Contact pressure-overclosure relationships

For general contact in Abaqus/Explicit involving two rigid bodies with complete displacement control loading, the contact forces may be noisy due to effects of the number of contact interactions involving each rigid body and the contact penalty stiffness. This same effect will not occur with force control loading. The solution of the analysis should still remain stable.

The “softened” contact pressure-overclosure relationships might be used to model a soft, thin layer on one or both surfaces. In Abaqus/Standard they are also sometimes useful for numerical reasons because they can make it easier to resolve the contact condition.

Use the softened contact relationship with caution in implicit dynamic impact simulations. If this relationship is used in such a simulation, Abaqus/Standard will not use the impact algorithm, which destroys kinetic energy of the nodes on the surface when impact occurs, but will instead assume a perfectly elastic collision. The consequence of this change is that the slave nodes bounce back immediately after impact with the master surface; hence, extensive “chattering” may result, leading to convergence problems and small time increments.

However, softened contact may work well in implicit dynamic calculations where impact effects are not important; for example, if contact changes are primarily due to sliding motion along a curved surface, such as may occur in low-speed metal forming applications.

In Abaqus/Explicit softened contact can be enforced with either the kinematic or the penalty constraint enforcement method (see Contact constraint enforcement methods in Abaqus/Explicit for details). With penalty enforcement the contact collisions are elastic except for the influence of contact damping, whereas with softened kinematic contact some energy will be absorbed by the impact because of algorithmic characteristics: the energy absorbed tends to increase as the contact stiffness increases. Another consideration is the effect on the time increment: with kinematic enforcement the stable time increment is independent of the contact stiffness, but with penalty contact the time increment decreases as the contact stiffness increases.

In a linear pressure-overclosure relationship the surfaces transmit contact pressure when the overclosure between them, measured in the contact (normal) direction, is greater than zero. The linear pressure-overclosure relationship is identical to a tabular relationship with two data points, where the first point is located at the origin.

You specify the slope of the pressure-overclosure relationship, k.

SURFACE BEHAVIOR, PRESSURE-OVERCLOSURE=LINEAR
k

Interaction module: contact property editor: MechanicalNormal Behavior: Constraint enforcement method: Default: Pressure-Overclosure: Linear, Contact stiffness: k

To define a piecewise-linear pressure-overclosure relationship in tabular form, as shown in Figure 2, you specify data pairs ($p_i$, $h_i$) of pressure versus overclosure (where overclosure corresponds to negative clearance). You must specify the data as an increasing function of pressure and overclosure. In this relationship the surfaces transmit contact pressure when the overclosure between them, measured in the contact (normal) direction, is greater than $h_1$, where $h_1$ is the overclosure at zero pressure. For the general contact algorithm in Abaqus/Explicit $h_1$ must be zero. For overclosures greater than $h_n$ the pressure-overclosure relationship is extrapolated based on the last slope computed from the user-specified data (see Figure 2).

Figure 2. “Softened” pressure-overclosure relationship defined in tabular form.

SURFACE BEHAVIOR, PRESSURE-OVERCLOSURE=TABULAR

Interaction module: contact property editor: MechanicalNormal Behavior: Constraint enforcement method: Default: Pressure-Overclosure: Tabular

An alternative piecewise linear tabular pressure-overclosure relationship can be constructed by geometrically scaling the default contact stiffness. This model provides a simple interface to increase the default contact stiffness when a critical penetration is exceeded. A penetration measure, $d$, is defined either directly or as a fraction, $r$, of the minimum element length, $L_{elem}$, in the contact region. Each time the current penetration exceeds a multiple of this penetration measure, the contact stiffness is scaled by a factor, $s$ (see Figure 3). The initial stiffness is set equal to the default contact stiffness, $k_{dflt}$, multiplied by a factor, $s_0$.

Figure 3. “Softened” scale factor pressure-overclosure relationship.

This option is available only for the general contact algorithm in Abaqus/Explicit.

SURFACE BEHAVIOR, PRESSURE-OVERCLOSURE=SCALE FACTOR

Interaction module: contact property editor: MechanicalNormal Behavior: Constraint enforcement method: Default: Pressure-Overclosure: Scale Factor (General Contact)

In an exponential (soft) contact pressure-overclosure relationship the surfaces begin to transmit contact pressure once the clearance between them, measured in the contact (normal) direction, reduces to $c_0$. The contact pressure transmitted between the surfaces then increases exponentially as the clearance continues to diminish. Figure 4 illustrates this behavior in Abaqus/Standard. In Abaqus/Explicit this behavior is available only for the contact pair algorithm.

Figure 4. Exponential “softened” pressure-overclosure relationship in Abaqus/Standard.

In Abaqus/Explicit you can specify an optional limit on the contact stiffness that the model can attain, $k_{max}$ (see Figure 5); this limit is useful for penalty contact to mitigate the effect that large stiffnesses have on reducing the stable time increment.

Figure 5. Exponential “softened” pressure-overclosure relationship in Abaqus/Explicit.

By default, $k_{max}$ will be set to infinity for kinematic contact and to the default penalty stiffness for penalty contact.

You specify $c_0$; the contact pressure at zero clearance, $p_0$; and, optionally in Abaqus/Explicit, $k_{max}$.

SURFACE BEHAVIOR, PRESSURE-OVERCLOSURE=EXPONENTIAL
$c_0$, $p_0$, $k_{max}$

Interaction module: contact property editor: MechanicalNormal Behavior: Constraint enforcement method: Default: Pressure-Overclosure: Exponential, Pressure $p_0$, Clearance $c_0$, Specify: $k_{max}$

In Abaqus/Explicit if a softened contact relationship is specified with the no separation relationship, the pressure-overclosure relationship will include tensile behavior. The exponential relationship cannot be used with no separation behavior. For the tabular relationship, a point must be specified on the zero pressure axis, and the slope will continue into the tensile regime following the same slope as the first two data points (see Figure 6). The linear relationship will have a linear tensile pressure-overclosure relationship with the same slope that is used for the compressive behavior.

Figure 6. Piecewise linear “softened” pressure-overclosure relationship with tensile behavior in Abaqus/Explicit.