Product: ABAQUS/Explicit
The problems in this section demonstrate modeling of frictional behavior with user subroutine VFRIC.
The first example uses a VFRIC user subroutine that is 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
is the coefficient of friction and p is normal pressure.The second example uses a VFRIC user subroutine for rate-dependent Coulomb friction behavior where the evolution of the coefficient of friction, , is given by an exponential law
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 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,” Section 1.7.5.
For the Coulomb model 
0.15; for the rate-dependent Coulomb model 
0.15, 
0.05, and 
0.01 s/in.
The results for the two models are discussed below.
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 subroutine VFRIC 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.
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 subroutine VFRIC (see Table 4.1.25–1). 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 has additional differences due to default viscous contact damping, which contributes to the contact forces opposing the motion of the block.
Input data that refer to the user subroutine VFRIC with the Coulomb model.
User subroutine for the Coulomb model.
Input data (with the model defined in terms of an assembly of part instances) that refer to the user subroutine VFRIC with the Coulomb model and the utility routine VGETPARTINFO.
User subroutine for the Coulomb model that illustrates the use of the utility routine VGETPARTINFO.
Input data (with the model defined in terms of an assembly of part instances) that refer to the user subroutine VFRIC with the Coulomb model and the utility routine VGETINTERNAL.
User subroutine for the Coulomb model that illustrates the use of the utility routine VGETINTERNAL.
Input data that refer to the user subroutine VFRIC with the rate-dependent Coulomb model.
User subroutine for the rate-dependent Coulomb model.
Input data that refer to the user subroutine VFRIC with the rate-dependent Coulomb model and penalty contact.
User subroutine to define frictional behavior for contact surfaces in a coupled temperature-displacement analysis.
The problem described in Part II of “FRIC,” Section 4.1.4, 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.
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.
Coupled temperature-displacement analysis.
User subroutine for the coupled temperature-displacement analysis.