This is a concrete subsystem that handles simple, frictionless contact situations with a model due to Hunt & Crossley: K.
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Public Member Functions |
| | HuntCrossleyContact () |
| | HuntCrossleyContact (MultibodySystem &) |
| int | addSphere (MobilizedBodyIndex body, const Vec3 ¢er, 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) |
| | ForceSubsystem () |
| | SimTK_PIMPL_DOWNCAST (ForceSubsystem, Subsystem) |
| Guts & | updRep () |
| const Guts & | getRep () const |
| | Subsystem () |
| | Subsystem (const Subsystem &) |
| Subsystem & | operator= (const Subsystem &) |
| | ~Subsystem () |
| const String & | getName () const |
| const String & | getVersion () const |
| QIndex | allocateQ (State &, const Vector &qInit) const |
| UIndex | allocateU (State &, const Vector &uInit) const |
| ZIndex | allocateZ (State &, const Vector &zInit) const |
| DiscreteVariableIndex | allocateDiscreteVariable (State &, Stage invalidates, AbstractValue *v) const |
| DiscreteVariableIndex | allocateAutoUpdateDiscreteVariable (State &, Stage invalidates, AbstractValue *v, Stage updateDependsOn) const |
| CacheEntryIndex | allocateCacheEntry (const State &, Stage dependsOn, Stage computedBy, AbstractValue *v) const |
| CacheEntryIndex | allocateCacheEntry (const State &state, Stage g, AbstractValue *v) const |
| CacheEntryIndex | allocateLazyCacheEntry (const State &state, Stage earliest, AbstractValue *v) const |
| QErrIndex | allocateQErr (const State &, int nqerr) const |
| UErrIndex | allocateUErr (const State &, int nuerr) const |
| UDotErrIndex | allocateUDotErr (const State &, int nudoterr) const |
| EventTriggerByStageIndex | allocateEventTriggersByStage (const State &, Stage, int ntriggers) const |
| const Vector & | getQ (const State &) const |
| const Vector & | getU (const State &) const |
| const Vector & | getZ (const State &) const |
| const Vector & | getQDot (const State &) const |
| const Vector & | getUDot (const State &) const |
| const Vector & | getZDot (const State &) const |
| const Vector & | getQDotDot (const State &) const |
| const Vector & | getQErr (const State &) const |
| const Vector & | getUErr (const State &) const |
| const Vector & | getUDotErr (const State &) const |
| const Vector & | getMultipliers (const State &) const |
| const Vector & | getEventTriggersByStage (const State &, Stage) const |
| Vector & | updQ (State &) const |
| Vector & | updU (State &) const |
| Vector & | updZ (State &) const |
| void | setQ (State &s, const Vector &q) const |
| void | setU (State &s, const Vector &u) const |
| void | setZ (State &s, const Vector &z) const |
| Vector & | updQDot (const State &) const |
| Vector & | updUDot (const State &) const |
| Vector & | updZDot (const State &) const |
| Vector & | updQDotDot (const State &) const |
| Vector & | updQErr (const State &) const |
| Vector & | updUErr (const State &) const |
| Vector & | updUDotErr (const State &) const |
| Vector & | updMultipliers (const State &) const |
| Vector & | updEventTriggersByStage (const State &, Stage) const |
| Stage | getStage (const State &) const |
| const AbstractValue & | getDiscreteVariable (const State &s, DiscreteVariableIndex dx) const |
| Real | getDiscreteVarLastUpdateTime (const State &s, DiscreteVariableIndex dx) const |
| CacheEntryIndex | getDiscreteVarUpdateIndex (const State &s, DiscreteVariableIndex dx) const |
| const AbstractValue & | getDiscreteVarUpdateValue (const State &s, DiscreteVariableIndex dx) const |
| AbstractValue & | updDiscreteVarUpdateValue (const State &s, DiscreteVariableIndex dx) const |
| bool | isDiscreteVarUpdateValueRealized (const State &s, DiscreteVariableIndex dx) const |
| void | markDiscreteVarUpdateValueRealized (const State &s, DiscreteVariableIndex dx) const |
| AbstractValue & | updDiscreteVariable (State &, DiscreteVariableIndex) const |
| const AbstractValue & | getCacheEntry (const State &, CacheEntryIndex) const |
| AbstractValue & | updCacheEntry (const State &, CacheEntryIndex) const |
| bool | isCacheValueRealized (const State &, CacheEntryIndex) const |
| void | markCacheValueRealized (const State &, CacheEntryIndex) const |
| void | markCacheValueNotRealized (const State &, CacheEntryIndex) const |
| SystemQIndex | getQStart (const State &) const |
| int | getNQ (const State &) const |
| SystemUIndex | getUStart (const State &) const |
| int | getNU (const State &) const |
| SystemZIndex | getZStart (const State &) const |
| int | getNZ (const State &) const |
| SystemQErrIndex | getQErrStart (const State &) const |
| int | getNQErr (const State &) const |
| SystemUErrIndex | getUErrStart (const State &) const |
| int | getNUErr (const State &) const |
| SystemUDotErrIndex | getUDotErrStart (const State &) const |
| int | getNUDotErr (const State &) const |
| SystemMultiplierIndex | getMultipliersStart (const State &) const |
| int | getNMultipliers (const State &) const |
| SystemEventTriggerByStageIndex | getEventTriggerStartByStage (const State &, Stage) const |
| int | getNEventTriggersByStage (const State &, Stage) const |
| bool | isInSystem () const |
| bool | isInSameSystem (const Subsystem &otherSubsystem) const |
| const System & | getSystem () const |
| System & | updSystem () |
| SubsystemIndex | getMySubsystemIndex () const |
| bool | isOwnerHandle () const |
| bool | isEmptyHandle () const |
| bool | isSameSubsystem (const Subsystem &otherSubsystem) const |
| bool | subsystemTopologyHasBeenRealized () const |
| void | invalidateSubsystemTopologyCache () const |
| MeasureIndex | adoptMeasure (AbstractMeasure &) |
| AbstractMeasure | getMeasure (MeasureIndex) const |
| template<class T > |
| Measure_< T > | getMeasure_ (MeasureIndex mx) const |
| const Subsystem::Guts & | getSubsystemGuts () const |
| Subsystem::Guts & | updSubsystemGuts () |
| void | adoptSubsystemGuts (Subsystem::Guts *g) |
| void | setSystem (System &, SubsystemIndex) |
| | Subsystem (Subsystem::Guts *g) |
| bool | hasGuts () const |
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.
Inheritance diagram for SimTK::HuntCrossleyContact:
1.8.1.2 
