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
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
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
and ,
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
to .
- 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
).
- condDflt(nSlvNod)
-
Values of the default penalty conductances for each slave node (units of
).
- 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.
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