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# 28.1.4 THREE-DIMENSIONAL SOLID ELEMENT LIBRARY

Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE

# References

• “Solid (continuum) elements,” Section 28.1.1   
• \*SOLID SECTION

# Overview

This section provides a reference to the three-dimensional solid elements available in Abaqus/Standard and Abaqus/Explicit.

# Element types

Stress/displacement elements 

<table><tr><td>C3D4</td><td>4-node linear tetrahedron</td></tr><tr><td>C3D4H(S)</td><td>4-node linear tetrahedron, hybrid with linear pressure</td></tr><tr><td>C3D5(S)</td><td>5-node linear pyramid</td></tr><tr><td>C3D5H(S)</td><td>5-node linear pyramid, hybrid with constant pressure</td></tr><tr><td>C3D6(S)</td><td>6-node linear triangular prism</td></tr><tr><td>C3D6(E)</td><td>6-node linear triangular prism, reduced integration with hourglass control</td></tr><tr><td>C3D6H(S)</td><td>6-node linear triangular prism, hybrid with constant pressure</td></tr><tr><td>C3D8</td><td>8-node linear brick</td></tr><tr><td>C3D8H(S)</td><td>8-node linear brick, hybrid with constant pressure</td></tr><tr><td>C3D8I</td><td>8-node linear brick, incompatible modes</td></tr><tr><td>C3D8IH(S)</td><td>8-node linear brick, incompatible modes, hybrid with linear pressure</td></tr><tr><td>C3D8R</td><td>8-node linear brick, reduced integration with hourglass control</td></tr><tr><td>C3D8RH(S)</td><td>8-node linear brick, reduced integration with hourglass control, hybrid with constant pressure</td></tr><tr><td>C3D8S(S)</td><td>8-node linear brick, improved surface stress visualization</td></tr><tr><td>C3D8HS(S)</td><td>8-node linear brick, hybrid with constant pressure, improved surface stress visualization</td></tr><tr><td>C3D10(S)</td><td>10-node quadratic tetrahedron</td></tr></table>

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<table><tr><td>C3D10H(S)</td><td>10-node quadratic tetrahedron, hybrid with constant pressure</td></tr><tr><td>C3D10HS(S)</td><td>10-node general-purpose quadratic tetrahedron, improved surface stress visualization</td></tr><tr><td>C3D10M</td><td>10-node modified tetrahedron, with hourglass control</td></tr><tr><td>C3D10MH(S)</td><td>10-node modified tetrahedron, with hourglass control, hybrid with linear pressure</td></tr><tr><td>C3D15(S)</td><td>15-node quadratic triangular prism</td></tr><tr><td>C3D15H(S)</td><td>15-node quadratic triangular prism, hybrid with linear pressure</td></tr><tr><td>C3D20(S)</td><td>20-node quadratic brick</td></tr><tr><td>C3D20H(S)</td><td>20-node quadratic brick, hybrid with linear pressure</td></tr><tr><td>C3D20R(S)</td><td>20-node quadratic brick, reduced integration</td></tr><tr><td>C3D20RH(S)</td><td>20-node quadratic brick, reduced integration, hybrid with linear pressure</td></tr></table>

Active degrees of freedom

1, 2, 3

Additional solution variables

The constant pressure hybrid elements have one additional variable relating to pressure, and the linear pressure hybrid elements have four additional variables relating to pressure.

Element types C3D8I and C3D8IH have thirteen additional variables relating to the incompatible modes.

Element types C3D10M and C3D10MH have three additional displacement variables.

Stress/displacement variable node elements 

<table><tr><td>C3D15V(S)</td><td>15 to 18-node triangular prism</td></tr><tr><td>C3D15VH(S)</td><td>15 to 18-node triangular prism, hybrid with linear pressure</td></tr><tr><td>C3D27(S)</td><td>21 to 27-node brick</td></tr><tr><td>C3D27H(S)</td><td>21 to 27-node brick, hybrid with linear pressure</td></tr><tr><td>C3D27R(S)</td><td>21 to 27-node brick, reduced integration</td></tr><tr><td>C3D27RH(S)</td><td>21 to 27-node brick, reduced integration, hybrid with linear pressure</td></tr></table>

Active degrees of freedom

1, 2, 3

Additional solution variables

The hybrid elements have four additional variables relating to pressure.

Coupled temperature-displacement elements 

<table><tr><td>C3D4T</td><td>4-node linear displacement and temperature</td></tr><tr><td>C3D6T(S)</td><td>6-node linear displacement and temperature</td></tr></table>

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<table><tr><td>C3D6T(E)</td><td>6-node linear displacement and temperature, reduced integration with hourglass control</td></tr><tr><td>C3D6HT(S)</td><td>6-node linear displacement and temperature, hybrid with constant pressure</td></tr><tr><td>C3D8T</td><td>8-node trilinear displacement and temperature</td></tr><tr><td>C3D8HT(S)</td><td>8-node trilinear displacement and temperature, hybrid with constant pressure</td></tr><tr><td>C3D8RT</td><td>8-node trilinear displacement and temperature, reduced integration with hourglass control</td></tr><tr><td>C3D8RHT(S)</td><td>8-node trilinear displacement and temperature, reduced integration with hourglass control, hybrid with constant pressure</td></tr><tr><td>C3D10T(S)</td><td>10-node triquadratic displacement, trilinear temperature</td></tr><tr><td>C3D10HT(S)</td><td>10-node triquadratic displacement, trilinear temperature, hybrid with constant pressure</td></tr><tr><td>C3D10MT</td><td>10-node modified displacement and temperature tetrahedron, with hourglass control</td></tr><tr><td>C3D10MHT(S)</td><td>10-node modified displacement and temperature tetrahedron, with hourglass control, hybrid with linear pressure</td></tr><tr><td>C3D20T(S)</td><td>20-node triquadratic displacement, trilinear temperature</td></tr><tr><td>C3D20HT(S)</td><td>20-node triquadratic displacement, trilinear temperature, hybrid with linear pressure</td></tr><tr><td>C3D20RT(S)</td><td>20-node triquadratic displacement, trilinear temperature, reduced integration</td></tr><tr><td>C3D20RHT(S)</td><td>20-node triquadratic displacement, trilinear temperature, reduced integration, hybrid with linear pressure</td></tr></table>

# Active degrees of freedom

1, 2, 3, 11 at corner nodes   
1, 2, 3 at midside nodes of second-order elements in Abaqus/Standard   
1, 2, 3, 11 at midside nodes of modified displacement and temperature elements in Abaqus/Standard

# Additional solution variables

The constant pressure hybrid element has one additional variable relating to pressure, and the linear pressure hybrid elements have four additional variables relating to pressure.

Element types C3D10MT and C3D10MHT have three additional displacement variables and one additional temperature variable.

# Coupled thermal-electrical-structural elements

<table><tr><td>Q3D4(S)</td><td>4-node linear displacement, electric potential and temperature</td></tr><tr><td>Q3D6(S)</td><td>6-node linear displacement, electric potential and temperature</td></tr><tr><td>Q3D8(S)</td><td>8-node trilinear displacement, electric potential and temperature</td></tr></table>

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<table><tr><td>Q3D8H(S)</td><td>8-node trilinear displacement, electric potential and temperature, hybrid with constant pressure</td></tr><tr><td>Q3D8R(S)</td><td>8-node trilinear displacement, electric potential and temperature, reduced integration with hourglass control</td></tr><tr><td>Q3D8RH(S)</td><td>8-node trilinear displacement, electric potential and temperature, reduced integration with hourglass control, hybrid with constant pressure</td></tr><tr><td>Q3D10M(S)</td><td>10-node modified displacement, electric potential and temperature tetrahedron, with hourglass control</td></tr><tr><td>Q3D10MH(S)</td><td>10-node modified displacement, electric potential and temperature tetrahedron, with hourglass control, hybrid with linear pressure</td></tr><tr><td>Q3D20(S)</td><td>20-node triquadratic displacement, trilinear electric potential and trilinear temperature</td></tr><tr><td>Q3D20H(S)</td><td>20-node triquadratic displacement, trilinear electric potential, trilinear temperature, hybrid with linear pressure</td></tr><tr><td>Q3D20R(S)</td><td>20-node triquadratic displacement, trilinear electric potential, trilinear temperature, reduced integration</td></tr><tr><td>Q3D20RH(S)</td><td>20-node triquadratic displacement, trilinear electric potential, trilinear temperature, reduced integration, hybrid with linear pressure</td></tr></table>

# Active degrees of freedom

1, 2, 3, 9, 11 at corner nodes   
1, 2, 3 at midside nodes of second-order elements in Abaqus/Standard   
1, 2, 3, 9, 11 at midside nodes of modified displacement and temperature elements in Abaqus/Standard

# Additional solution variables

The constant pressure hybrid element has one additional variable relating to pressure, and the linear pressure hybrid elements have four additional variables relating to pressure.

Element types Q3D10M and Q3D10MH have three additional displacement variables, one additional electric potential variable, and one additional temperature variable.

# Diffusive heat transfer or mass diffusion elements

<table><tr><td>DC3D4(S)</td><td>4-node linear tetrahedron</td></tr><tr><td>DC3D6(S)</td><td>6-node linear triangular prism</td></tr><tr><td>DC3D8(S)</td><td>8-node linear brick</td></tr><tr><td>DC3D10(S)</td><td>10-node quadratic tetrahedron</td></tr><tr><td>DC3D15(S)</td><td>15-node quadratic triangular prism</td></tr><tr><td>DC3D20(S)</td><td>20-node quadratic brick</td></tr></table>

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Active degree of freedom

11

Additional solution variables

None.

# Forced convection/diffusion elements

DCC3D8(S) 8-node

DCC3D8D(S) 8-node with dispersion control

Active degree of freedom

11

Additional solution variables

None.

# Coupled thermal-electrical elements

DC3D4E(S) 4-node linear tetrahedron

DC3D6E(S) 6-node linear triangular prism

DC3D8E(S) 8-node linear brick

DC3D10E(S) 10-node quadratic tetrahedron

DC3D15E(S) 15-node quadratic triangular prism

DC3D20E(S) 20-node quadratic brick

Active degrees of freedom

9, 11

Additional solution variables

None.

# Pore pressure elements

C3D4P(S) 4-node linear displacement and pore pressure

C3D4PH(S) 4-node linear displacement and pore pressure, hybrid with linear pressure

C3D6P(S) 6-node linear displacement and pore pressure

C3D6PH(S) 6-node linear displacement and pore pressure, hybrid with constant pressure

C3D8P(S) 8-node trilinear displacement and pore pressure

C3D8PH(S) 8-node trilinear displacement and pore pressure, hybrid with constant pressure

C3D8RP(S) 8-node trilinear displacement and pore pressure, reduced integration

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<table><tr><td>C3D8RPH(S)</td><td>8-node trilinear displacement and pore pressure, reduced integration, hybrid with constant pressure</td></tr><tr><td>C3D10P(S)</td><td>10-node triquadratic displacement, trilinear pore pressure</td></tr><tr><td>C3D10PH(S)</td><td>10-node triquadratic displacement, trilinear pore pressure, hybrid with constant pressure</td></tr><tr><td>C3D10MP(S)</td><td>10-node modified displacement and pore pressure tetrahedron, with hourglass control</td></tr><tr><td>C3D10MPH(S)</td><td>10-node modified displacement and pore pressure tetrahedron, with hourglass control, hybrid with linear pressure</td></tr><tr><td>C3D20P(S)</td><td>20-node triquadratic displacement, trilinear pore pressure</td></tr><tr><td>C3D20PH(S)</td><td>20-node triquadratic displacement, trilinear pore pressure, hybrid with linear pressure</td></tr><tr><td>C3D20RP(S)</td><td>20-node triquadratic displacement, trilinear pore pressure, reduced integration</td></tr><tr><td>C3D20RPH(S)</td><td>20-node triquadratic displacement, trilinear pore pressure, reduced integration, hybrid with linear pressure</td></tr></table>

# Active degrees of freedom

1, 2, 3 at midside nodes for all elements except C3D10MP and C3D10MPH, which also have degree of freedom 8 active at midside nodes

1, 2, 3, 8 at corner nodes

# Additional solution variables

The constant pressure hybrid elements have one additional variable relating to the effective pressure stress, and the linear pressure hybrid elements have four additional variables relating to the effective pressure stress to permit fully incompressible material modeling.

Element types C3D10MP and C3D10MPH have three additional displacement variables and one additional pore pressure variable.

# Coupled temperature–pore pressure elements

<table><tr><td>C3D4PT(S)</td><td>4-node trilinear displacement, pore pressure, and temperature</td></tr><tr><td>C3D4PHT(S)</td><td>4-node trilinear displacement, pore pressure, and temperature; hybrid with linear pressure</td></tr><tr><td>C3D6PT(S)</td><td>6-node trilinear displacement, pore pressure, and temperature</td></tr><tr><td>C3D6PHT(S)</td><td>6-node trilinear displacement, pore pressure, and temperature; hybrid with constant pressure</td></tr><tr><td>C3D8PT(S)</td><td>8-node trilinear displacement, pore pressure, and temperature</td></tr><tr><td>C3D8PHT(S)</td><td>8-node trilinear displacement, pore pressure, and temperature; hybrid with constant pressure</td></tr></table>

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<table><tr><td>C3D8RPT(S)</td><td>8-node trilinear displacement, pore pressure, and temperature; reduced integration</td></tr><tr><td>C3D8RPHT(S)</td><td>8-node trilinear displacement, pore pressure, and temperature; reduced integration, hybrid with constant pressure</td></tr><tr><td>C3D10MPT(S)</td><td>10-node modified displacement, pore pressure, and temperature tetrahedron, with hourglass control</td></tr><tr><td>C3D10PT(S)</td><td>10-node triquadratic displacement, trilinear pore pressure, and temperature</td></tr><tr><td>C3D10PHT(S)</td><td>10-node triquadratic displacement, trilinear pore pressure, and temperature; hybrid with constant pressure</td></tr></table>

Active degrees of freedom

1, 2, 3, 8, 11

# Additional solution variables

The constant pressure hybrid elements have one additional variable relating to the effective pressure stress to permit fully incompressible material modeling.

Element type C3D10MPT has three additional displacement variables, one additional pore pressure variable, and one additional temperature variable.

Acoustic elements 

<table><tr><td>AC3D4</td><td>4-node linear tetrahedron</td></tr><tr><td>AC3D5</td><td>5-node linear pyramid</td></tr><tr><td>AC3D6</td><td>6-node linear triangular prism</td></tr><tr><td>AC3D8(S)</td><td>8-node linear brick</td></tr><tr><td>AC3D8R(E)</td><td>8-node linear brick, reduced integration with hourglass control</td></tr><tr><td>AC3D10(S)</td><td>10-node quadratic tetrahedron</td></tr><tr><td>AC3D15(S)</td><td>15-node quadratic triangular prism</td></tr><tr><td>AC3D20(S)</td><td>20-node quadratic brick</td></tr></table>

Active degree of freedom

8

Additional solution variables

None.

Piezoelectric elements 

<table><tr><td>C3D4E(S)</td><td>4-node linear tetrahedron</td></tr><tr><td>C3D6E(S)</td><td>6-node linear triangular prism</td></tr><tr><td>C3D8E(S)</td><td>8-node linear brick</td></tr></table>

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<table><tr><td>C3D10E(S)</td><td>10-node quadratic tetrahedron</td></tr><tr><td>C3D15E(S)</td><td>15-node quadratic triangular prism</td></tr><tr><td>C3D20E(S)</td><td>20-node quadratic brick</td></tr><tr><td>C3D20RE(S)</td><td>20-node quadratic brick, reduced integration</td></tr></table>

Active degrees of freedom

1, 2, 3, 9

Additional solution variables

None.

Electromagnetic elements 

<table><tr><td>EMC3D4(S)</td><td>4-node zero-order</td></tr><tr><td>EMC3D6(S)</td><td>6-node zero-order</td></tr><tr><td>EMC3D8(S)</td><td>8-node zero-order</td></tr></table>

Active degree of freedom

Magnetic vector potential (for more information, see “Boundary conditions” in “Eddy current analysis,” Section 6.7.5, and “Boundary conditions” in “Magnetostatic analysis,” Section 6.7.6).

Additional solution variables

None.

Nodal coordinates required

X, Y, Z

Element property definition 

<table><tr><td>Input File Usage:</td><td>*SOLID SECTION</td></tr><tr><td>Abaqus/CAE Usage:</td><td>Property module: Create Section: select Solid as the section Category and Homogeneous or Electromagnetic, Solid as the section Type</td></tr></table>

Element-based loading

# Distributed loads

Distributed loads are available for all elements with displacement degrees of freedom. They are specified as described in “Distributed loads,” Section 34.4.3.

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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>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>CENT(S)</td><td>Not supported</td><td> $FL^{-4}(ML^{-3}T^{-2})$ </td><td>Centrifugal load (magnitude is input as  $\rho\omega^{2}$ , where  $\rho$  is the mass density per unit volume,  $\omega$  is the angular velocity). Not available for pore pressure elements.</td></tr><tr><td>CENTRIF(S)</td><td>Rotational body force</td><td> $T^{-2}$ </td><td>Centrifugal load (magnitude is input as  $\omega^{2}$ , where  $\omega$  is the angular velocity).</td></tr><tr><td>CORIO(S)</td><td>Coriolis force</td><td> $FL^{-4}T (ML^{-3}T^{-1})$ </td><td>Coriolis force (magnitude is input as  $\rho\omega$ , where  $\rho$  is the mass density per unit volume,  $\omega$  is the angular velocity). Not available for pore pressure elements.</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>HPn(S)</td><td>Not supported</td><td> $FL^{-2}$ </td><td>Hydrostatic pressure on face n, linear in global Z.</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>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><tr><td> $ROTA^{(S)}$ </td><td>Rotational body force</td><td> $T^{-2}$ </td><td>Rotary acceleration load (magnitude is input as  $\alpha$ , where  $\alpha$  is the rotary acceleration).</td></tr><tr><td> $ROTDYNF^{(S)}$ </td><td>Not supported</td><td> $T^{-1}$ </td><td>Rotordynamic load (magnitude is input as  $\omega$ , where  $\omega$  is the angular velocity).</td></tr><tr><td> $SBF^{(E)}$ </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> $SPn^{(E)}$ </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> $TRSHRnNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform shear traction on face n with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr><tr><td> $TRVECn$ </td><td>Surface traction</td><td> $FL^{-2}$ </td><td>General traction on face n.</td></tr><tr><td> $TRVECnNU^{(S)}$ </td><td>Not supported</td><td> $FL^{-2}$ </td><td>Nonuniform general traction on face n with magnitude and direction supplied via user subroutine UTRACLOAD.</td></tr><tr><td> $VBF^{(E)}$ </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> $VPn^{(E)}$ </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>
