields::Vector{Symbol}: A Vector specifying multiple output fields.

  If spatial_setup is a MultibodySetup, the fields keyword can also be specified for every body separately:

  • fields::Dict{Symbol,T}: A Dictionary containing the fields separately for every body. T is here every possible type of the fields keyword that can be used for a single body.

Example

julia> job = Job(multibody_setup, verlet_solver; path="my_results/sim1")
Job:
  spatial_setup  25880-point MultibodySetup
  time_solver    VelocityVerlet(n_steps=2000, safety_factor=0.7)
  options        export_allowed=true, freq=10

submit(job::Job; quiet=false)

Run the simulation by submitting the job.

Arguments

• job::Job: Job that contains all defined parameters and conditions.

Keywords

• quiet::Bool: If true, no outputs are printed in the terminal. (default: false)

read_vtk(file::AbstractString)

Read vtu or pvtu file containing simulation results of a time step.

Arguments

• file::String: Path to VTK file in vtu or pvtu format

Returns

• Dict{String, VecOrMat{Float64}}: Simulation results as a dictionary

Examples

julia> read_vtk("results/fragmenting_cylinder/vtk/timestep_000520.pvtu")
Dict{Symbol, VecOrMat{Float64}} with 4 entries:
  :position     => [0.0263309 0.027315 … 0.0293543 0.030339; 0.000292969 0.000294475…
  :displacement => [0.00583334 0.00581883 … 0.00585909 0.00584271; -0.000162852 -0.0…
  :damage       => [0.616071, 0.569343, 0.528571, 0.463415, 0.438776, 0.553571, 0.56…
  :time         => [9.69363e-5]

process_each_export(f, vtk_path; kwargs...)
process_each_export(f, job; kwargs...)

A function for postprocessing every exported file. This function works with multithreading and MPI and determines the backend exactly like the submit function.

Arguments

• f::Function: The processing function with signature f(r0, r, id).
  • r0: The results of read_vtk for the exported file of the reference results.
  • r: The results of read_vtk for a time step.
  • id::Ind: An ID indicating the number of the exported file (counted from 1, starting with the reference file).
• vtk_path::AbstractString: A path that should contain the export results of a simulation.
• job::Job: A job object. The path of the VTK files will then be processed from the job options.

Keywords

• serial::Bool: If true, all results will be processed in the correct order of the time steps and on a single thread, cf. the MPI root rank.