Geometry - Functions

compute_shape_tensors!(nodes::AbstractVector{Int64}, nlist, volume, omega, bond_damage, undeformed_bond, shape_tensor, inverse_shape_tensor)

Calculate the shape tensor and its inverse for a set of nodes in a computational mechanics context.

Arguments

• nodes::AbstractVector{Int64}: A vector of integers representing node IDs.
• dof::Int64: An integer representing the degrees of freedom.
• nlist: A data structure (e.g., a list or array) representing neighboring node IDs for each node.
• volume: A vector or array containing volume information for each node.
• omega: A vector or array containing omega information for each node.
• bond_damage: A data structure representing bond damage for each node.
• undeformed_bond: A data structure representing bond geometries for each node.
• shape_tensor: A preallocated 3D array to store the shape tensors for each node.
• inverse_shape_tensor: A preallocated 3D array to store the inverse shape tensors for each node.

Output

• shape_tensor: An updated shape_tensor array with calculated shape tensors.
• inverse_shape_tensor: An updated inverse_shape_tensor array with calculated inverse shape tensors.

Description

This function calculates the shape tensor and its inverse for a set of nodes in a computational mechanics context. The shape tensor is a key quantity used in continuum mechanics to describe material deformation. It is calculated based on bond damage, bond geometries, volume, and omega information for each node.

For each node in nodes, the function iterates through degrees of freedom (dof) and computes elements of the shape tensor. The inverse of the shape tensor is also calculated and stored in inverse_shape_tensor.

Example

```julia nodes = [1, 2, 3] dof = 3 nlist = [[2, 3], [1, 3], [1, 2]] volume = [0.1, 0.2, 0.3] omega = [0.5, 0.4, 0.6] bonddamage = zeros(Float64, length(nodes), length(nlist[1])) undeformedbond = rand(Float64, length(nodes), length(nlist[1]), dof) shapetensor = zeros(Float64, length(nodes), dof, dof) inverseshape_tensor = zeros(Float64, length(nodes), dof, dof)

function compute_strain(nodes::Union{Base.OneTo{Int64},Vector{Int64}, SubArray}, deformation_gradient, strain)

Calculate strains for specified nodes based on deformation gradients.

Arguments

• nodes::AbstractVector{Int64}: List of nodes
• deformation_gradient: Deformation gradient at current time step (2D or 3D array).

Returns

• Updated strain array containing strains.

This function iterates over the specified nodes and computes strain at each node using the given deformation gradients.

function rotation_tensor(angles::Vector{Float64})

Creates the rotation tensor for 2D or 3D applications. Uses Rotations.jl package.

Arguments

• angles::Vector{Float64}: Vector of angles definede in degrees of length one or three

Returns

• Rotation tensor