The results of an
Eulerian analysis must be interpreted differently than those from a Lagrangian
analysis. In particular, any results based on nodal displacements are
meaningless in an Eulerian model because the Eulerian part is fixed and rigid.
Details concerning how Eulerian results are written to the output database are
available in
Output.
Special steps must be taken in
the Visualization module
of
Abaqus/CAE
to view material instances within an Eulerian part. By default,
Abaqus/CAE
displays the full Eulerian part mesh in both undeformed and deformed plot
states with no indication of the material instance boundaries within the mesh.
Visualization of material instances is based on output variable EVF, the Eulerian material volume fraction. Output variable EVF measures the amount of a particular material instance within an
element as a relative fraction. An EVF value of one indicates that the element is completely filled
with the specified material instance; an EVF value of zero indicates that the element is completely devoid
of the specified material instance.
For elements that are partially filled or filled with multiple materials,
Abaqus
estimates a simple boundary between materials by interpolating the EVF values in adjacent elements. These simple boundaries may be
slightly discontinuous across elements. To improve display of Eulerian
materials, you should instruct
Abaqus/CAE
either to use a results averaging threshold of 100% or to compute scalars after
averaging results;
Abaqus/CAE
remaps the material boundaries so they appear smooth and continuous across
elements. For more information about results averaging, see
Controlling result averaging;
for a more detailed discussion of how
Abaqus
calculates Eulerian material boundaries, see
Material Interfaces.
Output variable EVF is written to the output database if you request the
Preselected defaults in the field output request editor
(see
Modifying field output requests).
When you request output for EVF,
Abaqus
creates a separate material volume fraction output variable for each material
instance in the model; for example, EVF_WATER
is the volume fraction for the material instance named
Water. An output variable named
EVF_VOID is created to measure the volume
fraction of empty regions in an Eulerian part.
The following techniques can be used in
the Visualization module
to view the initial and deformed states of material in an Eulerian part:
Contour plots
A contour plot of output variable EVF for a particular material instance allows you to visualize
which areas of the model are occupied by the material during the analysis.
Areas occupied by the material (EVF equal to one) appear as a uniform color from the top of the
contour spectrum, while areas unoccupied by the material appear as a different
color from the bottom of the contour spectrum; depending on your contour plot
settings, the boundary of the material instance appears in a range of colors as
EVF transitions from one to zero (see
Figure 1).
Figure 1. Contour plot of an Eulerian material instance.
Contour plots are of limited usefulness when visualizing Eulerian materials
because the contours appear on the faces of the Eulerian parts. You cannot
effectively visualize material volume fraction contours on the interior of
Eulerian parts.
To visualize the behavior of a material on the interior of an Eulerian part,
activate a view cut along an isosurface of the EVF variable associated with that material instance.
Abaqus/CAE
automatically creates these isosurface view cuts for each material instance in
the model, but you must activate them in the View Cut
Manager. Using the view cut options, you can eliminate portions of
the part that do not include a selected material by rendering them unfilled,
rendering them translucent, or removing them from the display (see
Figure 2).
Figure 2. View cut along an Eulerian material instance isosurface.
If your Eulerian part includes regions without a material assignment, it may
be helpful to activate an isosurface view cut based on the
EVF_VOID output variable. By cutting away all
regions in which EVF_VOID is greater than
0.5, you are able to see the shape of materials
within the part.
After activating an isosurface view cut based on the EVF variable, you can change the primary field output variable
without affecting the view cut. This enables you to visualize results contours
along the boundaries of material instances instead of on Eulerian part faces
(see
Figure 3).
Figure 3. Contour plot of stresses in a cut Eulerian part.
Isosurface view cuts based on output variable EVF do not affect Lagrangian part instances in a coupled
Eulerian-Lagrangian model. The Lagrangian parts remain visible when the cut is
active. Therefore, this technique is useful for visualizing the interaction
between a Lagrangian part and an Eulerian material instance.
For further details on using view cuts in
the Visualization module,
see
Cutting through a model.
Combining view
cuts and contour plots
In an Eulerian part that includes three material instances, you can use a
combination of view cuts and contour plots to distinguish material instances in
the undeformed and deformed model states. First, use an isosurface view cut to
remove one of the material instances from the display, as discussed above.
Then, create a contour plot of output variable EVF for one of the remaining material instances. The resulting
colors in the model distinguish one material from the other. To produce a more
defined boundary between the materials, you can reduce the number of contour
intervals to two.
For example,
Figure 4
depicts an Eulerian model of a lead projectile impacting a brass plate. The
void regions of the Eulerian part are cut away. A two-interval contour plot is
applied, rendering the brass in one color and the lead (i.e., not brass) in
another color. The resulting plot offers a useful generalization of the
deformed shape of the projectile and plate.
Figure 4. A contour plot is used to distinguished two Eulerian materials in a
projectile impact analysis.
Currently there is no way to visually distinguish more than three Eulerian
material instances simultaneously using
Abaqus/CAE.
Color
coding
Color coding cannot be used to visualize material behavior in Eulerian
parts. The color coding tool in
Abaqus/CAE
does not recognize Eulerian section or material assignments. Color coding based
on element sets is also ineffective for deformed shape plots because the
Eulerian elements do not deform with the material.
However, in coupled Eulerian-Lagrangian models, color coding can distinguish
between Eulerian and Lagrangian part instances or Eulerian and Lagrangian
element types. When used with the visualization techniques discussed above,
color coding can be helpful in distinguishing Lagrangian bodies from Eulerian
materials in a model.
Certain types of coupled Eulerian-Lagrangian models involve a single
Eulerian material instance throughout the Eulerian part; for example, a
Lagrangian penetrator moving through a uniform Eulerian material. In these
analyses the deformation of the Eulerian material is not as important as the
interaction between the Eulerian material and the Lagrangian body. You can use
a display group to remove the Eulerian elements from the display and visualize
results (such as contact pressure or stress) on only the Lagrangian body.
