VUINTER

User subroutine to define the interaction between contact surfaces.

User subroutine VUINTER:

can be used to define the mechanical and thermal interaction between contacting surfaces;
must provide the entire definition of the interaction between the contacting surfaces;
can use and update solution-dependent state variables; and
must be used with the penalty contact constraint algorithm.

The following topics are discussed:

Terminology
Local coordinate system
Conventions for heat flux and stress
User subroutine interface
Variables to be defined
Variables that can be updated
Variables passed in for information

Terminology

The use of user subroutine VUINTER 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 $n, n = 1, 2...$ nSlvNod, is the surface node number of the nth node in this list; jSlvUid $(n)$ 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 Assembly definition). 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).

Local coordinate system

The array alocaldir defines the direction cosines of a local coordinate system for each slave node. The first local direction corresponds to the contact normal direction from the perspective of the slave node. For a two-dimensional VUINTER model the second local direction is the tangent direction defined by the cross product of the vector into the plane of the model (0., 0., −1.0) and the slave normal. For a three-dimensional VUINTER model the second and third local directions correspond to two orthogonal tangent directions $t_{1}$ and $t_{2}$ , which are set as follows:

If the master surface is a cylindrical analytical surface, the second local direction corresponds to the generator direction (see Analytical rigid surface definition), and the third local direction is the cross product of the first and second local directions.
If the master surface is an analytical surface of revolution, the third local direction corresponds to the hoop direction, and the second local direction is the cross product of the third and first local directions.
If the master surface is a three-dimensional, element-based surface, the tangent directions are based on the slave normal, using the standard convention for calculating surface tangents (see Conventions).

For the two cases listed above involving three-dimensional analytical surfaces, the local tangent directions will reflect a rotation of the master surface. For the last case (three-dimensional, element-based master surface) the tangent directions may not follow the rotation of either the master or slave surfaces; for example, the local system would remain fixed with respect to the global system if a slave node and its surrounding facets rotate about an axes parallel to the slave normal.

The 2 × 2 array stored in drot for each slave node represents the incremental rotation of the tangent directions within the tangent plane corresponding to the tracked point of a three-dimensional master surface. (This incremental rotation array is equal to a unit matrix if nDir is equal to 2.) This incremental rotation matrix is provided so that vector- or tensor-valued state variables defined within the tangent plane can be rotated in this subroutine. For example, the second and third components of the rdisp array (i.e., the relative slip components) are rotated by this amount before VUINTER is called. However, as already mentioned, the rotation of the tangent directions may not reflect a physical rotation of the master or slave surface.

Conventions for heat flux and stress

A positive flux indicates heat flowing into a surface, and a negative flux denotes heat leaving the surface. Flux must be specified for both surfaces, and they need not be equal and opposite so that effects such as frictional dissipation and differential surface heating can be modeled.

A positive normal stress denotes a pressure directed into the surface (opposite the local normal direction). Positive shear stresses denote shear tractions in the direction of the local surface tangents.

User subroutine interface

      subroutine vuinter(
C Write only
     1 sfd, scd, spd, svd,
C Read/Write - 
     2 stress, fluxSlv, fluxMst, sed, statev,
C Read only - 
     3 kStep, kInc, nFacNod, nSlvNod, nMstNod, nSurfDir,
     4 nDir, nStateVar, nProps, nTemp, nPred, numDefTfv,
     5 jSlvUid, jMstUid, jConMstid, timStep, timGlb,
     6 dTimCur, surfInt, surfSlv, surfMst,
     7 rdisp, drdisp, drot, stiffDflt, condDflt,
     8 shape, coordSlv, coordMst, alocaldir, props,
     9 areaSlv, tempSlv, dtempSlv, preDefSlv, dpreDefSlv,
     1 tempMst, dtempMst, preDefMst, dpreDefMst) 
C
      include `vaba_param.inc'
C
      character*80 surfInt, surfSlv, surfMst
C
      dimension props(nProps), statev(nStateVar,nSlvNod), 
     1 drot(2,2,nSlvNod), sed(nSlvNod), sfd(nSlvNod),
     2 scd(nSlvNod), spd(nSlvNod), svd(nSlvNod),
     3 rdisp(nDir,nSlvNod), drdisp(nDir,nSlvNod),
     4 stress(nDir,nSlvNod), fluxSlv(nSlvNod),
     5 fluxMst(nSlvNod), areaSlv(nSlvNod),
     6 stiffDflt(nSlvNod), condDflt(nSlvNod),
     7 alocaldir(nDir,nDir,nSlvNod), shape(nFacNod,nSlvNod),
     8 coordSlv(nDir,nSlvNod), coordMst(nDir,nMstNod),
     9 jSlvUid(nSlvNod), jMstUid(nMstNod),
     1 jConMstid(nFacNod,nSlvNod), tempSlv(nSlvNod),
     2 dtempSlv(nSlvNod), preDefSlv(nPred,nSlvNod),
     3 dpreDefSlv(nPred,nSlvNod), tempMst(numDefTfv),
     4 dtempMst(numDefTfv), preDefMst(nPred,numDefTfv),
     5 dpreDefMst(nPred,numDefTfv)

      user coding to define stress,
      and, optionally, fluxSlv, fluxMst, statev, sed, sfd, scd, spd,
      and svd

      return
      end

Variables to be defined

stress(nDir, nSlvNod): On entry this array contains the stress at the interface during the previous time increment. It must be updated to the stress at the interface in the current time increment.

Variables that can be updated

fluxSlv(nSlvNod): On entry this array contains the flux entering the slave surface during the previous time increment. It must be updated to the flux entering the slave surface during the current increment.
fluxMst(nSlvNod): On entry this array contains the flux entering the master surface during the previous time increment. It must be updated to the flux entering the master surface during the current time increment.
sfd(nSlvNod): This array can be updated to contain the increment in frictional dissipation at each node (units of energy per unit area). These values contribute to the output variables SFDR and ALLFD and have no effect on other solution variables.
scd(nSlvNod): This array can be updated to contain the increment in creep dissipation at each node (units of energy per unit area). These values contribute to the output variables SFDR and ALLCD and have no effect on other solution variables.
spd(nSlvNod): This array can be updated to contain the increment in plastic dissipation at each node (units of energy per unit area). These values contribute to the output variables SFDR and ALLPD and have no effect on other solution variables.
svd(nSlvNod): This array can be updated to contain the increment in viscous dissipation at each node (units of energy per unit area). These values contribute to the output variables SFDR and ALLVD and have no effect on other solution variables.
sed(nSlvNod): On entry this array contains the elastic energy density at the slave nodes at the beginning of the increment. It can be updated to contain the elastic energy density at the end of the current time increment. These values contribute to the output variable ALLSE and have no effect on other solution variables.
statev(nstateVar, nSlvNod): This array contains the user-defined solution-dependent state variables for all the nodes on the slave surface. You define the size of this array (see User-defined interfacial constitutive behavior for more information). This array will be passed in containing the values of these variables prior to the call to user subroutine VUINTER. If any of the solution-dependent state variables is being used in conjunction with the surface interaction, it must be updated in this subroutine.

Variables passed in for information

kStep: Step number.
kInc: Increment number.
nFacNod: Number of nodes on each master surface facet. nFacNod is 2 for two-dimensional surfaces, and nFacNod is 4 for three-dimensional surfaces (the first and last nodes are the same for triangular facets). If the master surface is an analytical rigid surface, this variable is passed in as 0.
nSlvNod: Number of slave nodes.
nMstNod: Number of master surface nodes, if the master surface is made up of facets. If the master surface is an analytical rigid surface, this variable is passed in as 0.
nSurfDir: Number of tangent directions at the contact points (nSurfDir = nDir - 1).
nDir: Number of coordinate directions at the contact points. (In a three-dimensional model nDir will be 2 if the surfaces in the contact pair are two-dimensional analytical rigid surfaces or are formed by two-dimensional elements.)
nStateVar: Number of user-defined state variables.
nProps: User-specified number of property values associated with this surface interaction model.
nTemp: 1 if the temperature is defined and 0 if the temperature is not defined.
nPred: Number of predefined field variables.
numDefTfv: Equal to nSlvNod if the master surface is made up of facets. If the master surface is an analytical rigid surface, this variable is passed in as 1.
jSlvUid(nSlvNod): This array lists the user-defined global node numbers (or internal node numbers for models defined in terms of an assembly of part instances) of the nodes on the slave surface.
jMstUid(nMstNod): This array lists the user-defined global node numbers (or internal node numbers for models defined in terms of an assembly of part instances) of the nodes on the master surface. If the master surface is an analytical rigid surface, this array is passed in as a dummy array.
jConMstid(nFacNod, nSlvNod): This array lists the surface node numbers of the master surface nodes that make up the facet onto which each slave node projects. If the master surface is an analytical rigid surface, this array is passed in as a dummy array.
timStep: Value of step time.
timGlb: Value of total time.
dtimCur: Current increment in time from $t = t_{c u r r} - Δ t$ to $t = t_{c u r r}$ .
surfInt: User-specified surface interaction name, left justified.
surfSlv: Slave surface name.
surfMst: Master surface name.
rdisp(nDir, nSlvNod): An array containing the relative positions between the two surfaces. The first component is the relative position of the slave node, with respect to the master surface, in the normal direction (a positive value indicates a penetration, and a negative value indicates a gap). The second and third components, if applicable, are the accumulated incremental relative tangential displacements of the slave node, measured from the beginning of the step in which the contact pair is defined. The local directions in which the relative displacements are defined are stored in alocaldir. If the master surface is an analytical surface, the elements in rdisp are set to r_MaxVal for the slave nodes that are far from the master surface.
drdisp(nDir, nSlvNod): An array containing the increments in relative positions between the two surfaces during the current time increment. If the master surface is an analytical surface, the elements in drdisp are set to r_MaxVal for the slave nodes that are far from the master surface.
drot(2, 2, nSlvNod): Rotation increment matrix. This matrix represents the incremental rotation of the local surface tangent directions for a three-dimensional surface. This rotation matrix for each slave node is defined as a unit matrix for two-dimensional surfaces. If the master surface is an analytical surface, the elements in drot are set to r_MaxVal for the slave nodes that are far from the master surface.
stiffDflt(nSlvNod): Values of the default penalty stiffnesses for each slave node (units of ${FL}^{- 3}$ ).
condDflt(nSlvNod): Values of the default penalty conductances for each slave node (units of ${J θ}^{- 1} T^{- 1}$ ).
shape(nFacNod, nSlvNod): For each contact point this array contains the shape functions of the nodes of its master surface facet, 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, nSlvNod): Array containing the nDir components of the current coordinates of the slave nodes.
coordMst(nDir, nMstNod): 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 the coordinates of the contact points on the master surface.
alocaldir(nDir, nDir, nSlvNod): Direction cosines of the local surface coordinate system. The first array index corresponds to the components of the local directions, and the second array index corresponds to the local direction number. The first direction (alocaldir(1..nDir,1,...)) is the normal to the surface. The second direction (alocaldir(1..nDir,2,...)) is the first surface tangent. For a three-dimensional surface, the third direction (alocaldir(1..3,3,...)) is the second surface tangent. If the master surface is an analytical rigid surface, the numbers in alocaldir are valid only if the corresponding parts in rdisp are valid (i.e., not equal to r_MaxVal).
props(nProps): User-specified vector of property values to define the behavior between the contacting surfaces.
areaSlv(nSlvNod): Area associated with the slave nodes (equal to 1 for node-based surface nodes).
tempSlv(nSlvNod): Current temperature at the slave nodes.
dtempSlv(nSlvNod): Increment in temperature during the previous time increment at the slave nodes.
preDefSlv(nPred, nSlvNod): Current user-specified predefined field variables at the slave nodes (initial values at the beginning of the analysis and current values during the analysis).
dpreDefSlv(nPred, nSlvNod): Increment in the predefined field variables at the slave nodes during the previous time increment.
tempMst(numDefTfv): Current temperature at the nearest points on the master surface.
dtempMst(numDefTfv): Increment in temperature during the previous time increment at the nearest points on the master surface.
preDefMst(nPred, numDefTfv): 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).
dpreDefMst(nPred, numDefTfv): Increment in the predefined field variables during the previous time increment at the nearest points on the master surface.