In a
pure Lagrangian analysis a section definition includes a reference to a single
material. When you assign a section to a region or element in the Lagrangian
part, that region or element is completely filled with the referenced material.
The geometry of the region or element, therefore, defines the geometry of the
material.
In a pure Eulerian analysis the relationship between the section definition
and material is fundamentally different. An Eulerian section definition can
reference a list of materials. When you assign the Eulerian section to an
Eulerian part, you are defining which materials may be present in the part over
the course of the analysis. The part, however, is initially empty of material.
To introduce material to the initial state of an Eulerian part, you must use a
material assignment predefined field.
Material assignment predefined fields rely on the concept of material volume
fractions. During an Eulerian analysis,
Abaqus
tracks the material present in each element in terms of a volume fraction
assigned to each material instance; the volume fraction represents the
percentage of the element's volume that is occupied by a given material
instance. For elements that are partially filled or filled with multiple
materials, the exact geometric composition of the material within the element
is not known;
Abaqus
interpolates the material volume fractions from adjacent elements to estimate
the material boundaries within the element. These calculations are discussed in
more detail in
Material Interfaces.
In
Abaqus/CAE
the initial material volume fractions in an Eulerian part are specified by
creating a material assignment predefined field in the
Load module.
The predefined field associates each region in an Eulerian part instance with a
volume fraction for each material instance. The regions to which volume
fractions are assigned can be cells (in geometry), mesh elements, or groups of
elements. If you select a cell or a group of elements, the volume fraction
values are propagated to each of the underlying Eulerian elements in the cell
or group.
Volume fractions in a material assignment predefined field are expressed as
a number between zero and one; a volume fraction of one indicates that the
region is completely filled with the specified material. A volume fraction of
less than one indicates that the region is only partially filled with the
specified material; for example, a volume fraction of 0.25 means that the
specified material instance occupies 25% of the region. As mentioned
previously,
Abaqus
determines the material boundaries for partially filled elements based on the
volume fractions in adjacent elements; to achieve greater control over the
material boundaries within a region, you must refine the part mesh or redefine
the region boundaries.
If material volume fractions are not defined for a region of an Eulerian
part instance, that region is assigned a void. Similarly, if the volume
fractions for all materials in a region do not sum to one, the remainder of the
volume fraction in that region is assigned a void. Void regions do not have
material properties, but other materials can flow into and through a void
region during an analysis.
The material assignment predefined field effectively defines the topology of
materials in the initial configuration of your model. The Eulerian part is
typically arbitrary in shape; the material assignment predefined field adds to
the part the Eulerian materials that will interact during the analysis. For
example, consider the cross-section of the coupled Eulerian-Lagrangian model in
Figure 1.
The Eulerian part is simply an empty cube. Four regions defined on the part
determine the slope of the earth and the amount of water in the tank, and
material is assigned to these regions accordingly.
Figure 1. Material assignments in an Eulerian-Lagrangian model.
Material assignment predefined fields can be created only in the initial
step of an Eulerian analysis. In subsequent steps the materials deform from
their initial configuration and flow across the Eulerian mesh according to the
forces present in the model.
Abaqus/CAE
offers two techniques for defining material assignment predefined fields:
Uniform
definitions
Uniform material assignment field definitions are created by selecting
regions from an Eulerian part instance and directly specifying the volume
fraction of each material instance within those regions. Geometry must be
partitioned into separate cells representing the material regions. In part
instances that include orphan elements you can select individual elements to
act as regions.
Figure 2
illustrates a material assignment field created using uniform definitions. The
Eulerian part is partitioned into three regions, and material volume fractions
are defined in each region; each region is completely filled with a single
material instance. Volume fractions are not defined for the void region, since
void is the default material assignment.
Figure 2. A uniform material assignment field.
The uniform material assignment definition should be used only for
relatively simple regions that are uniformly filled with material. The
partitions needed to create complex regions can negatively impact the quality
of the Eulerian mesh, and partially filled regions are difficult to define and
interpret, particularly when working with geometry.
Material assignments for meshed geometry and orphan meshes can be defined
using a scalar discrete field. For each material instance in the part you
create a discrete field that associates individual elements with a volume
fraction for that material instance. For more information on creating discrete
fields, see
The Discrete Field toolset.
When you are assigning materials using a discrete field, you still must
select the region of the part instance to which the discrete field applies. If
the discrete field includes data for elements outside of the selected region,
these data are ignored. The default value associated with the discrete field is
assigned to any elements within the selected region that are not explicitly
listed in the discrete field.
Figure 3
shows a very simple example of a material assignment defined using discrete
fields. The Eulerian part consists of four elements and two material instances.
Two discrete fields, as defined in
Table 1,
are used to specify the material composition within the elements. The boundary
between the water and the sand is an estimation based on interpolation of the
material volume fractions in adjacent elements.
Figure 3. A discrete field material assignment.
Table 1. Volume fractions defined in discrete fields.
Discrete Field
Element 3
Default
Water_Field
0.5
1
Sand_Field
0.5
0
Note:
In any given element the sum of all material volume fractions should not
be greater than one.
Abaqus/CAE
assigns volume fractions incrementally by reading the discrete fields in the
Volume Fractions table from right to left; once the volume
fraction for an element reaches one, additional volume fractions assigned to
that element are ignored.
Since the discrete field can assign unique volume fractions to each
individual element, it allows more complicated material boundaries than the
uniform definition method without the need for excessive partitioning. The
volume fraction tool in
Abaqus/CAE
creates discrete fields specifically for use in material assignment predefined
fields. Through this tool, you can define complex Eulerian material regions
using the part modeling techniques available in
Abaqus/CAE.
For more information, see
Using the volume fraction tool.
For details on creating a discrete field material assignment in
Abaqus/CAE,
see
Defining a material assignment field.
An example of a discrete field material assignment definition (including the
use of the volume fraction tool) is illustrated in the Python script provided
in
Rivet forming.
