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INTERACTION BETWEEN SURFACES
Abaqus makes a distinction between analyses where the magnitude of sliding is small and those where
the magnitude of sliding may be finite. It is much less expensive computationally to model problems
where the sliding between the surfaces is small. What constitutes “small sliding” is often difficult to
define, but a general guideline to follow is that problems can use the “small-sliding” approximation if a
point contacting a surface does not slide more than a small fraction of a typical element dimension.
Small sliding is not available for general contact.
12.2.3
Friction models
When surfaces are in contact, they usually transmit shear as well as normal forces across their interface.
Thus, the analysis may need to take frictional forces, which resist the relative sliding of the surfaces,
into account. Coulomb friction is a common friction model used to describe the interaction of contacting
surfaces. The model characterizes the frictional behavior between the surfaces using a coefficient of
friction, .
The default friction coefficient is zero. The tangential motion is zero until the surface traction
reaches a critical shear stress value, which depends on the normal contact pressure, according to the
following equation:
where is the coefficient of friction and is the contact pressure between the two surfaces. This equation
gives the limiting frictional shear stress for the contacting surfaces. The contacting surfaces will not slip
(slide relative to each other) until the shear stress across their interface equals the limiting frictional shear
stress, . For most surfaces is normally less than unity. Coulomb friction can be defined with or
. The solid line in Figure 12–2 summarizes the behavior of the Coulomb friction model: there is zero
relative motion (slip) of the surfaces when they are sticking (the shear stresses are below ). Optionally,
a friction stress limit can be specified if both contacting surfaces are element-based surfaces.
In Abaqus/Standard the discontinuity between the two states—sticking or slipping—can result in
convergence problems during the simulation. You should include friction in your Abaqus/Standard
simulations only when it has a significant influence on the response of the model. If your contact
simulation with friction encounters convergence problems, one of the first modifications you should
try in diagnosing the difficulty is to rerun the analysis without friction. In general, friction presents no
additional computational difficulties for Abaqus/Explicit.
Simulating ideal friction behavior can be very difficult; therefore, by default in most cases,
Abaqus uses a penalty friction formulation with an allowable “elastic slip,” shown by the dotted line in
Figure 12–2. The “elastic slip” is the small amount of relative motion between the surfaces that occurs
when the surfaces should be sticking. Abaqus automatically chooses the penalty stiffness (the slope of
the dotted line) so that this allowable “elastic slip” is a very small fraction of the characteristic element
length. The penalty friction formulation works well for most problems, including most metal forming
applications.
12–3
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