is a spatially varying field defined over elements, nodes, or element
faces in an
Abaqus
model;

can be used to define shell thicknesses for shell elements with
displacement degrees of freedom;

can be used to define shell stiffness;

can be used to define local coordinate systems on solid continuum and
shell elements that have displacement degrees of freedom;

can be used to define orientation angles on the layers of composite
shell elements that have displacement degrees of freedom;

can be used to define orientation angles for connector elements;

can be used to define thicknesses on the layers of conventional
composite shell elements;

can be used to specify initial contact clearances;

can be used to specify the volume fraction, aspect ratio, and
second-order orientation tensor of a constituent in a multiscale material; and

in an
Abaqus/Standard
analysis can be used to define mass density, linear elastic material behavior,
and thermal expansion for solid continuum elements; shell offsets; orientation
angles on the layers of composite solid continuum elements; local coordinate
systems on membrane elements; and membrane thickness on an element-by-element
basis.

A distribution is a spatial analogy of an amplitude definition (see
Amplitude Curves).
Amplitude definitions are used to provide arbitrary time variations of loads,
displacements, and other prescribed variables. Distributions are used to
specify arbitrary spatial variations of selected element properties, material
properties, local coordinate systems, boundary conditions, and spatial
variations of initial contact clearances.

The two main components of a distribution are its
location and field
data. The location identifies where the distribution is defined,
either on elements, nodes, or element faces. Field data are a specified number
of floating point values defined for each element, node, or element face in the
distribution.

To define a distribution, you must assign it a unique name. You must also
specify the number and physical dimension of each data value in the
distribution by referring to a distribution table.

Input File Usage

DISTRIBUTION, NAME=name, TABLE=distribution table name

Abaqus/CAE Usage

Abaqus/CAE
supports distributions using discrete fields.

Property, Interaction, or Load module: ToolsDiscrete FieldCreate

Specifying the location of a distribution

You can define a distribution on elements or nodes. Distributions on nodes
are supported only for defining initial contact clearances as described in
Controlling initial contact status for general contact in Abaqus/Explicit.
All other applications of distributions require distributions defined on
elements.

There is no limit on the number of distributions to which a given element or
node may belong. Elements and nodes cannot be combined within the same
distribution definition.

Defining a distribution on elements

Defining a distribution on elements requires you to specify field data for
each element or element set included in the distribution definition. All
distributions on elements require that default data be defined. Default data
are used for all elements that are not specifically assigned a value in the
distribution.

Input File Usage

DISTRIBUTION, LOCATION=ELEMENTblank space, field dataelement set or element number, field data

Default data are defined by using a blank space instead of an
element number or element set for the first data item on the first data line of
a distribution definition. Only one set of default data can be defined for a
distribution. If you specify only default data, all elements that reference
that distribution use the default values.

If an element is
specified more than once in a given distribution definition, the last
specification given is used.

Abaqus/CAE Usage

Property, Interaction, or Load module: ToolsDiscrete FieldCreate: Definition: Elements

Defining a distribution on nodes

Defining a distribution on nodes requires you to specify field data for each
node or node set included in the distribution definition.

Input File Usage

DISTRIBUTION, LOCATION=NODEnode set or node number, field data

If a node is specified more than once in a given distribution
definition, the last specification given is used.

Abaqus/CAE Usage

Defining a
distribution on nodes for initial contact clearances is not supported in
Abaqus/CAE.

Defining a distribution table

Every distribution definition must refer to a distribution table. A
distribution table defines the number of field data items needed for each
element or node in a distribution. The distribution table also defines the
physical dimension of each data value in a distribution. A distribution table
can be referred to as many times as needed by different distributions. The
distribution table consists of a list of predefined labels shown in
Table 1.
The combination of labels needed for a given distribution is determined by how
the distribution is applied.

Table 1. Distribution table labels—Abaqus/Standard
and
Abaqus/Explicit.

Label

Physical dimension

Number of data items per label

ANGLE

angle in degrees

1

COORD3D

(L, L, L)

3

DENSITY

ML^{−3}

1

EXPANSION

$\theta $^{−1}

1

LENGTH

L

1

MODULUS

FL^{−2}

1

RATIO

dimensionless

1

SHELLSTIFF1

FL^{-1}

1

SHELLSTIFF2

F

1

SHELLSTIFF3

FL

1

ORIENTS

dimensionless

6

Input File Usage

Use the following option to define a distribution
table:

Abaqus/CAE
creates a distribution table when you specify a distribution by selecting a
discrete field.

Applying distributions

The data defined in a distribution are not used in an
Abaqus
analysis unless the distribution is referred to by name by a feature that
supports distributions, and the distribution is applied only to the elements,
nodes, or element faces that are associated with the referenced feature. In
addition, a distribution definition can be referenced more than one time in a
given model. These points are illustrated in the examples below.

If an element in an
Abaqus/Standard
or
Abaqus/Explicit
analysis is declared rigid (see
Rigid body definition)
any distributions used to define element properties, material properties (with
the exception of density), or local coordinate systems are ignored.

Examples

The simple examples below illustrate how distributions are defined. A large
number of illustrative example problems using distributions can be found in
Spatially varying element properties.

Example 1

A distribution for shell thickness is defined and applied to two different
shell section definitions through the SHELL THICKNESS parameter—as noted above the distribution
dist0 would not be used if it is not referred to
by a feature that supports distributions. See
Using a shell section integrated during the analysis to define the section behavior
for more details. The distribution table defines both the number of data values
(one) and the physical dimension (LENGTH) of
the thickness data. The thicknesses defined in distribution
dist0 are assigned only to shell elements that
belong to the element set elset1 or
elset2. The default thickness (t_{0})
defined in the first data line of dist0 will be
assigned to all elements in elset1 and
elset2 that are not explicitly assigned a
thickness in dist0.

DISTRIBUTION TABLE, NAME=tab0
LENGTH
DISTRIBUTION, NAME=dist0, LOCATION=element, TABLE=tab0
, t_{0}
element set or number, t_{1}
element set or number, t_{2}
…
SHELL SECTION, ELSET=elset1, SHELL THICKNESS=dist0
SHELL SECTION, ELSET=elset2, SHELL THICKNESS=dist0

Example 2

A distribution for spatially varying isotropic elastic material behavior is
defined and applied to a material definition (Linear elastic behavior).
This material is then referred to by a solid section definition. This is
important because like any material definition, a material defined by a
distribution is not used unless it is referred to by a section definition, and
then it is applied only to the elements associated with the section definition.
The distribution table defines both the number of data values (two) and the
physical dimensions (MODULUS and
RATIO) of the isotropic elastic data. Other
material behaviors (in this case plasticity) can also be included in the
material definition. The default elastic constants (E_{0},
$\nu $_{0})
in distribution dist1 will be assigned to all
elements in elset3 that are not explicitly
assigned elastic constants in dist1.

DISTRIBUTION TABLE, NAME=tab1
MODULUS, RATIO
DISTRIBUTION, NAME=dist1, LOCATION=element, TABLE=tab1
, E_{0}, $\nu $_{0}
element set or number, E_{1}, $\nu $_{1}
element set or number, E_{2}, $\nu $_{2}
…
MATERIAL, NAME=MAT
ELASTIC
dist1
PLASTIC
…
SOLID SECTION, ELSET=elset3, MATERIAL=MAT

Example 3

A spatially varying local coordinate system (
Orientations)
is defined by specifying both spatially varying coordinates for points
a and b as well as a spatially
varying additional rotation angle. This orientation is then referred to by a
general shell section definition. This is important because like any
orientation definition, an orientation defined by a distribution is not used
unless it is referred to by a section definition, and then it is applied only
to the elements associated with the section definition. The distribution table
for the coordinates specifies COORD3D twice to
indicate that data for two three-dimensional coordinates points must be
specified for each element in the distribution.

DISTRIBUTION TABLE, NAME=tab2
COORD3D, COORD3D
DISTRIBUTION, NAME=dist2, LOCATION=element, TABLE=tab2
, aX_{0},aY_{0},aZ_{0},bX_{0},bY_{0},bZ_{0}
element set or number, aX_{1},aY_{1},aZ_{1},bX_{1},bY_{1},bZ_{1}
element set or number, aX_{2},aY_{2},aZ_{2},bX_{2},bY_{2},bZ_{2}
…
DISTRIBUTION TABLE, NAME=tab3
ANGLE
DISTRIBUTION, NAME=dist3, LOCATION=element, TABLE=tab3
, $\theta $_{0}
element set or number, $\theta $_{1}
element set or number, $\theta $_{2}
…
ORIENTATION, NAME=ORI, DEFINITION=COORDINATES
dist2
3, dist3
SHELL GENERAL SECTION, ELSET=elset4, ORIENTATION=ORI

Example 4

Spatially varying thicknesses and orientation angles are defined on the
layers of a composite shell element. The distribution table for the thicknesses
specifies LENGTH, and the distribution table
for the orientation angles specifies ANGLE. A
distribution of thicknesses is used on layers 1 and 3, while a distribution of
angles is used on layers 2 and 3.

DISTRIBUTION TABLE, NAME=tableThick
LENGTH
DISTRIBUTION, NAME=thickPly1, LOCATION=element, TABLE=tableThick
, t_{0}
element set or number, t_{1}
element set or number, t_{2}
…
DISTRIBUTION, NAME=thickPly3, LOCATION=element, TABLE=tableThick
, t_{0}
element set or number, t_{1}
element set or number, t_{2}
…
DISTRIBUTION TABLE, NAME=tableOriAngle
ANGLE
DISTRIBUTION, NAME=oriAnglePly2, LOCATION=element,
TABLE=tableOriAngle
, $\varphi $_{0}
element set or number, $\varphi $_{1}
element set or number, $\varphi $_{2}
…
DISTRIBUTION, NAME=oriAnglePly3, LOCATION=element,
TABLE=tableOriAngle
, $\varphi $_{0}
element set or number, $\varphi $_{1}
element set or number, $\varphi $_{2}
…
SHELL SECTION, ELSET=elset1, COMPOSITE
thickPly1, 3, mat1, 0.
1., 3, mat2, oriAnglePly2
thickPly3, 3, mat3, oriAnglePly3

Example 5

A distribution for a spatially varying volume fraction is defined in
distribution distVF. A distribution for a
spatially varying aspect ratio is defined in distribution
distAR, and a distribution for the second-order
orientation tensor is defined in distribution
distOriTens. These distributions are then
applied to the definition of a constituent, which is then used in the material
definition of a multiscale material with mean-field homogenization (Mean-field homogenization).
The distribution table for the volume fraction and aspect ratio specifies
RATIO, and the distribution table for the
orientation tensor specifies ORITENS.