User subroutines testing static and dynamic friction in a stress/displacement analysis
Elements tested
CPE3
C3D8R
MASS
Features tested
User subroutines VFRIC, VFRIC_COEF, and VFRICTION to define frictional behavior.
Problem description
The problems in this section demonstrate modeling of frictional behavior with user subroutines VFRIC, VFRIC_COEF, and VFRICTION.
The first example uses user subroutines VFRIC, VFRIC_COEF, and VFRICTION that are coded with the Coulomb model for frictional behavior, which is also the default model in Abaqus. The critical shear stress, , at which surfaces begin to slide with respect to each other is given as
where is the coefficient of friction and p is normal pressure.
The second example uses user subroutines VFRIC, VFRIC_COEF, and VFRICTION for rate-dependent Coulomb friction behavior where the evolution of the coefficient of friction, , is given by an exponential law
where is the static coefficient of friction, is the kinetic coefficient of friction, is the decay coefficient, and is the magnitude of the tangential slip velocity.
Both friction models are tested on a mesh of a rectangular block (length 5 in, height 1 in, and depth 1 in, elastic modulus 30 × 106 psi, density 7.3 × 10−4 lbf s2/in4) of two CPE3 or C3D8R elements sliding over a flat analytical rigid surface along its length in the x-direction. 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 on the block. The same problem is used to test the friction models provided in Abaqus/Explicit in Friction models in Abaqus/Explicit.
For the Coulomb model 0.15; for the rate-dependent Coulomb model 0.15, 0.05, and 0.01 s/in.
Results and discussion
The results for the two models are discussed below.
Results for the default Coulomb model
The prescribed external load gives a normal pressure of 2000 psi and a frictional stress of 300 psi. This corresponds to a negative acceleration of 4.109589 × 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 over a distance of 4.866 × 10−2 in over a time period of 4.866 × 10−4 s. The corresponding values of sliding distance and time period for the finite element model with user subroutines are 4.866 × 10−2 in 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; even after the block stops sliding, there is some oscillation of the block in a shear mode.
Results for the rate-dependent Coulomb model
In this model the velocity of the node in contact corresponds to the slip rate for the friction model. To verify the friction model, we compare the velocity values obtained using the analytical expression with the average velocity values of the nodes in contact obtained from the finite element model with user subroutines (see Table 1 and Table 2). Small differences occur between the analytical and numerical values of velocity because of small oscillations in a shear mode in the finite element model. The analysis using penalty contact with user subroutines VFRIC and VFRIC_COEF has additional differences due to default viscous contact damping, which contributes to the contact forces opposing the motion of the block.
Time | Velocity | Velocity |
---|---|---|
10−4 s | (Analytical) in/s | (VFRIC) in/s |
1.0301 | 181.7 | 181.8 |
2.0042 | 163.6 | 164.2 |
3.0001 | 144.1 | 143.5 |
4.0064 | 123.1 | 123.9 |
5.0000 | 100.6 | 100.6 |
6.0284 | 74.73 | 75.19 |
7.0022 | 46.87 | 47.97 |
8.0017 | 12.88 | 11.89 |
8.2289 | 4.054 | 2.965 |
Time | Velocity | Velocity |
---|---|---|
10−4 s | (VFRIC_COEF) in/s | (VFRICTION) in/s |
1.0142 | 183.0 | 183.0 |
2.0145 | 164.7 | 164.7 |
3.0159 | 143.7 | 143.7 |
4.0162 | 121.0 | 121.0 |
5.0000 | 99.92 | 99.95 |
6.0146 | 77.09 | 77.12 |
7.0149 | 46.92 | 46.98 |
8.0156 | 10.90 | 11.00 |
8.2289 | 2.85 | 4.69 |
Input files
- vfric_coul.inp
Input data that refer to user subroutine VFRIC with the Coulomb model.
- vfric_coul.f
User subroutine VFRIC for the Coulomb model.
- vfric_coul_part1.inp
Input data (with the model defined in terms of an assembly of part instances) that refer to user subroutine VFRIC with the Coulomb model and the utility routine VGETPARTINFO.
- vfric_coul_part1.f
User subroutine VFRIC for the Coulomb model that illustrates the use of the utility routine VGETPARTINFO.
- vfric_coul_part2.inp
Input data (with the model defined in terms of an assembly of part instances) that refer to user subroutine VFRIC with the Coulomb model and the utility routine VGETINTERNAL.
- vfric_coul_part2.f
User subroutine VFRIC for the Coulomb model that illustrates the use of utility routine VGETINTERNAL.
- vfric_rdcoul.inp
Input data that refer to user subroutine VFRIC with the rate-dependent Coulomb model.
- vfric_rdcoul.f
User subroutine VFRIC for the rate-dependent Coulomb model.
- vfric_rdcoulpnlty.inp
Input data that refer to user subroutine VFRIC with the rate-dependent Coulomb model and penalty contact.
- vfric_coef_coul.inp
Input data that refer to user subroutine VFRIC_COEF with the Coulomb model.
- vfric_coef_coul.f
User subroutine VFRIC_COEF for the Coulomb model.
- vfriction_coul.inp
Input data that refer to user subroutine VFRICTION with the Coulomb model.
- vfriction_coul.f
User subroutine VFRICTION for the Coulomb model.
- vfric_coef_rdcoul.inp
Input data that refer to user subroutine VFRIC_COEF with the rate-dependent Coulomb model.
- vfric_coef_rdcoul.f
User subroutine VFRIC_COEF for the rate-dependent Coulomb model.
- vfriction_rdcoul.inp
Input data that refer to user subroutine VFRICTION with the rate-dependent Coulomb model.
- vfriction_rdcoul.f
User subroutine VFRICTION for the rate-dependent Coulomb model.