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# 33.1.2 DISCRETE PARTICLE ELEMENT LIBRARY

# Product: Abaqus/Explicit

# References

• “Discrete element method,” Section 15.1.1   
• “Discrete particle elements,” Section 33.1.1   
• \*DISCRETE SECTION

# Overview

This section provides a reference to the particle elements available in Abaqus/Explicit.

# Element type

# Force/displacement element

PD3D 1-node discrete particle

Active degrees of freedom

1, 2, 3, 4, 5, 6

# Nodal coordinates required

X, Y, Z

# Element property definition

Input File Usage: \*DISCRETE SECTION

# Element-based loading

# Distributed loads

Gravity loads as described in “Distributed loads,” Section 34.4.3, are the most commonly applied distributed loads for discrete particle elements. You define gravity loading in a specified direction, and the magnitude is input as acceleration.

# Element output

Discrete particle elements have no element output associated with them. Resultant of all contact normal force CNORMF and resultant of all frictional shear force CSHEARF acting on a discrete particle element are the only output variables of interest currently available for this element, see “Abaqus/Explicit output variable identifiers,” Section 4.2.2, for details.

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# Nodes associated with the element

1 node.

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# 33.2 Continuum particle elements

• “Continuum particle elements,” Section 33.2.1   
• “Continuum particle element library,” Section 33.2.2

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# 33.2.1 CONTINUUM PARTICLE ELEMENTS

Product: Abaqus/Explicit

# References

• “Smoothed particle hydrodynamics,” Section 15.2.1   
• “Continuum particle element library,” Section 33.2.2   
• \*SOLID SECTION

# Overview

Continuum particle elements:

• can be used only in explicit dynamic analyses;   
• must have one node only;   
• have one integration point;   
• can be initialized similarly to continuum elements; and   
• are fully filled with material.

# Typical applications

Continuum particle elements (PC3D) are useful for simulations involving material that undergoes extreme deformation such as open-surface fluid flow or obliteration/fragmentation of solid structures. They are defined using only one node; however, the element centered at a given node (particle) receives contributions from all particles within a sphere of influence whose radius is commonly referred to as the smoothing length. The smoothed particle hydrodynamic (SPH) formulation determines at every increment of the analysis the connectivity associated with a given particle. Since nodal connectivity is not fixed, severe element distortion is avoided and, hence, the formulation allows for very high strain gradients.

The 1-node PC3D element is used to define points both on the surface and in the interior of the body to be modeled. You define these nodes similarly to mass elements, and the nodes can be placed in space the same as the nodes of a regular brick mesh. A smoothed particle hydrodynamic mesh is typically a uniformly spaced grid of elements that conforms to the shape of the body being modeled.

For more information, see “Smoothed particle hydrodynamics,” Section 15.2.1.

# Defining the element’s section properties

You must associate a solid section definition with a set of continuum particle elements. The section definition provides the material associated with the PC3D elements.

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As part of the solid section definition, you can define a characteristic length. This characteristic length, not to be confused with the smoothing length, is used to compute the particle volume. The volume is assumed to be a cube whose sides are equal to twice the specified characteristic length.

# Input File Usage:

\*SOLID SECTION, ELSET=element\_set\_name

characteristic length associated with the particle volume

where the ELSET parameter refers to a set of particle elements.

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# 33.2.2 CONTINUUM PARTICLE ELEMENT LIBRARY

# Product: Abaqus/Explicit

# References

• “Smoothed particle hydrodynamics,” Section 15.2.1   
• “Continuum particle elements,” Section 33.2.1   
• \*SOLID SECTION

# Overview

This section provides a reference to the particle elements available in Abaqus/Explicit.

# Element type

# Stress/displacement element

PC3D 1-node continuum particle

Active degrees of freedom

1, 2, 3

# Nodal coordinates required

X, Y, Z

# Element property definition

Input File Usage: \*SOLID SECTION

# Element-based loading

# Distributed loads

Gravity loads as described in “Distributed loads,” Section 34.4.3, are the only distributed loads that are available for particle elements. You define gravity loading in a specified direction, and the magnitude is input as acceleration.

# Element output

Output is in global directions unless a local coordinate system is assigned to the element through the section definition (“Orientations,” Section 2.2.5), in which case output is in the local coordinate system (which rotates with the motion in large-displacement analysis). See “State storage,” Section 1.5.4 of the Abaqus Theory Guide, for details.

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# Stress, strain, and other tensor components

Stress, strain, and other tensors are available. All tensors have the same components. For example, the stress components are as follows:

<table><tr><td>S11</td><td>XX, direct stress.</td></tr><tr><td>S22</td><td>YY, direct stress.</td></tr><tr><td>S33</td><td>ZZ, direct stress.</td></tr><tr><td>S12</td><td>XY, shear stress.</td></tr><tr><td>S13</td><td>XZ, shear stress.</td></tr><tr><td>S23</td><td>YZ, shear stress.</td></tr></table>

Note: the order shown above is not the same as that used in user subroutine VUMAT.

# Nodes associated with the element

1 node.

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# EI.1 Abaqus/Standard ELEMENT INDEX

This index provides a reference to all of the element types that are available in Abaqus/Standard. Elements are listed in alphabetical order, where numerical characters precede the letter “A” and two-digit numbers are put in numerical, rather than “alphabetical,” order. Thus, AC1D2 precedes ACAX4, and AC3D20 follows AC3D8.

For certain options, such as contact and surface-based distributing coupling, Abaqus may generate internal elements (such as IDCOUP3D for surface-based distributing coupling). These internal element names are not included in the index below but may appear in an output database (.odb) or data (.dat) file.

<table><tr><td>AC1D2</td><td>2-node acoustic link</td><td>28.1.2</td></tr><tr><td>AC1D3</td><td>3-node acoustic link</td><td>28.1.2</td></tr><tr><td>AC2D3</td><td>3-node linear 2D acoustic triangle</td><td>28.1.3</td></tr><tr><td>AC2D4</td><td>4-node linear 2D acoustic quadrilateral</td><td>28.1.3</td></tr><tr><td>AC2D6</td><td>6-node quadratic 2D acoustic triangular prism</td><td>28.1.3</td></tr><tr><td>AC2D8</td><td>8-node quadratic 2D acoustic quadrilateral</td><td>28.1.3</td></tr><tr><td>AC3D4</td><td>4-node linear acoustic tetrahedron</td><td>28.1.4</td></tr><tr><td>AC3D5</td><td>5-node linear acoustic pyramid</td><td>28.1.4</td></tr><tr><td>AC3D6</td><td>6-node linear acoustic triangular prism</td><td>28.1.4</td></tr><tr><td>AC3D8</td><td>8-node linear acoustic brick</td><td>28.1.4</td></tr><tr><td>AC3D10</td><td>10-node quadratic acoustic tetrahedron</td><td>28.1.4</td></tr><tr><td>AC3D15</td><td>15-node quadratic acoustic triangular prism</td><td>28.1.4</td></tr><tr><td>AC3D20</td><td>20-node quadratic acoustic brick</td><td>28.1.4</td></tr><tr><td>ACAX3</td><td>3-node linear axisymmetric acoustic triangle</td><td>28.1.6</td></tr><tr><td>ACAX4</td><td>4-node linear axisymmetric acoustic quadrilateral</td><td>28.1.6</td></tr><tr><td>ACAX6</td><td>6-node quadratic axisymmetric acoustic triangle</td><td>28.1.6</td></tr><tr><td>ACAX8</td><td>8-node quadratic axisymmetric acoustic quadrilateral</td><td>28.1.6</td></tr><tr><td>ACIN2D2</td><td>2-node linear 2D acoustic infinite element</td><td>28.3.2</td></tr><tr><td>ACIN2D3</td><td>3-node quadratic 2D acoustic infinite element</td><td>28.3.2</td></tr><tr><td>ACIN3D3</td><td>3-node linear 3D acoustic infinite element</td><td>28.3.2</td></tr><tr><td>ACIN3D4</td><td>4-node linear 3D acoustic infinite element</td><td>28.3.2</td></tr><tr><td>ACIN3D6</td><td>6-node quadratic 3D acoustic infinite element</td><td>28.3.2</td></tr><tr><td>ACIN3D8</td><td>8-node quadratic 3D acoustic infinite element</td><td>28.3.2</td></tr><tr><td>ACINAX2</td><td>2-node linear axisymmetric acoustic infinite element</td><td>28.3.2</td></tr><tr><td>ACINAX3</td><td>3-node quadratic axisymmetric acoustic infinite element</td><td>28.3.2</td></tr><tr><td>ASI1</td><td>1-node acoustic interface element</td><td>32.13.2</td></tr></table>

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<table><tr><td>ASI2</td><td>2-node linear 2D acoustic interface element (this element has been renamed to ASI2D2)</td><td>32.13.2</td></tr><tr><td>ASI2A</td><td>2-node linear axisymmetric acoustic interface element (this element has been renamed to ASIAX2)</td><td>32.13.2</td></tr><tr><td>ASI2D2</td><td>2-node linear 2D acoustic interface element</td><td>32.13.2</td></tr><tr><td>ASI2D3</td><td>3-node quadratic 2D acoustic interface element</td><td>32.13.2</td></tr><tr><td>ASI3</td><td>3-node quadratic 2D acoustic interface element (this element has been renamed to ASI2D3)</td><td>32.13.2</td></tr><tr><td>ASI3A</td><td>3-node quadratic axisymmetric acoustic interface element (this element has been renamed to ASIAX3)</td><td>32.13.2</td></tr><tr><td>ASI3D3</td><td>3-node linear 3D acoustic interface element</td><td>32.13.2</td></tr><tr><td>ASI3D4</td><td>4-node linear 3D acoustic interface element</td><td>32.13.2</td></tr><tr><td>ASI3D6</td><td>6-node quadratic 3D acoustic interface element</td><td>32.13.2</td></tr><tr><td>ASI3D8</td><td>8-node quadratic 3D acoustic interface element</td><td>32.13.2</td></tr><tr><td>ASI4</td><td>4-node linear 3D acoustic interface element (this element has been renamed to ASI3D4)</td><td>32.13.2</td></tr><tr><td>ASI8</td><td>8-node quadratic 3D acoustic interface element (this element has been renamed to ASI3D8)</td><td>32.13.2</td></tr><tr><td>ASIAX2</td><td>2-node linear axisymmetric acoustic interface element</td><td>32.13.2</td></tr><tr><td>ASIAX3</td><td>3-node quadratic axisymmetric acoustic interface element</td><td>32.13.2</td></tr><tr><td>B21</td><td>2-node linear beam in a plane</td><td>29.3.8</td></tr><tr><td>B21H</td><td>2-node linear beam in a plane, hybrid formulation</td><td>29.3.8</td></tr><tr><td>B22</td><td>3-node quadratic beam in a plane</td><td>29.3.8</td></tr><tr><td>B22H</td><td>3-node quadratic beam in a plane, hybrid formulation</td><td>29.3.8</td></tr><tr><td>B23</td><td>2-node cubic beam in a plane</td><td>29.3.8</td></tr><tr><td>B23H</td><td>2-node cubic beam in a plane, hybrid formulation</td><td>29.3.8</td></tr><tr><td>B31</td><td>2-node linear beam in space</td><td>29.3.8</td></tr><tr><td>B31H</td><td>2-node linear beam in space, hybrid formulation</td><td>29.3.8</td></tr><tr><td>B31OS</td><td>2-node linear open-section beam in space</td><td>29.3.8</td></tr><tr><td>B31OSH</td><td>2-node linear open-section beam in space, hybrid formulation</td><td>29.3.8</td></tr><tr><td>B32</td><td>3-node quadratic beam in space</td><td>29.3.8</td></tr><tr><td>B32H</td><td>3-node quadratic beam in space, hybrid formulation</td><td>29.3.8</td></tr><tr><td>B32OS</td><td>3-node quadratic open-section beam in space</td><td>29.3.8</td></tr><tr><td>B32OSH</td><td>3-node quadratic open-section beam in space, hybrid formulation</td><td>29.3.8</td></tr><tr><td>B33</td><td>2-node cubic beam in space</td><td>29.3.8</td></tr><tr><td>B33H</td><td>2-node cubic beam in space, hybrid formulation</td><td>29.3.8</td></tr><tr><td>C3D4</td><td>4-node linear tetrahedron</td><td>28.1.4</td></tr></table>
