# PyElastica Examples

This directory contains number of examples of elastica. Each [example cases](#example-cases) are stored in separate subdirectories, containing case descriptions, run file, and all other data/script necessary to run. More [advanced cases](#advanced-cases) are stored in separate repository with its description.

## Case Examples

Some examples provide additional files or links to published paper for a complete description. Examples can serve as a starting template for customized usages.

• [AxialStretchingCase](./AxialStretchingCase)

  • __Purpose__: Physical convergence test of simple stretching rod.

  • __Features__: CosseratRod, OneEndFixedRod, EndpointForces

• [TimoshenkoBeamCase](./TimoshenkoBeamCase)

  • __Purpose__: Physical convergence test of simple Timoshenko beam.

  • __Features__: CosseratRod, OneEndFixedRod, EndpointForces,

• [FlexibleSwingingPendulumCase](./FlexibleSwingingPendulumCase)

  • __Purpose__: Physical convergence test of simple pendulum with flexible rod.

  • __Features__: CosseratRod, HingeBC, GravityForces

• [ContinuumSnakeCase](./ContinuumSnakeCase)

  • __Purpose__: Demonstrate simple case of modeling biological creature using PyElastica. The example uses friction to create slithering snake, and optimize the speed using [CMA](CMA-ES/pycma).

  • __Features__: CosseratRod, MuscleTorques, RodPlaneContactWithAnisotropicFriction, Gravity, CMA Optimization

• [ContinuumSnakeWithLiftingWaveCase](./ContinuumSnakeWithLiftingWaveCase)

  • __Purpose__: Demonstrate simple case of modeling biological creature using PyElastica. The example uses friction to create slithering snake with lift.

  • __Features__: CosseratRod, MuscleTorquesLifting(custom implemented), SnakeRodPlaneContact(custom implemented), Gravity

• [MuscularSnake](./MuscularSnake)

  • __Purpose__: Example of [Parallel connection module](../elastica/experimental/connection_contact_joint/parallel_connection.py) and customized [Force module](./MuscularSnake/muscle_forces.py) to implement muscular snake.

  • __Features__: MuscleForces(custom implemented)

• [ButterflyCase](./ButterflyCase)

  • __Purpose__: Demonstrate simple restoration with initial strain.

  • __Features__: CosseratRod

• [CantileverDistributedLoad](./CantileverDistributedLoad)

  • __Purpose__: Demonstrate the demformation of a straight cantilever under both conservative (like water pressure) and non-conservative (like gravity) distributed load, compared with numerical solutions from Tschisgale, Silvio (2019).[<strong>”Chapter 3: Numerical models of partitioned problems”</strong>](https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa2-387063) Technische Univerisitat Dresden Institution of Fluid Mechanics

  • __Features__: CosseratRod

• [CantileverTransversalLoadCase](./CantileverTransversalLoadCase)

  • __Purpose__: Demonstrate the demformation of a curved cantilever under transversal one-end load, and also do Physical convergence test, compared with numerical solutions from Tschisgale, Silvio (2019).

  • __Features__: CosseratRod

• [TumblingUnconstrainedRod](./TumblingUnconstrainedRod)

  • __Purpose__: Demostrate the dynamics of tumbling uncontrained rod, compared with analytical solution from [Hisao, Kou Hou (1998).](https://www.sciencedirect.com/science/article/pii/S0045782598001522), Computer methods in applied mechanics and engineering.

  • __Features__: CosseratRod

• [FrictionValidationCases](./FrictionValidationCases)

  • __Purpose__: Physical validation of rolling and translational friction.

  • __Features__: CosseratRod, UniformForces, RodPlaneContactWithAnisotropicFriction

• [JointCases](./JointCases)

  • __Purpose__: Demonstrate various joint usage with Cosserat Rod.

  • __Features__: FreeJoint, FixedJoint, HingeJoint, OneEndFixedRod, EndpointForcesSinusoidal

• [RigidBodyCases](./RigidBodyCases)

  • __Purpose__: Demonstrate usage of rigid body on simulation.

  • __Features__: Cylinder, Sphere

  • [RodRigidBodyContact](./RigidBodyCases/RodRigidBodyContact)

    • __Purpose__: Demonstrate contact between cylinder and rod, for different intial conditions.

    • __Features__: Cylinder, CosseratRods, RodCylinderContact

• [HelicalBucklingCase](./HelicalBucklingCase)

  • __Purpose__: Demonstrate helical buckling with extreme twisting boundary condition.

  • __Features__: HelicalBucklingBC

• [ContinuumFlagellaCase](./ContinuumFlagellaCase)

  • __Purpose__: Demonstrate flagella modeling using PyElastica.

  • __Features__: SlenderBodyTheory, MuscleTorques,

• [MuscularFlagella](./MuscularFlagella)

  • __Purpose__: Example of customizing [Joint module](./MuscularFlagella/connection_flagella.py) and [Force module](./MuscularFlagella/muscle_forces_flagella.py) to implement muscular flagella.

  • __Features__: MuscleForces(custom implemented)

• [RodContactCase](./RodContactCase)

  • [RodRodContact](./RodContactCase/RodRodContact)

    • __Purpose__: Demonstrates contact between two rods, for different initial conditions.

    • __Features__: CosseratRod, RodRodContact

  • [RodSelfContact](./RodContactCase/RodSelfContact)

    • [PlectonemesCase](./RodContactCase/RodSelfContact/PlectonemesCase)

      • __Purpose__: Demonstrates rod self contact with Plectoneme example, and how to use link-writhe-twist after simulation completed.

      • __Features__: CosseratRod, SelonoidsBC, RodSelfContact, Link-Writhe-Twist

    • [SolenoidsCase](./RodContactCase/RodSelfContact/SolenoidsCase)

      • __Purpose__: Demonstrates rod self contact with Solenoid example, and how to use link-writhe-twist after simulation completed.

      • __Features__: CosseratRod, SelonoidsBC, RodSelfContact, Link-Writhe-Twist

• [BoundaryConditionsCases](./BoundaryConditionsCases)

  • __Purpose__: Demonstrate the usage of boundary conditions for constraining the movement of the system.

  • __Features__: GeneralConstraint, CosseratRod

• [DynamicCantileverCase](./DynamicCantileverCase)

  • __Purpose__: Validation of dynamic cantilever vibration for multiple modes.

  • __Features__: CosseratRod, OneEndFixedRod

• [RingRodCase](./RingRodCase)

  • __Purpose__: Demonstrate simulation of ring rod.

  • __Features__: RingCosseratRod, OneEndFixedRod, GravityForce

• [CatenaryCase](./CatenaryCase)

  • __Purpose__: Demonstrate simulation of cosserat rod under gravity with fixed ends, compared with Catenary Analytical Solution from Routh, Edward John (1891). [<strong>”Chapter X: On Strings”</strong>](https://books.google.com/books?id=3N5JAAAAMAAJ&pg=PA315#v=onepage&q&f=false). A Treatise on Analytical Statics. University Press.

  • __Features__: CosseratRod, FixedConstraint, GravityForce

• [KnotCase](./KnotCase)

  • __Purpose__: Demonstrate simulation of rod forming a knot using a tip-pose control.

  • __Features__: CosseratRod, KnotTheory, FixedConstraint, RodSelfContact, Custom p-controller for SO3.

## Functional Examples

• [RestartExample](./RestartExample)

  • __Purpose__: Demonstrate the usage of restart module.

  • __Features__: save_state, load_state

## Advanced Cases

• [Elastica RL control](GazzolaLab/Elastica-RL-control) - Case presented in [<strong>Elastica: A compliant mechanics environment for soft robotic control</strong>](https://doi.org/10.1109/LRA.2021.3063698)

• [Gym Softrobot](skim0119/gym-softrobot) - Soft-robot control environment developed in OpenAI-gym format to study slender body control with reinforcement learning.

## Experimental Cases

• [ParallelConnectionExample](./ExperimentalCases/ParallelConnectionExample)

  • __Purpose__: Demonstrate the usage of parallel connection.

  • __Features__: connect two parallel rods

Timoshenko Beam

Timoshenko Beam

Axial Stretching

Axial Stretching

Knot Simulation

Knot Simulation

Catenary

Catenary

Butterfly

Butterfly

Continuum Snake

Continuum Snake