Your submodel analysis is driven, either partly or completely, from the
results obtained from a global model analysis. The results from the global
model are interpolated onto the surfaces on the appropriate parts of the
boundary of the submodel. Thus, the response at the boundary of the local
region is defined by the solution for the global model. The driven surfaces and
any loads applied to the local region determine the solution in the submodel.
Surface-based submodeling should be used only when the node-based technique
cannot provide adequate results. For a comparison of the two submodeling
techniques and recommendations for their application, refer to
About Submodeling.
Saving the Results from the Global Model
The results from the global analysis must be saved at all elements required
for the interpolation of the driven variables to the boundary surface of the
submodel. Only the output database (in ODB or
SIM format) can be used for this purpose.
In each step of the global model whose solution will be used to drive the submodel, write the
stress results to the output database (see Output to the Output Database).
Referring to the Global Model Results from the Submodel Analysis
You must define the source of the global solution results and provide the
name of the output database file (in ODB or
SIM format); the file extension is optional.
If the file extension is omitted,
Abaqus
will use in order, the ODB output database
file or the SIM database file.
Specifying the Driven Surfaces in the Submodel
Specifying the driven element-based surfaces does not activate the driven
surface loads: they must be activated by specifying the appropriate submodel
distributed surface loads.
All surface facets of the submodel to be driven by stresses in any step must
be specified as driven surfaces since the list of surfaces cannot be extended
subsequent to its initial definition (even at restart). However, variables at
the surfaces given do not have to be driven in all steps: the choice of which
surfaces are driven in a particular step is made as part of a submodel
distributed surface load definition, as discussed in
Defining the Driven Surface Tractions in the Submodel
later in this section.
Defining Geometric Tolerances
A geometric tolerance is used to define how far driven element-based surface
nodes in the submodel can lie outside the exterior surface of the global model,
as that surface is interpolated in the global, undeformed finite element model.
By default, surface nodes in the submodel must lie within a distance calculated
by multiplying the average element size in the global model by 0.05. You can
change the tolerance, which is useful in cases where submodel driven surfaces
lie to a greater extent outside the global model exterior surface. Tolerances
larger than this default value, however, can result in significantly greater
computation times and lower accuracy in the driven solution for driven surface
regions significantly outside the global model exterior surface.
You can define the geometric tolerance as a fraction of the size of the
average element in the global model or as an absolute distance in the length
units chosen for the model. If both tolerances are defined,
Abaqus
uses the tighter tolerance.
The Exterior Tolerance in Solid-to-Solid Submodeling
The exterior tolerance for a solid-to-solid submodel analysis is indicated
by the shaded region in
Figure 2.
If the distance between the driven surface nodes and the free surface of the
global model falls within the specified tolerance, the solution variables from
the global model are extrapolated to the submodel.
Defining the Driven Surface Tractions in the Submodel
The actual driven surface tractions are defined in any step as submodel
distributed surface loads. The stresses resulting in these tractions are
“driven variables” obtained from the output database file of the global
analysis.
All stress components from the global model elements that will drive the
submodel boundary surface must have been written to the output database. They
will be used to create traction, shear, and normal stresses at integration
points of driven surfaces (as non-uniform distributed surface loads). All
applicable stress components are calculated and applied to the surface
integration points at each time increment.
Specifying the Step Number from the Global Analysis
You specify the step of the global model history that is to be used for the
driven variables in the current submodel analysis step.
Modifying the Set of Driven Surface Tractions
You can modify the submodel distributed surface load definitions from step
to step to change the global step reference, you can remove surface load
definitions, and you can reintroduce them later (see
About Loads).
Submodel distributed surface loads do not propagate between steps. At each new
step all submodel distributed surface loads defined in previous steps will be
removed unless they are modified or redefined. New surfaces cannot be added to
the total set of driven surface defined for the submodel; this set of driven
surfaces is a fixed part of the model definition.
Guidelines for Obtaining Adequate Solution Accuracy
Unlike node-based submodeling, surface-based submodeling can in many cases
provide incorrect or misleading submodel results. This risk follows from the
methods used to interpolate stresses from the global model to the submodel:
The global model material point stresses are smoothed and associated
with the global model nodes.
These global model node-located stresses are then interpolated to the
submodel surface integration points and applied as tractions.
This process is generally nonconservative, resulting in a submodel traction
field that is not equivalent to the global model stress field in an equilibrium
sense.
Modeling Guidelines
You can improve accuracy and achieve reasonable submodel solutions by
observing the following guidelines:
Design your models so that your submodel surface intersects the global
model in regions of relatively low stress gradients.
Design your models so that your submodel surface intersects the global
model in regions of uniform element size. A warning message is provided in the
data (.dat) file in cases where significant nonuniform
element size distributions are seen.
Checking Your Results
To understand whether your modeling approach results in a reasonably
accurate solution, the following guidelines are recommended:
Compare the stress distributions on the submodel-driven surfaces with
the stress distributions in the global model.
The degree to which the global model's stress distributions agree with those in
the submodel-driven surface is generally an indication of the level of accuracy
of your submodel solution.
When using inertia relief in the submodel for cases where submodeling
does not remove all rigid body modes, compare the inertia relief forces to the
prevailing force level in your submodel. If the inertia relief force is large
compared to the prevailing force level, your submodel results may be
inaccurate.
Special Considerations
There are several special considerations that are worth noting.
Handling of Rigid-Body Modes
When you use surface-based submodeling exclusively to drive your submodel
response, your displacement solution will not be unique; you will generally
encounter rigid-body modes and accompanying numerical issues. You can address
these rigid-body modes by
providing sufficient node-based submodel displacement boundary condition
definitions in the submodel analysis,
providing sufficient boundary condition definitions in the submodel
analysis, or
providing an inertia relief load definition in the submodel analysis
(see
Inertia Relief).
You can combine these definitions, as necessary and appropriate to your
model, to address all rigid body modes.
Cases of Finite Rotation
Global model stress results are stored in the output database in the global
coordinate system. Submodel tractions are calculated from these stresses and
the current configuration surface normal in the submodel. Hence, when your
global model result involves significant finite rotation, your submodel results
will generally be inaccurate unless you provide sufficient node-based submodel
displacement boundary condition definitions to impart similar rigid-body
rotations to the submodel; exclusive use of surface-based submodeling
definitions is not adequate to provide these rigid-body motions. You may also
experience convergence difficulties in the submodel when it is not properly
rotated.
Inelastic Behavior
When surface-based submodeling is used to drive a submodel region with an
inelastic material definition, you may encounter rigid-body modes and
accompanying numerical issues. For example, numerical issues will prevent
convergence if the submodel material definition includes plasticity and the
submodel loading results in a shear band formation beyond the material
hardening definition, such that unconstrained motion can occur (i.e., if the
submodel loads exceed the limit load capacity). In these cases node-based
submodeling should be used.
Procedures
Only the static procedure is allowed. Both general (possibly nonlinear) and
linear perturbation steps can be used in submodeling (see
General and Perturbation Procedures
for a discussion of general and linear perturbation steps).
Obtaining a Solution at a Particular Point in Time Using Linear Perturbation Analysis
In
Abaqus/Standard
it is possible to study the submodel's linearized response corresponding to a
particular point in time in the global solution by using a static, linear
perturbation procedure in the submodel analysis. You can select the increment
in the global analysis step that is to be used as the basis for calculating the
values for the driven variables. If you do not select an increment in a static
linear perturbation step, the last increment of the selected step in the global
analysis is used as the basis for calculating the values for the driven
variables. You cannot select an increment in a general submodel step.
Mixing General and Linear Perturbation Steps
It is possible to mix general steps and linear perturbation steps in both
the global and the submodel analyses.
Abaqus
allows general analysis steps to be treated as linear perturbation steps during
submodeling, and vice versa.
Example: Submodeling with General and Linear Perturbation Steps
For an example of submodeling that uses both general and linear
perturbation steps, consider the following situation. The global analysis
consists of a static preload—done as a general, nonlinear, analysis
step—followed by extraction of the eigenmodes of the preloaded structure, then
a step of 5 seconds of modal dynamic response analysis:
STEP
** Apply preload
STATIC
0.1, 1.0
…
** Write out stress results for elements needed to
** interpolate to the submodel's surfaces
ELEMENT OUTPUT, ELSET=DETAILSEND STEPSTEP
** Calculate modes and frequencies
FREQUENCY
…
** The ELEMENT OUTPUT option is repeated because
** this is the first linear perturbation step
ELEMENT OUTPUT, ELSET=DETAILUEND STEPSTEP
** Dynamic response of preloaded system
MODAL DYNAMIC
0.01, 5.0
…
END STEP
We wish to study the local, possibly nonlinear, response of a part of this
model that is so small that we do not need to model dynamic effects locally and
can, thus, perform two steps of static analysis:
** Define submodel surfaces (driven surfaces)
SUBMODEL,TYPE=SURFACE
PERIM
STEP
** Preload
STATIC
0.1, 1.0
DSLOAD, SUBMODEL, STEP=1
…
END STEPSTEP
** Local static response to global dynamic step
STATIC
0.01, 5.0
DSLOAD, SUBMODEL, STEP=3
…
END STEP
It is perfectly acceptable that the submodel analysis requests general,
possibly nonlinear, analysis for both steps, while in the global analysis the
dynamic step was a linear perturbation step (modal dynamics is always a linear
perturbation analysis). It is your responsibility to judge that this use of the
submodeling feature is reasonable. For example, suppose that the global
analysis were continued with a fourth step of general, nonlinear static
response:
RESTART, READ, STEP=3
** Read state at end of initial preload
** (could equally well use RESTART, READ, STEP=1)
STEP
** Add more preload
STATIC
0.2, 1.0
…
END STEP
This fourth general analysis step starts with the state at the end of
general analysis Step 1 because the frequency extraction and the modal dynamic
steps are both linear perturbation steps. However, if we restart the submodel
analysis in the same way, the solution may not be comparable with the global
model solution:
RESTART, READ, STEP=2
** Read state at end of step 2
STEP
** Add more preload
STATIC
0.2, 1.0
DSLOAD, SUBMODEL, STEP=4
…
END STEP
The second step in the submodel is a general analysis step, to which the
response may be nonlinear, thus changing the state of the model. A valid
alternative would be to apply the Step 4 response to the submodel immediately
after the first step:
RESTART, READ, STEP=1
** Read state at end of preload step
STEP
** Add more preload
STATIC
0.2, 1.0
DSLOAD, SUBMODEL, STEP=4
…
END STEP
Loads
Any loads that are applied in the submodel region of the global analysis
must be imposed in the submodel analysis in the usual way. It is your
responsibility to apply such loads to the submodel correctly so that they
correspond to the loading of the global model. See
About Loads
for an overview of the loads available in
Abaqus.
As described above, element stress output requests to the output database
file must be used in the global analysis to save the values of the driven
variables at the submodel boundary.
HEADING
…
SUBMODEL,TYPE=SURFACE, EXTERIOR TOLERANCE=toleranceList of all surfaces to be driven
**
STEPSTATIC (or any other allowable procedure)
Data line to define step time and control incrementation.
…DSLOAD, SUBMODEL, STEP=1
Data lines listing surfaces to be driven in this step
…
END STEP