1. Chapter Four
Friction

2. Friction What is friction?
The tangential or sliding behavior of two contacting bodies may be frictionless, or it may involve friction.
Frictionless behavior allows the bodies to slide relative to one another without any resistance.
When friction is included, shear forces can develop between the two bodies.
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3. ... Friction
Friction dissipates energy, and is therefore a path-dependent behavior.
The loading must be applied in the same manner as it occurs on the physical parts.
Time steps must be small for good accuracy.
Note that, unlike for plasticity, auto time stepping does not take into account the size of the frictional response increment.
True displacement path
Small time steps A
Coarse time steps B
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4. ... Friction
Physical friction is a complex phenomenon that is a function of:
The contacting materials (including lubricants).
Surface roughness.
Temperature.
Relative velocity of the bodies.
The mechanisms involved in friction are not yet well understood.
In fact, a single friction test, run at low speed with constant pressure, will frequently display a fairly erratic force-displacement behavior: F u
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5. ... Friction
In ANSYS, friction is implemented using a Coulomb model, with additional complexity of response available through cohesion and shear friction behavior.
The Coulomb law is a macroscopic model that states that the equivalent tangential force FT transmitted between two bodies cannot exceed a fraction of the normal force FN:
FT  m x FN
Where m is the friction coefficient.
Once FT is exceeded, the two bodies will slide relative to each other.
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6. ... Friction
Elastic Coulomb Model: Allows sticking and sliding
When a tangential load, Ft , trying to move two bodies relative to each other, is smaller then m Fn , the two bodies will stick together.
If this tangential load, Ft , is larger then m Fn , the two bodies will slide relative to each other. An opposing shear stress, TAU, will still be experienced by both bodies.
Sticking when: Ft < m Fn
Sliding when: Ft > m Fn
or when: TAU > TAUMAX
Where: TAU = Shear Stress
Default: TAUMAX = 1e20 Fn Ft
m Fn
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7. … Friction
Elastic Coulomb Model (cont’d): Allows sticking and sliding
Some elements model this limit with the real constant, TAUMAX.
A common upper estimate for TAUMAX is:
Where y is the von Mises yield stress of the material adjacent to the surface. Empirical data is often the best source for TAUMAX.
||
TAUMAX  p
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8. ... Friction
Elastic Coulomb Model (cont’d): Allows sticking and sliding
The sticking zone is treated as elastic, with a tangent stiffness KT.
The tangent stiffness has a similar effect to that of the normal stiffness: better accuracy when stiffer, better convergence when softer.
You can specify KT, or the program will specify KT to be a fraction of KN (usually 1% of KN). FT u KT
mFN
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9. ... Friction Rigid Coulomb Model: Allows only sliding friction.
The contact response cannot “stick.”
This model is good only for analyses that have continuous sliding motion in a consistent direction.
A part being shaped against a grinding wheel, for example.
The discontinuity at u = 0 is akin to an infinite stiffness. Convergence difficulties are guaranteed if the sliding stops or reverses direction.
Allows only sliding friction. FT u
mFN
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10. … Friction
The Coulomb model implies that as the normal pressure increases, the maximum shear stress transmitted will also increase. FT
Sliding force increases with increasing pressure p2 p1 u
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11. … Friction
Of course, shear yield of the contacting surfaces places a physical limit to how large a shear stress can be transmitted.
Shear yield in rubber causes skid marks – and limits the friction force that can be transmitted between tire and pavement.
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12. … Friction
Sometimes, surfaces will stick together, providing sliding resistance even when no normal pressure is acting.
Some elements can model this with a cohesion value (COHE).
||
TAUMAX 
COHE p
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13. ... Friction Coefficient of Friction:
The coefficient of friction is usually less when a body is sliding than when it is at rest.
Sliding: dynamic coefficient of friction.
At rest: static coefficient of friction.
Not all ANSYS contact elements support a distinction between static and dynamic coefficients of friction.
For all ANSYS contact elements, m is specified as a material property (MU).
For node to node and node to surface elements, a real constant FACT (the ratio of static to dynamic friction) allows the distinction between static and dynamic coefficients.
For surface to surface elements, a dynamic friction coefficient is calculated as a variable function of relative surface velocity.
For frictionless behavior, set m = 0.
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14. ... Friction Coefficient of Friction (cont’d):
For surface to surface contact elements, the dynamic friction coefficient as an exponential function of velocity is modeled with the following formula:
m = m k + (m s-m k)e- dcVt
OR MU = MUK*(1+(FACT-1)exp(-dc*vtfs/deltaT))
Where: MUK = dynamic friction coefficient (defined by user)
FACT = MUS/MUK (defined by user)
MUS = static friction coefficient
dc = decaying coefficient (defined by user)
vtfs/deltaT = relative velocity between surfaces
Defaults: FACT = 1, MUS=MUK=0
dc = 0
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15. ... Friction Coefficient of Friction (cont’d):
The dynamic coefficient of friction offers a smooth transition from static to dynamic as a function of surface velocity
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16. … Friction
Contact problems involving friction produce an unsymmetric stiffness matrix.
However, using an unsymmetric equation solver is more computationally expensive than a symmetric solver.
For this reason ANSYS uses a symmetrization algorithm by which most contact problems involving friction can be solved.
If you are experiencing a slow rate of convergence, an unsymmetric solution option ( NROPT, USYM) is available for some of the elements.
In this case you would need to use either the sparse (preferred) or the frontal solver, both of which will automatically switch to an unsymmetric solver option when unsymmetric matrices are present.
The PCG is not valid for unsymmetric matrices.
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17. … Friction Summary of friction options for ANSYS contact elements:
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18. Friction Workshop
Please refer to your Workshop Supplement for instructions on:
W2. Contact with friction (constant coefficient)
W3. Contact with friction (dynamic coefficient)
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