SimTK::HuntCrossleyContact Class Reference

This is a concrete subsystem that handles simple, frictionless contact situations with a model due to Hunt & Crossley: K. More...

#include <HuntCrossleyContact.h>

Inheritance diagram for SimTK::HuntCrossleyContact:

List of all members.

Public Member Functions
	HuntCrossleyContact ()
	HuntCrossleyContact (MultibodySystem &)
int	addSphere (MobilizedBodyIndex body, const Vec3 &center, const Real &radius, const Real &stiffness, const Real &dissipation)
int	addHalfSpace (MobilizedBodyIndex body, const UnitVec3 &normal, const Real &height, const Real &stiffness, const Real &dissipation)
	SimTK_PIMPL_DOWNCAST (HuntCrossleyContact, ForceSubsystem)

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Detailed Description

This is a concrete subsystem that handles simple, frictionless contact situations with a model due to Hunt & Crossley: K.

H. Hunt and F. R. E. Crossley, "Coefficient of Restitution Interpreted as Damping in Vibroimpact," ASME Journal of Applied Mechanics, pp. 440-445, June 1975. This is a continuous model based on Hertz elastic contact theory, which correctly reproduces the empirically observed dependence on velocity of coefficient of restitution, where e=(1-cv) for (small) impact velocity v and a material property c with units 1/v. Note that c can be measured right off the coefficient of restitution-vs.-velocity curves: it is the absolute value of the slope at low velocities.

Given a collision between two spheres, or a sphere and a plane, we can generate a contact force from this equation f = kx^n(1 + 3/2 cv) where k is a stiffness constant incorporating material properties and geometry (to be defined below), x is penetration depth and v = dx/dt is penetration rate (positive during penetration and negative during rebound). Exponent n depends on the surface geometry. For Hertz contact where the geometry can be approximated by sphere (or sphere-plane) interactions, which is all we are currently handling here, n=3/2.

Stiffness k is defined in terms of the relative radius of curvature R and effective plane-strain modulus E, each of which is a combination of the description of the two individual contacting elements. TODO: derivation of the following results should be in the SimTK Engr J; you'll have to take my word for it now:

R1*R2 E2^(2/3) R = -------, E = (s1 * E1^(2/3))^(3/2), s1= ------------------- R1 + R2 E1^(2/3) + E2^(2/3)

c = c1*s1 + c2*(1-s1) k = (4/3) sqrt(R) E f = k x^(3/2) (1 + 3/2 c xdot) pe = 2/5 k x^(5/2) Also, we can calculate the contact patch radius a as a = sqrt(R*x)

In the above, E1 and E2 are the *plane strain* moduli. If you have instead Young's modulus Y1 and Poisson's ratio p1, then E1=Y1/(1-p1^2). The interface to this subsystem asks for E1 (pressure/strain) and c1 (1/velocity), and E2,c2 only.

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Constructor & Destructor Documentation

SimTK::HuntCrossleyContact::HuntCrossleyContact

(

)

SimTK::HuntCrossleyContact::HuntCrossleyContact

(

MultibodySystem &

)

[explicit]

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Member Function Documentation

int SimTK::HuntCrossleyContact::addSphere	(	MobilizedBodyIndex	body,
		const Vec3 &	center,
		const Real &	radius,
		const Real &	stiffness,
		const Real &	dissipation
	)

int SimTK::HuntCrossleyContact::addHalfSpace	(	MobilizedBodyIndex	body,
		const UnitVec3 &	normal,
		const Real &	height,
		const Real &	stiffness,
		const Real &	dissipation
	)

SimTK::HuntCrossleyContact::SimTK_PIMPL_DOWNCAST	(	HuntCrossleyContact	,
		ForceSubsystem
	)

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The documentation for this class was generated from the following file:

• HuntCrossleyContact.h