Friction models in Abaqus/Explicit

The friction models provided in Abaqus/Explicit are tested on a simple problem, and the results are compared to analytical solutions.

The first example uses the classical Coulomb friction model. The critical shear stress, ${\tau }_{crit}$ , at which surfaces begin to slide with respect to each other is given by

where $\mu$ is the coefficient of friction and p is the normal pressure.

The second example uses the classical Coulomb friction model explained above with softened tangential behavior. While under the condition of sticking friction, the surfaces are allowed to slip, generating “elastic” slip. The amount of elastic slip, ${\gamma }_{el}$ , is given by

where $\kappa$ is the slope of the shear stress versus elastic slip curve and $\tau$ is the shear stress calculated from the friction law. While under the condition of slipping friction, the behavior is identical to the classical Coulomb friction model without softened tangential behavior.

The third example uses a rate-dependent friction model in which the static friction coefficient, ${\mu }_s$ , decays to the kinetic friction coefficient, ${\mu }_k$ , according to the exponential form,

where $d_c$ is a user-defined decay parameter and ${\dot{\gamma }}_{eq}$ is the slip rate. This model is referred to as the exponential decay friction model.

The fourth example uses the Coulomb friction model with dependencies to simulate slip-rate-dependent friction. The coefficient of friction is defined as a function of the slip rate and the normal contact pressure. To facilitate comparison of the analyses, the tabular data are synthesized to approximate the exponential decay model.

The fifth example uses a rough friction model with softened tangential behavior. With this model, all tangential motion is in the form of elastic slip. This model differs from the second example in that the shear stress is no longer limited by ${\tau }_{crit}$ , so no frictional slip can occur.

The problem consists of a rectangular block of two CPE3 elements sliding on a rigid surface. The block is 5 inches long, 1 inch high, and 1 inch thick. The elastic modulus is 3 × 10⁷ psi, and the density is 7.3 × 10⁻⁴ lbf s²/in⁴. A uniform pressure of 2000 psi is applied on the top face of the block, and an initial velocity of 200 in/s is prescribed at each node of the block. The same problem is used to test user subroutine VFRIC in VFRIC, VFRIC_COEF, and VFRICTION.

For the classical Coulomb friction model $\mu =$ 0.15; for the exponential decay friction model ${\mu }_s=$ 0.15, ${\mu }_k=$ 0.05, and $d_c=$ 0.01 s/in; for the models including softened tangential behavior $\kappa =$ 10⁴ psi/in.