VFRIC, VFRIC_COEF, and VFRICTION

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, $τ_{c r i t}$ , at which surfaces begin to slide with respect to each other is given as

τ_{c r i t} = μ p,

where $μ$ 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, $μ$ , is given by an exponential law

μ = μ_{k} + (μ_{s} - μ_{k}) e^{- d_{c} {\dot{γ}}_{e q}},

where $μ_{s}$ is the static coefficient of friction, $μ_{k}$ is the kinetic coefficient of friction, $d_{c}$ is the decay coefficient, and ${\dot{γ}}_{e q}$ 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 $μ =$ 0.15; for the rate-dependent Coulomb model $μ_{s} =$ 0.15, $μ_{k} =$ 0.05, and $d_{c} =$ 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.

Table 1. Comparison of velocity values for the rate-dependent Coulomb model for user subroutine VFRIC.
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

Table 2. Comparison of velocity values for the rate-dependent Coulomb model for user subroutines VFRIC_COEF and VFRICTION.
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.

User subroutine tested in a coupled temperature-displacement analysis

Elements tested

C3D8RT

Features tested

User subroutine to define frictional behavior for contact surfaces in a coupled temperature-displacement analysis.

Problem description

The problem described in Part II of FRIC is solved using Abaqus/Explicit. A transient analysis is performed. The mechanical and thermal properties are identical to those used in the analysis performed with Abaqus/Standard. Only two steps are required for the Abaqus/Explicit simulation: a downward force is applied in the first step to establish and maintain contact between the blocks, and a tangential force is applied in the second step to promote sliding between the blocks. In each step the mechanical and thermal loads are applied gradually to ensure a quasi-static response. The total applied tangential force is 0.18 (versus 100 in Abaqus/Standard); this is the force required to generate a total slip of 0.15 over a time interval of 1000 when the load is prescribed with a ramp function.

Results and discussion

The results obtained with Abaqus/Explicit compare well with the analytical solution for the total slip (the total slip predicted by Abaqus/Explicit is 0.145). Closer agreement with the analytical solution can be obtained by reducing the loading rate. This further reduces the effects of material inertia on the response.

Input files

vfric_c3d8rt.inp: Coupled temperature-displacement analysis.
vfric_c3d8rt.f: User subroutine for the coupled temperature-displacement analysis.