1.2.6 VFRICTION

1.2.6 VFRICTION
User subroutine to define frictional behavior for contact surfaces.

Product: Abaqus/Explicit

References

Overview

User subroutine VFRICTION:

can be used to define the frictional behavior between contacting surfaces;
can be used when the classical Coulomb friction model is too restrictive and a more complex definition of shear transmission between contacting surfaces is required;
must provide the entire definition of shear interaction between the contacting surfaces;
can use and update solution-dependent state variables for node-to-face and node-to-analytical rigid surface contact;
cannot be used in conjunction with softened tangential surface behavior; and
can be used only with the general contact algorithm.

Terminology

The use of user subroutine VFRICTION requires familiarity with the following terminology.

Surface node numbers

The “surface node number” refers to the position of a particular node in the list of nodes on the surface. For example, there are nSlvNod nodes on the slave surface. Number nSlvNod, is the surface node number of the nth node in this list; jSlvUid is the user-defined global number of this node. An Abaqus/Explicit model can be defined in terms of an assembly of part instances (see “Defining an assembly,” Section 2.9.1 of the Abaqus Analysis User's Manual). In such models a node number in jSlvUid is an internally generated node number. If the original node number and part instance name are required, call the utility routine VGETPARTINFO (see “Obtaining part information,” Section 2.1.5).

Contact points

The nodes on the slave surface that are in contact in the current time increment are defined as “contact points.” The number of contact points is passed into user subroutine VFRICTION as nContact. The array jConSlvid(nContact) gives the surface node numbers for the contact points.

Local coordinate system

A local coordinate system is defined for each contact point to facilitate specification of frictional forces and incremental slip. The local 1-direction is tangential to the master surface; it is defined by , where is the incremental slip vector. The incremental slip vector used to define corresponds to the incremental slip in the current time increment. The master surface normal direction, , is the local 3-direction. The local 2-direction is given by , which is also tangent to the master surface. The vectors are shown in Figure 1.2.6–1. The direction cosines for and with respect to the global coordinate system are available in dirCosS1 and dirCosN, respectively. In the case of zero incremental slip () we choose an arbitrary direction for that is orthogonal to the normal direction, .

Figure 1.2.6–1 Local coordinate system for three-dimensional contact with VFRICTION.

Frictional forces

You specify the frictional force, fTangential, at each contact point in local coordinates in this subroutine. The array fTangential is dimensioned such that only the tangential components can be specified. Any components of the frictional force that are not specified will remain equal to zero. For isotropic friction, only the first component of the frictional force need be specified since the second component should be zero. A “stick force” at each contact point is provided in the array fStickForce to assist you in setting appropriate frictional force values. The stick force is the force required to prevent additional “plastic” slipping. The stick force at each contact point is provided as a scalar value as it would act in the direction opposite to . The stick force is computed prior to calling user subroutine VFRICTION. The first component of the frictional force should be in the range between zero and the negative of the stick force value. Typically, the stick force will be positive and the first component of the applied frictional force will be negative, opposing the incremental slip. Penalty contact includes an elastic slip regime due to finite penalty stiffness; so occasionally the stick force will be negative during recovery of elastic slip, indicating that it is appropriate for the first component of the frictional force to be positive (i.e., acting in the same direction as the incremental slip). A noisy or unstable solution is likely to result if the first component of fTangential is set outside the range between zero and the negative of the stick force value.

After user subroutine VFRICTION is called, frictional forces that oppose the forces specified at the contact points are distributed to the master nodes.

User subroutine interface

       subroutine vfriction (
C Write only - 
     *   fTangential, 
C Read/Write - 
     *   state,
C Read only - 
     *   nBlock, nBlockAnal, nBlockEdge, 
     *   nNodState, nNodSlv, nNodMst, 
     *   nFricDir, nDir, 
     *   nStates, nProps, nTemp, nFields, 
     *   jFlags, rData, 
     *   surfInt, surfSlv, surfMst, 
     *   jConSlvUid, jConMstUid, props, 
     *   dSlipFric, fStickForce, fTangPrev, fNormal, 
     *   areaSlv, dircosN, dircosS1, 
     *   shapeSlv, shapeMst, 
     *   coordSlv, coordMst, 
     *   velSlv, velMst, 
     *   tempSlv, tempMst, 
     *   fieldSlv, fieldMst )
C
      include `vaba_param.inc'
C
      dimension fTangential(nFricDir,nBlock),
     *   state(nStates,nNodState,nBlock),
     *   jConSlvUid(nNodSlv,nBlock), 
     *   jConMstUid(nNodMst,nBlockAnal), 
     *   props(nProps),
     *   dSlipFric(nDir,nBlock),
     *   fStickForce(nBlock), 
     *   fTangPrev(nDir,nBlock),
     *   fNormal(nBlock), 
     *   areaSlv(nBlock),
     *   dircosN(nDir,nBlock),
     *   dircosS1(nDir,nBlock), 
     *   shapeSlv(nNodSlv,nBlockEdge), 
     *   shapeMst(nNodMst,nBlockAnal), 
     *   coordSlv(nDir,nNodSlv,nBlock), 
     *   coordMst(nDir,nNodMst,nBlockAnal), 
     *   velSlv(nDir,nNodSlv,nBlock), 
     *   velMst(nDir,nNodMst,nBlockAnal), 
     *   tempSlv(nBlock), 
     *   tempMst(nBlockAnal),
     *   fieldSlv(nFields,nBlock),
     *   fieldMst(nFields,nBlockAnal)
C
      parameter( iKStep    = 1,
     *           iKInc     = 2,
     *           iLConType = 3,
     *           nFlags    = 3 )
C
      parameter( iTimStep      = 1,
     *           iTimGlb       = 2,
     *           iDTimCur      = 3,
     *           iFrictionWork = 4, 
     *           nData         = 4 )
C
      dimension jFlags(nFlags), rData(nData)
C
      character*80 surfInt, surfSlv, surfMst 
C
      user coding to define fTangential
      and, optionally, state
C
      return
      end

Variable to be defined

fTangential(nFricDir,nBlock)

This array must be updated to the current values of the frictional force components for all contact points in the local tangent directions. See Figure 1.2.6–1 for a definition of the local coordinate system. This array will be zero (no friction force) until it is set.

Variable that can be updated

state(nStates,nNodState,nBlock)

This array contains the user-defined, solution-dependent state variables for all the nodes on the slave surface. The use of state variables is applicable for node-to-face and node-to-analytical rigid surface contact. See “Frictional behavior,” Section 32.1.5 of the Abaqus Analysis User's Manual, for more information on the size of this array. This array will be passed in containing the values of these variables prior to the call to user subroutine VFRICTION.

If any of the solution-dependent state variables are being used in conjunction with the friction behavior, they must be updated in this subroutine. These state variables need to be updated with care, as a slave node can be in contact with multiple master surfaces. Such a slave node may be passed into the user subroutine at a given increment multiple times, possibly on separate calls to the user subroutine, and you may end up advancing the state variables for that node multiple times for a single time increment. One trick to keep track of whether or not a node state is advanced is to use one of the state variables exclusively for this purpose. You could set that selected state variable to the current increment number and update the state only if it is not already set to the current increment number.

Variables passed in for information

nBlock

Number of contacting points to be processed in this call to VFRICTION.

nBlockAnal

1 for analytical rigid master surface; nBlock otherwise.

nBlockEdge

nBlock for edge-type slave surface; 1 otherwise.

nNodState

1 for node-to-face contact and node-to-analytical rigid surface contact.

nNodSlv

1 for node-to-face and node-to-analytical rigid surface contact; 2 for edge-to-edge contact.

nNodMst

1 for analytical rigid master surface; 2 for edge-type master surface; 4 for facet-type master surface.

nFricDir

Number of tangent directions at the contact points (nFricDir = nDir - 1).

nDir

Number of coordinate directions at the contact points (equal to 3).

nStates

Number of user-defined state variables.

nProps

User-specified number of property values associated with this friction model.

nTemp

1 if the temperature is defined and 0 if the temperature is not defined.

nFields

Number of predefined field variables.

jFlag(1)

Step number.

jFlag(2)

Increment number.

jFlag(3)

1 for node-to-face contact, 2 for edge-to-edge contact, and 3 for node-to-analytical rigid surface contact.

rData(1)

Value of step time.

rData(2)

Value of total time.

rData(3)

Current increment in time from to .

rData(4)

This variable contains the value of the total frictional dissipation in the entire model from the beginning of the analysis. The units are energy per unit area.

surfInt

User-specified surface interaction name, left justified.

surfSlv

Slave surface name, not applicable to general contact.

surfMst

Master surface name, not applicable to general contact.

jConSlvUid(nNodSlv,nBlock)

This array lists the surface node numbers of the slave surface nodes that are in contact.

jConMstUid(nNodMst,nBlockAnal)

This array lists the surface node numbers of the master surface nodes that make up the facet with which each slave node is in contact.

props(nProps)

User-specified vector of property values to define the frictional behavior between the contacting surfaces.

dSlipFric(nDir,nBlock)

This array contains the incremental frictional slip during the current time increment for each contacting point in the current local coordinate system. These incremental slips correspond to tangential motion in the time increment from to . This incremental slip is used to define the local coordinate system at each contact point (see Figure 1.2.6–1) so that only the first component of dSlipFric can be nonzero in the local system. If the slip direction changes between increments, dSlipFric may have a nonzero component in the local 2-direction and, if the surface is faceted and the contact point moves from one facet to another, in the local 3-direction.

fStickForce(nBlock)

This array contains the magnitude of frictional force required to enforce stick conditions at each contact point. This force depends on the previous frictional force, the value of the penalty stiffness, and the previous incremental slip. The penalty stiffness is assigned automatically. Occasionally, during recovery of elastic slip associated with the penalty method, the stick force will be assigned a negative value.

fTangPrev(nDir,nBlock)

This array contains the values of the frictional force components calculated in the previous increment but provided in the current local coordinate system (zero for nodes that were not in contact).

fNormal(nBlock)

This array contains the magnitude of the normal force for the contact points applied at the end of current time increment; i.e., at time .

areaSlv(nBlock)

Area associated with the slave nodes (equal to 1 for node-based surface nodes).

dircosN(nDir,nBlock)

Direction cosines of the normals to the master surface at the contact points.

dirCosS1(nDir,nBlock)

Direction cosines of the incremental slip at the contact points. The direction cosines are undefined (all components zero) if the incremental frictional slip is zero.

shapeSlv(nNodSlv,nBlockEdge)

For each contact point this array contains the shape functions of the nodes of its slave surface, evaluated at the location of the contact point. If the master surface is an analytical rigid surface, this array is passed in as a dummy array.

shapeMst(nNodMst,nBlockAnal)

For each contact point this array contains the shape functions of the nodes of its master surface, evaluated at the location of the contact point. If the master surface is an analytical rigid surface, this array is passed in as a dummy array.

coordSlv(nDir,nNodSlv,nBlock)

Array containing the nDir components of the current coordinates of the slave nodes.

coordMst(nDir,nNodMst,nBlockAnal)

Array containing the nDir components of the current coordinates of the master nodes. If the master surface is an analytical rigid surface, this array is passed in as a dummy array.

velSlv(nDir,nNodSlv,nBlock)

Array containing the nDir components of the current velocity of the slave nodes.

velMst(nDir,nNodMst,nBlockAnal)

Array containing the nDir components of the current velocity of the master nodes. If the master surface is an analytical rigid surface, this array is passed in as a dummy array.

tempSlv(nBlock)

Current temperature at the slave nodes.

tempMst(nBlockAnal)

Current temperature at the nearest points on the master surface.

fieldSlv(nFields,nBlock)

Current user-specified predefined field variables at the slave nodes (initial values at the beginning of the analysis and current values during the analysis).

fieldMst(nFields,nBlockAnal)

Current user-specified predefined field variables at the nearest points on the master surface (initial values at the beginning of the analysis and current values during the analysis).