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# Planar

![](images/page-1071_2b91332a5807b0228aaca0ff2e69bfcd9b57a2c66279ac484b79b3299fc5f5b4.jpg)  
ASI2D2

![](images/page-1071_dbe9d6ff1af77a1a09e1405edf1d1283234cf378a9fcc3f474d815a312a10cd4.jpg)

<details>
<summary>flowchart</summary>

```mermaid
graph TD
    1 --> 2
    2 --> 3
```
</details>

ASI2D3

# 3D

![](images/page-1071_a692ed975916790f9ee8f0d5eee9d0b3564d115823fd19636ab046e24167a474.jpg)

<details>
<summary>text_image</summary>

1
2
3
</details>

ASI3D3

![](images/page-1071_6456c09f3457914ec009d1c4de1762dc6eea25b3e56f99463686544ec975a912.jpg)

<details>
<summary>text_image</summary>

1
2
3
4
</details>

ASI3D4

![](images/page-1071_3203b7ebfea57611400cf2734cf21c80db8f1a1480fd117dddb187ea0de77222.jpg)

<details>
<summary>flowchart</summary>

```mermaid
graph TD
    1 --> 2
    1 --> 4
    2 --> 5
    2 --> 6
    3 --> 5
    3 --> 6
    4 --> 6
    5 --> 6
```
</details>

ASI3D6

![](images/page-1071_e78b5846101934a90a97298de071d9e03677085cfc41dd60d6fa9df9420c5dde.jpg)

<details>
<summary>flowchart</summary>

```mermaid
graph TD
    1 --> 2
    2 --> 3
    3 --> 4
    4 --> 5
    5 --> 6
    6 --> 7
    7 --> 8
    8 --> 1
```
</details>

ASI3D8

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# Axisymmetric

![](images/page-1072_554e2860c689d3460f21e642d59cd691a730d917dbb665d34bb05a2c13cc0543.jpg)

<details>
<summary>natural_image</summary>

Simple line diagram with two labeled points (1 and 2) connected by a straight line (no text or symbols beyond labels)
</details>

ASIAX2

![](images/page-1072_8c7c2b168638eca6dd19ded7ddd0c76ebc2f86890257c763c7c23c81e10bd4de.jpg)

<details>
<summary>flowchart</summary>

```mermaid
graph TD
    A["1"] --> B["2"]
    B --> C["3"]
```
</details>

ASIAX3

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# 32.14 Eulerian elements

• “Eulerian elements,” Section 32.14.1   
• “Eulerian element library,” Section 32.14.2

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# 32.14.1 EULERIAN ELEMENTS

Products: Abaqus/Explicit Abaqus/CAE

# References

• “Eulerian analysis,” Section 14.1.1   
• “Eulerian element library,” Section 32.14.2   
• \*EULERIAN SECTION   
• “Creating Eulerian sections,” Section 12.13.3 of the Abaqus/CAE User’s Guide, in the HTML version of this guide

# Overview

Eulerian elements:

• can be used only in explicit dynamic analyses;   
• must have eight unique nodes;   
• are filled with void material by default;   
• can be initialized with nonvoid material;   
• can contain multiple materials simultaneously; and   
• can be partially filled with material.

# Typical applications

Eulerian elements are useful for simulations involving material that undergoes extreme deformation, up to and including fluid flow. The Eulerian formulation allows material to flow from one element to another, even as the Eulerian mesh remains fixed. Applications that utilize Eulerian elements are discussed in “Eulerian analysis of a collapsing water column,” Section 1.7.1 of the Abaqus Benchmarks Guide, and “Rivet forming,” Section 2.3.1 of the Abaqus Example Problems Guide.

For more information on Eulerian analyses, see “Eulerian analysis,” Section 14.1.1.

# Choosing an appropriate element

The available Eulerian elements are the three-dimensional, 8-node element EC3D8R and the three-dimensional, 8-node thermally coupled element EC3D8RT. Two-dimensional simulations can be approximated using a one-element thick mesh or a wedge-shaped mesh with appropriate boundary conditions. The Eulerian mesh is typically a simple rectangular grid of elements that does not conform to the shape of the Eulerian materials. Complex material shapes can be represented inside this mesh using a combination of fully and partially filled elements surrounded by void regions.

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# Defining the Eulerian element’s section properties

You must associate the Eulerian section definition with a set of Eulerian elements. This set of elements must not share nodes with other types of elements. The section definition provides a list of materials that may occupy the Eulerian elements.

Input File Usage: \*EULERIAN SECTION, ELSET=element\_set\_name data lines giving list of materials

Abaqus/CAE Usage: Property module: Create Section: select Solid as the section Category and Eulerian as the section Type Assign→Section: select part

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# 32.14.2 EULERIAN ELEMENT LIBRARY

Products: Abaqus/Explicit Abaqus/CAE

# References

• “Eulerian analysis,” Section 14.1.1   
• \*EULERIAN SECTION

# Overview

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

# Element types

# Eulerian stress/displacement element

EC3D8R 8-node linear brick, multimaterial, reduced integration with hourglass control

Active degrees of freedom 1, 2, 3

Additional solution variables None.

# Eulerian thermally coupled element

EC3D8RT 8-node thermally coupled linear brick, multimaterial, reduced integration with hourglass control

Active degrees of freedom 1, 2, 3,11

Additional solution variables None.

# Nodal coordinates required

X, Y, Z

# Element property definition

You must specify a list of materials that may be present in the Eulerian element. You can also assign a material instance name to each material (see “Eulerian section definition” in “Eulerian analysis,” Section 14.1.1).

Input File Usage: \*EULERIAN SECTION

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# Abaqus/CAE Usage: Property module: Create Section: select Solid as the section Category and Eulerian as the section Type

# Element-based loading

# Distributed loads

Distributed loads are available only for Eulerian elements. They are specified as described in “Distributed loads,” Section 34.4.3.

<table><tr><td>Load ID (*DLOAD)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>BX</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in global X-direction.</td></tr><tr><td>BY</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in global Y-direction.</td></tr><tr><td>BZ</td><td>Body force</td><td> $FL^{-3}$ </td><td>Body force in global Z-direction.</td></tr><tr><td>BXNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in global X-direction with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td>BYNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in global Y-direction with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td>BZNU</td><td>Body force</td><td> $FL^{-3}$ </td><td>Nonuniform body force in global Z-direction with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td>GRAV</td><td>Gravity</td><td> $LT^{-2}$ </td><td>Gravity loading in a specified direction (magnitude is input as acceleration).</td></tr><tr><td>Pn</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Pressure on face n.</td></tr><tr><td>PnNU</td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform pressure on face n with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr></table>

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<table><tr><td>Load ID (*DLOAD)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>SBF</td><td>Not supported</td><td> $FL^{-5}T^{2}$ </td><td>Stagnation body force in global X-, Y-, and Z-directions.</td></tr><tr><td>SPn</td><td>Not supported</td><td> $FL^{-4}T^{2}$ </td><td>Stagnation pressure on face n.</td></tr><tr><td>TRSHRn</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Shear traction on face n.</td></tr><tr><td>TRVECn</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>General traction on face n.</td></tr><tr><td>VBF</td><td>Not supported</td><td> $FL^{-4}T$ </td><td>Viscous body force in global X-, Y-, and Z-directions.</td></tr><tr><td>VPn</td><td>Not supported</td><td> $FL^{-3}T$ </td><td>Viscous pressure on face n, applying a pressure proportional to the velocity normal to the face and opposing the motion.</td></tr></table>

# Distributed heat fluxes

Distributed heat fluxes are available only for EC3D8RT elements. They are specified as described in “Thermal loads,” Section 34.4.4.

<table><tr><td>Load ID(*DFLUX)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>BF</td><td>Body heat flux</td><td> $JL^{-3}T^{-1}$ </td><td>Heat body flux per unit volume.</td></tr><tr><td>Sn</td><td>Surface heat flux</td><td> $JL^{-2}T^{-1}$ </td><td>Heat surface flux per unit area into face n.</td></tr></table>

# Film conditions

Film conditions are available only for EC3D8RT elements. They are specified as described in “Thermal loads,” Section 34.4.4.

<table><tr><td>Load ID(*FILM)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>Fn</td><td>Surface filmcondition</td><td> $JL^{-2}T^{-1}\theta^{-1}$ </td><td>Film coefficient and sink temperature(units of  $\theta$ ) provided on face n.</td></tr></table>

# Radiation types

Radiation conditions are available only for EC3D8RT elements. They are specified as described in “Thermal loads,” Section 34.4.4.

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<table><tr><td>Load ID(*RADIATE)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>Rn</td><td>Surface radiation</td><td>Dimensionless</td><td>Emissivity and sink temperature(units of θ) provided on face n.</td></tr></table>

Surface-based loading   
Distributed loads

Surface-based distributed loads are available for Eulerian elements. They are specified as described in “Distributed loads,” Section 34.4.3.

<table><tr><td>Load ID(*DSLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>P</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Pressure on the element surface.</td></tr><tr><td>PNU</td><td>Pressure</td><td> $FL^{-2}$ </td><td>Nonuniform pressure on the element surface with magnitude supplied via user subroutine DLOAD in Abaqus/Standard and VDLOAD in Abaqus/Explicit.</td></tr><tr><td>SP</td><td>Pressure</td><td> $FL^{-4}T^{2}$ </td><td>Stagnation pressure on the element surface.</td></tr><tr><td>TRSHR</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>Shear traction on the element surface.</td></tr><tr><td>TRVEC</td><td>Surface traction</td><td> $FL^{-2}$ </td><td>General traction on the element surface.</td></tr><tr><td>VP</td><td>Pressure</td><td> $FL^{-3}T$ </td><td>Viscous pressure applied on the element surface. The viscous pressure is proportional to the velocity normal to the element face and opposing the motion.</td></tr></table>

Distributed heat fluxes

Surface-based heat fluxes are available only for EC3D8RT elements. They are specified as described in “Thermal loads,” Section 34.4.4.

<table><tr><td>Load ID(*DSFLUX)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>S</td><td>Surface heat flux</td><td> $JL^{-2}T^{-1}$ </td><td>Heat surface flux per unit area into the element surface.</td></tr></table>
