Contact

Numba implementation module containing contact between rods and rigid bodies and other rods rigid bodies or surfaces.

Description

Note

(CAUTION) The contact is recommended to be added at last. This is because contact forces often includes friction that may depend on other normal forces and constraints to be calculated accurately. Be careful on the order of adding interactions.

Available Contact Classes

NoContact	This is the base class for contact applied between rod-like objects and allowed contact objects.
RodRodContact	This class is for applying contact forces between rod-rod.
RodCylinderContact	This class is for applying contact forces between rod-cylinder.
RodSelfContact	This class is modeling self contact of rod.
RodSphereContact	This class is for applying contact forces between rod-sphere.
RodPlaneContact	This class is for applying contact forces between rod-plane.
RodPlaneContactWithAnisotropicFriction	This class is for applying contact forces between rod-plane with friction.
CylinderPlaneContact	This class is for applying contact forces between cylinder-plane.

Built-in Contact Classes

class elastica.contact_forces.NoContact

This is the base class for contact applied between rod-like objects and allowed contact objects.

Notes

Every new contact class must be derived from NoContact class.

__init__()

NoContact class does not need any input parameters.

apply_contact(system_one, system_two, time=np.float64(0.0))

Apply contact forces and torques between two system objects. In NoContact class, this routine simply passes.

Return type:

None

Parameters:

system_oneSystemType

First system object.

system_twoSystemType

Second system object.

timefloat

The time of simulation.

class elastica.contact_forces.RodRodContact(k, nu)

This class is for applying contact forces between rod-rod.

Examples

How to define contact between rod and rod.

>>> simulator.detect_contact_between(first_rod, second_rod).using(
...    RodRodContact,
...    k=1e4,
...    nu=10,
... )

__init__(k, nu)

Parameters:

kfloat

Contact spring constant.

nufloat

Contact damping constant.

apply_contact(system_one, system_two, time=np.float64(0.0))

Apply contact forces and torques between RodType object and RodType object.

Return type:

None

Parameters:

system_oneRodType

First rod object.

system_twoRodType

Second rod object.

timefloat

The time of simulation.

class elastica.contact_forces.RodCylinderContact(k, nu, velocity_damping_coefficient=0.0, friction_coefficient=0.0)

This class is for applying contact forces between rod-cylinder. If you want to apply contact forces between rod and cylinder, first system is always rod and second system is always cylinder. In addition to the contact forces, user can define apply friction forces between rod and cylinder that are in contact. For details on friction model refer to this [1].

Notes

The velocity_damping_coefficient is set to a high value (e.g. 1e4) to minimize slip and simulate stiction (static friction), while friction_coefficient corresponds to the Coulombic friction coefficient.

Examples

How to define contact between rod and cylinder.

>>> simulator.detect_contact_between(rod, cylinder).using(
...    RodCylinderContact,
...    k=1e4,
...    nu=10,
... )

[1]

Preclik T., Popa Constantin., Rude U., Regularizing a Time-Stepping Method for Rigid Multibody Dynamics, Multibody Dynamics 2011, ECCOMAS. URL: https://www10.cs.fau.de/publications/papers/2011/Preclik_Multibody_Ext_Abstr.pdf

__init__(k, nu, velocity_damping_coefficient=0.0, friction_coefficient=0.0)

Parameters:

kfloat

Contact spring constant.

nufloat

Contact damping constant.

velocity_damping_coefficientfloat

Velocity damping coefficient between rigid-body and rod contact is used to apply friction force in the slip direction.

friction_coefficientfloat

For Coulombic friction coefficient for rigid-body and rod contact.

apply_contact(system_one, system_two, time=np.float64(0.0))

Apply contact forces and torques between RodType object and Cylinder object.

Return type:

None

Parameters:

system_oneRodType

Rod object.

system_twoCylinder

Cylinder object.

timefloat

The time of simulation.

class elastica.contact_forces.RodSelfContact(k, nu)

This class is modeling self contact of rod.

Examples

How to define contact rod self contact.

>>> simulator.detect_contact_between(rod, rod).using(
...    RodSelfContact,
...    k=1e4,
...    nu=10,
... )

__init__(k, nu)

Parameters:

kfloat

Contact spring constant.

nufloat

Contact damping constant.

apply_contact(system_one, system_two, time=np.float64(0.0))

Apply contact forces and torques between RodType object and itself.

Return type:

None

Parameters:

system_oneRodType

Rod object.

system_twoRodType

Same rod object as system_one (self-contact).

timefloat

The time of simulation.

class elastica.contact_forces.RodSphereContact(k, nu, velocity_damping_coefficient=0.0, friction_coefficient=0.0)

This class is for applying contact forces between rod-sphere. First system is always rod and second system is always sphere. In addition to the contact forces, user can define apply friction forces between rod and sphere that are in contact. For details on friction model refer to this [1].

[1]

Preclik T., Popa Constantin., Rude U., Regularizing a Time-Stepping Method for Rigid Multibody Dynamics, Multibody Dynamics 2011, ECCOMAS. URL: https://www10.cs.fau.de/publications/papers/2011/Preclik_Multibody_Ext_Abstr.pdf

Notes

The velocity_damping_coefficient is set to a high value (e.g. 1e4) to minimize slip and simulate stiction (static friction), while friction_coefficient corresponds to the Coulombic friction coefficient.

Examples

How to define contact between rod and sphere.

>>> simulator.detect_contact_between(rod, sphere).using(
...    RodSphereContact,
...    k=1e4,
...    nu=10,
... )

__init__(k, nu, velocity_damping_coefficient=0.0, friction_coefficient=0.0)

Parameters:

kfloat

Contact spring constant.

nufloat

Contact damping constant.

velocity_damping_coefficientfloat

Velocity damping coefficient between rigid-body and rod contact is used to apply friction force in the slip direction.

friction_coefficientfloat

For Coulombic friction coefficient for rigid-body and rod contact.

apply_contact(system_one, system_two, time=np.float64(0.0))

Apply contact forces and torques between RodType object and Sphere object.

Return type:

None

Parameters:

system_oneRodType

Rod object.

system_twoSphere

Sphere object.

timefloat

The time of simulation.

class elastica.contact_forces.RodPlaneContact(k, nu)

This class is for applying contact forces between rod-plane. First system is always rod and second system is always plane. For more details regarding the contact module refer to Eqn 4.8 of Gazzola et al. RSoS (2018).

Examples

How to define contact between rod and plane.

>>> simulator.detect_contact_between(rod, plane).using(
...    RodPlaneContact,
...    k=1e4,
...    nu=10,
... )

__init__(k, nu)

Parameters:

kfloat

Contact spring constant.

nufloat

Contact damping constant.

apply_contact(system_one, system_two, time=np.float64(0.0))

Apply contact forces and torques between RodType object and Plane object.

Return type:

None

Parameters:

system_oneRodType

Rod object.

system_twoPlane

Plane object.

timefloat

The time of simulation.

class elastica.contact_forces.RodPlaneContactWithAnisotropicFriction(k, nu, slip_velocity_tol, static_mu_array, kinetic_mu_array)

This class is for applying contact forces between rod-plane with friction. First system is always rod and second system is always plane. For more details regarding the contact module refer to Eqn 4.8 of Gazzola et al. RSoS (2018).

Examples

How to define contact between rod and plane.

>>> simulator.detect_contact_between(rod, plane).using(
...    RodPlaneContactWithAnisotropicFriction,
...    k=1e4,
...    nu=10,
...    slip_velocity_tol = 1e-4,
...    static_mu_array = np.array([0.0,0.0,0.0]),
...    kinetic_mu_array = np.array([1.0,2.0,3.0]),
... )

__init__(k, nu, slip_velocity_tol, static_mu_array, kinetic_mu_array)

Parameters:

kfloat

Contact spring constant.

nufloat

Contact damping constant.

slip_velocity_tol: float

Velocity tolerance to determine if the element is slipping or not.

static_mu_array: numpy.ndarray

1D (3,) array containing data with ‘float’ type. [forward, backward, sideways] static friction coefficients.

kinetic_mu_array: numpy.ndarray

1D (3,) array containing data with ‘float’ type. [forward, backward, sideways] kinetic friction coefficients.

apply_contact(system_one, system_two, time=np.float64(0.0))

Apply contact forces and torques between RodType object and Plane object with anisotropic friction.

Return type:

None

Parameters:

system_oneRodType

Rod object.

system_twoPlane

Plane object.

timefloat

The time of simulation.

class elastica.contact_forces.CylinderPlaneContact(k, nu)

This class is for applying contact forces between cylinder-plane. First system is always cylinder and second system is always plane. For more details regarding the contact module refer to Eqn 4.8 of Gazzola et al. RSoS (2018).

Examples

How to define contact between cylinder and plane.

>>> simulator.detect_contact_between(cylinder, plane).using(
...    CylinderPlaneContact,
...    k=1e4,
...    nu=10,
... )

__init__(k, nu)

Parameters:

kfloat

Contact spring constant.

nufloat

Contact damping constant.

apply_contact(system_one, system_two, time=np.float64(0.0))

Compute the plane force response on the cylinder in the case of contact.

Contact model given in Eqn 4.8 Gazzola et al. RSoS 2018 paper is used.

Return type:

None

Parameters:

system_oneCylinder

Cylinder object.

system_twoPlane

Plane object.

timefloat

The time of simulation.