Friction models in Abaqus/Explicit

The prescribed external load produces a normal pressure of 2000 psi and a frictional stress of 300 psi. This corresponds to a negative acceleration of 4.110 × 10⁵ in/s² in the tangential direction, since the frictional stress opposes the motion of the block. Given the initial velocity and the acceleration, the block should come to rest after sliding a distance of 4.866 × 10⁻² inches over a time period of 4.866 × 10⁻⁴ s. The corresponding values for sliding distance and time period obtained with the Coulomb finite element model are 4.866 × 10⁻² inches and 4.878 × 10⁻⁴ s, respectively. The numerical results show some oscillations in the normal reactions and frictional forces caused by the inertial effect of nodes on the top of the block; there is some oscillation of the block in a shear mode, even after the block stops sliding.

As in the preceding example, the critical frictional stress between the block and rigid surface is 300 psi. Elastic slip will be generated until the frictional stress exceeds the critical stress, and frictional slip will be initiated. The block then slows to zero velocity due to the frictional dissipation and reverses direction as the stored elastic slip is converted back into kinetic energy. The analytical solution for a rigid block with the given initial velocity predicts that the block will reverse its direction of travel at a time of 5.638 × 10⁻⁴ s at a distance of 6.367 × 10⁻² inches. The corresponding values for time and distance from the finite element model are 5.704 × 10⁻⁴ s and 6.338 × 10⁻² inches, respectively.

In this model the velocity of a node in contact corresponds to the slip rate for the friction model. Table 1 compares the velocity values obtained from a closed-form solution, which assumes the block to be rigid, to the average velocity of the contacting nodes in the finite element model. The differences are caused by the oscillations in the shear mode of the finite element model. The analysis using penalty contact has additional differences due to the default viscous contact damping, which contributes to the contact forces opposing the motion of the block.

The tabular data for this model are chosen to approximate the exponential decay model described in the previous subsection. Both slip rate and pressure dependence are included in the model to verify the code. The pressure dependence is defined such that the interpolated values at a pressure equal to 2000 psi correspond to the exponential decay model considered previously. Table 2 compares the average velocities of the contacting nodes in the finite element model with the velocity values obtained from a closed-form solution based on a rigid block. Small differences occur as a result of oscillations in the finite element model and the linear interpolation of the tabular data.

With rough frictional behavior and tangential softening (without viscous contact damping), this model essentially behaves like an undamped oscillator. The analytical solution to a point mass oscillating on a linear spring without damping gives the amplitude of the oscillation in slip to be 5.404 × 10^—2 inches and the time at which the slip direction first reverses to be 4.244 × 10⁻⁴ s. The corresponding values for amplitude and time from the finite element model using penalty contact are 5.403 × 10⁻² inches and 4.273 × 10⁻⁴ s, respectively. The corresponding values for the amplitude and time from the finite element model using kinematic contact are 5.378 × 10⁻² inches and 4.234 × 10⁻⁴ s, respectively.