ActiveFilaments.jl

ActiveFilaments.jl is a computationally efficient Julia implementation of the mechanical theory of active slender structures found in:

Kaczmarski, B., Moulton, D. E., Kuhl, E. & Goriely, A. Active filaments I: Curvature and torsion generation. Journal of the Mechanics and Physics of Solids 164, 104918 (2022).

Using this package, you can design the geometry and fiber architecture in a slender structure and simulate its deformation due to fibrillar activation. The package provides a library of analysis tools for exploratory biomechanics and soft-robotics research including fast workspace computation for active soft slender structures.

Installation

Run the following command in Julia 1.10.0+:

] add https://github.com/LivingMatterLab/ActiveFilaments.git

Wait for all dependencies to precompile. Slowdowns are possible during precompilation in parallelized BVP solutions if Julia version 1.9.0 or older is used.

Example usage

In the simplest case of uniform material properties and a single fiber ring, we can define an active filament by running

using ActiveFilaments

# Mechanical properties of the ring
E = 1.0e6 # Young's modulus
ν = 0.5   # Incompressible
ρ = 1000.0 # Volumetric density
mech = MechanicalProperties(E, ν)

# Geometry of the ring
L = 1.0 # Length of the filament
R2 = L / 20.0 # Outer radius of the ring
R1 = R2 * 0.8 # Inner radius of the ring
geom = Geometry(R1, R2)

# Fiber architecture of the ring
α2 = pi / 8.0 # Outer helical angle of the fiber architecture
arch = FiberArchitecture(α2)

# Define the filament structure
rings = [Ring(mech, geom, arch)]
filament = AFilament(rings; L = L, ρvol = ρ)

We can then prescribe a piecewise constant activation pattern with three independent 30° activation sectors uniformly spaced around the ring starting from 0° at the +x-axis. Let us choose contractile fiber activations (-2.0, -1.3, 0.0) for the three respective sectors:

activation = [ActivationPiecewiseGamma(3, [-2.0, -1.3, 0.0], 30.0 / 180.0 * pi, 0.0)]  

The deformation due to the above activation without external loading can then be computed as

sol = solveIntrinsic(filament, activation)

The resulting sol structure contains the following interpolating functions: $$\texttt{sol}(Z) = \big[r_X(Z), r_Y(Z), r_Z(Z), d_{1X}(Z), d_{1Y}(Z), d_{1Z}(Z), d_{2X}(Z), d_{2Y}(Z), d_{2Z}(Z), d_{3X}(Z), d_{3Y}(Z), d_{3Z}(Z)\big]$$ For example, evaluating sol at $L / 10$ gives

julia> sol(L / 10.0)
12-element StaticArraysCore.SVector{12, Float64} with indices SOneTo(12):
  0.008311388337878088
  0.009719221098605893
  0.09072971511373011
  0.9421455745518371
 -0.32511595347415
 -0.0816169905655878
  0.294271010395179
  0.9188022897556413
 -0.2630720904634142
  0.16051881133807738
  0.2238346915390569
  0.9613177113058022