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<table><tr><td>CPEG6(S)</td><td>6-node quadratic triangle</td></tr><tr><td>CPEG6H(S)</td><td>6-node quadratic triangle, hybrid with linear pressure</td></tr><tr><td>CPEG6M(S)</td><td>6-node modified, with hourglass control</td></tr><tr><td>CPEG6MH(S)</td><td>6-node modified, with hourglass control, hybrid with linear pressure</td></tr><tr><td>CPEG8(S)</td><td>8-node biquadratic quadrilateral</td></tr><tr><td>CPEG8H(S)</td><td>8-node biquadratic quadrilateral, hybrid with linear pressure</td></tr><tr><td>CPEG8R(S)</td><td>8-node biquadratic quadrilateral, reduced integration</td></tr><tr><td>CPEG8RH(S)</td><td>8-node biquadratic quadrilateral, reduced integration, hybrid with linear pressure</td></tr></table>

# Active degrees of freedom

1, 2 at all but the reference node   
3, 4, 5 at the reference node

# Additional solution variables

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

Element types CPEG4I and CPEG4IH have five additional variables relating to the incompatible modes.

Element types CPEG6M and CPEG6MH have two additional displacement variables.

# Coupled temperature-displacement plane strain elements

<table><tr><td>CPE3T</td><td>3-node linear displacement and temperature</td></tr><tr><td>CPE4T(S)</td><td>4-node bilinear displacement and temperature</td></tr><tr><td>CPE4HT(S)</td><td>4-node bilinear displacement and temperature, hybrid with constant pressure</td></tr><tr><td>CPE4RT</td><td>4-node bilinear displacement and temperature, reduced integration with hourglass control</td></tr><tr><td>CPE4RHT(S)</td><td>4-node bilinear displacement and temperature, reduced integration with hourglass control, hybrid with constant pressure</td></tr><tr><td>CPE6MT</td><td>6-node modified displacement and temperature, with hourglass control</td></tr><tr><td>CPE6MHT(S)</td><td>6-node modified displacement and temperature, with hourglass control, hybrid with constant pressure</td></tr><tr><td>CPE8T(S)</td><td>8-node biquadratic displacement, bilinear temperature</td></tr><tr><td>CPE8HT(S)</td><td>8-node biquadratic displacement, bilinear temperature, hybrid with linear pressure</td></tr><tr><td>CPE8RT(S)</td><td>8-node biquadratic displacement, bilinear temperature, reduced integration</td></tr><tr><td>CPE8RHT(S)</td><td>8-node biquadratic displacement, bilinear temperature, reduced integration, hybrid with linear pressure</td></tr></table>

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# Active degrees of freedom

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

# Additional solution variables

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

Element types CPE6MT and CPE6MHT have two additional displacement variables and one additional temperature variable.

# Coupled temperature-displacement plane stress elements

<table><tr><td>CPS3T</td><td>3-node linear displacement and temperature</td></tr><tr><td>CPS4T(S)</td><td>4-node bilinear displacement and temperature</td></tr><tr><td>CPS4RT</td><td>4-node bilinear displacement and temperature, reduced integration with hourglass control</td></tr><tr><td>CPS6MT</td><td>6-node modified displacement and temperature, with hourglass control</td></tr><tr><td>CPS8T(S)</td><td>8-node biquadratic displacement, bilinear temperature</td></tr><tr><td>CPS8RT(S)</td><td>8-node biquadratic displacement, bilinear temperature, reduced integration</td></tr></table>

# Active degrees of freedom

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

# Additional solution variables

Element type CPS6MT has two additional displacement variables and one additional temperature variable.

# Coupled temperature-displacement generalized plane strain elements

<table><tr><td>CPEG3T(S)</td><td>3-node linear displacement and temperature</td></tr><tr><td>CPEG3HT(S)</td><td>3-node linear displacement and temperature, hybrid with constant pressure</td></tr><tr><td>CPEG4T(S)</td><td>4-node bilinear displacement and temperature</td></tr><tr><td>CPEG4HT(S)</td><td>4-node bilinear displacement and temperature, hybrid with constant pressure</td></tr><tr><td>CPEG4RT(S)</td><td>4-node bilinear displacement and temperature, reduced integration with hourglass control</td></tr></table>

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<table><tr><td>CPEG4RHT(S)</td><td>4-node bilinear displacement and temperature, reduced integration with hourglass control, hybrid with constant pressure</td></tr><tr><td>CPEG6MT(S)</td><td>6-node modified displacement and temperature, with hourglass control</td></tr><tr><td>CPEG6MHT(S)</td><td>6-node modified displacement and temperature, with hourglass control, hybrid with constant pressure</td></tr><tr><td>CPEG8T(S)</td><td>8-node biquadratic displacement, bilinear temperature</td></tr><tr><td>CPEG8HT(S)</td><td>8-node biquadratic displacement, bilinear temperature, hybrid with linear pressure</td></tr><tr><td>CPEG8RHT(S)</td><td>8-node biquadratic displacement, bilinear temperature, reduced integration, hybrid with linear pressure</td></tr></table>

# Active degrees of freedom

1, 2, 11 at corner nodes   
1, 2 at midside nodes of second-order elements   
1, 2, 11 at midside nodes of modified displacement and temperature elements   
3, 4, 5 at the reference node

# Additional solution variables

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

Element types CPEG6MT and CPEG6MHT have two additional displacement variables and one additional temperature variable.

# Diffusive heat transfer or mass diffusion elements

DC2D3(S) 3-node linear

DC2D4(S) 4-node linear

DC2D6(S) 6-node quadratic

DC2D8(S) 8-node biquadratic

Active degree of freedom

11

Additional solution variables

None.

# Forced convection/diffusion elements

DCC2D4(S) 4-node

DCC2D4D(S) 4-node with dispersion control

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Active degree of freedom

11

Additional solution variables

Coupled thermal-electrical elements 

<table><tr><td>DC2D3E(S)</td><td>3-node linear</td></tr><tr><td>DC2D4E(S)</td><td>4-node linear</td></tr><tr><td>DC2D6E(S)</td><td>6-node quadratic</td></tr><tr><td>DC2D8E(S)</td><td>8-node biquadratic</td></tr></table>

Active degrees of freedom

9, 11

Additional solution variables

None.

Pore pressure plane strain elements 

<table><tr><td>CPE4P(S)</td><td>4-node bilinear displacement and pore pressure</td></tr><tr><td>CPE4PH(S)</td><td>4-node bilinear displacement and pore pressure, hybrid with constant pressure stress</td></tr><tr><td>CPE4RP(S)</td><td>4-node bilinear displacement and pore pressure, reduced integration with hourglass control</td></tr><tr><td>CPE4RPH(S)</td><td>4-node bilinear displacement and pore pressure, reduced integration with hourglass control, hybrid with constant pressure</td></tr><tr><td>CPE6MP(S)</td><td>6-node modified displacement and pore pressure, with hourglass control</td></tr><tr><td>CPE6MPH(S)</td><td>6-node modified displacement and pore pressure, with hourglass control, hybrid with linear pressure</td></tr><tr><td>CPE8P(S)</td><td>8-node biquadratic displacement, bilinear pore pressure</td></tr><tr><td>CPE8PH(S)</td><td>8-node biquadratic displacement, bilinear pore pressure, hybrid with linear pressure stress</td></tr><tr><td>CPE8RP(S)</td><td>8-node biquadratic displacement, bilinear pore pressure, reduced integration</td></tr><tr><td>CPE8RPH(S)</td><td>8-node biquadratic displacement, bilinear pore pressure, reduced integration, hybrid with linear pressure stress</td></tr></table>

Active degrees of freedom

1, 2, 8 at corner nodes

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1, 2 at midside nodes for all elements except CPE6MP and CPE6MPH, which also have degree of freedom 8 active at midside 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 three additional variables relating to the effective pressure stress to permit fully incompressible material modeling.

Element types CPE6MP and CPE6MPH have two additional displacement variables and one additional pore pressure variable.

# Coupled temperature–pore pressure plane strain elements

<table><tr><td>CPE4PT(S)</td><td>4-node bilinear displacement, pore pressure, and temperature</td></tr><tr><td>CPE4PHT(S)</td><td>4-node bilinear displacement, pore pressure, and temperature; hybrid with constant pressure stress</td></tr><tr><td>CPE4RPT(S)</td><td>4-node bilinear displacement, pore pressure, and temperature; reduced integration</td></tr><tr><td>CPE4RPHT(S)</td><td>4-node bilinear displacement, pore pressure, and temperature; reduced integration, hybrid with constant pressure stress</td></tr></table>

Active degrees of freedom

1, 2, 8, 11 at corner nodes

# Additional solution variables

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

# Acoustic elements

<table><tr><td>AC2D3</td><td>3-node linear</td></tr><tr><td>AC2D4(S)</td><td>4-node bilinear</td></tr><tr><td>AC2D4R(E)</td><td>4-node bilinear, reduced integration with hourglass control</td></tr><tr><td>AC2D6(S)</td><td>6-node quadratic</td></tr><tr><td>AC2D8(S)</td><td>8-node biquadratic</td></tr></table>

Active degree of freedom

8

Additional solution variables

None.

# Piezoelectric plane strain elements

<table><tr><td>CPE3E(S)</td><td>3-node linear</td></tr><tr><td>CPE4E(S)</td><td>4-node bilinear</td></tr></table>

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<table><tr><td>CPE6E(S)</td><td>6-node quadratic</td></tr><tr><td>CPE8E(S)</td><td>8-node biquadratic</td></tr><tr><td>CPE8RE(S)</td><td>8-node biquadratic, reduced integration</td></tr></table>

Active degrees of freedom

1, 2, 9

Additional solution variables

None.

Piezoelectric plane stress elements 

<table><tr><td>CPS3E(S)</td><td>3-node linear</td></tr><tr><td>CPS4E(S)</td><td>4-node bilinear</td></tr><tr><td>CPS6E(S)</td><td>6-node quadratic</td></tr><tr><td>CPS8E(S)</td><td>8-node biquadratic</td></tr><tr><td>CPS8RE(S)</td><td>8-node biquadratic, reduced integration</td></tr></table>

Active degrees of freedom

1, 2, 9

Additional solution variables

None.

Electromagnetic elements 

<table><tr><td>EMC2D3(S)</td><td>3-node zero-order</td></tr><tr><td>EMC2D4(S)</td><td>4-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

Element property definition

For all elements except generalized plane strain elements, you must provide the element thickness; by default, unit thickness is assumed.

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For generalized plane strain elements, you must provide three values: the initial length of the axial material fiber through the reference node, the initial value of $\Delta \phi _ { x }$ (in radians), and the initial value of $\Delta \phi _ { y }$ (in radians). If you do not provide these values, Abaqus assumes the default values of one unit as the initial length and zero for $\Delta \phi _ { x }$ and $\Delta \phi _ { y }$ . In addition, you must define the reference point for generalized plane strain elements.

<table><tr><td>Input File Usage:</td><td>Use the following option to define the element properties for all elements except generalized plane strain elements:*SOLID SECTIONUse the following option to define the element properties for generalized plane strain elements:*SOLID SECTION, REF NODE=node number or node set name</td></tr><tr><td>Abaqus/CAE Usage:</td><td>Property module:Create Section: selectSolidas the sectionCategoryand Homogeneous, Generalized plane strain, or Electromagnetic, Solidas the sectionTypeGeneralized plane strain sections must be assigned to regions of parts that have a reference point associated with them. To define the reference point:Part module:Tools→Reference Point: select reference point</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.

<table><tr><td>Load ID(*DLOAD)</td><td>Abaqus/CAELoad/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>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></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> $CENT^{(S)}$ </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  $Y$ .</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> $SBF^{(E)}$ </td><td>Not supported</td><td> $FL^{-5}T^{2}$ </td><td>Stagnation body force in global  $X$ - and  $Y$ -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></table>

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<table><tr><td>Load ID(*DLOAD)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</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- and Y-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>

# Foundations

Foundations are available for Abaqus/Standard elements with displacement degrees of freedom. They are specified as described in “Element foundations,” Section 2.2.2.

<table><tr><td>Load ID(*FOUNDATION)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $Fn^{(S)}$ </td><td>Elasticfoundation</td><td> $FL^{-3}$ </td><td>Elastic foundation on face  $n$ .</td></tr></table>

# Distributed heat fluxes

Distributed heat fluxes are available for all elements with temperature degrees of freedom. 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>BFNU</td><td>Body heat flux</td><td> $JL^{-3}T^{-1}$ </td><td>Nonuniform heat body flux per unit volume with magnitude supplied via user subroutine DFLUX in Abaqus/Standard and VDFLUX in Abaqus/Explicit.</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>

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<table><tr><td>Load ID(*DFLUX)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>SnNU</td><td>Not supported</td><td> $JL^{-2}T^{-1}$ </td><td>Nonuniform heat surface flux per unit area into face  $n$  with magnitude supplied via user subroutine DFLUX in Abaqus/Standard and VDFLUX in Abaqus/Explicit.</td></tr></table>

# Film conditions

Film conditions are available for all elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 34.4.4.

<table><tr><td>Load ID(*FILM)</td><td>Abaqus/CAE Load/Interaction</td><td>Units</td><td>Description</td></tr><tr><td>Fn</td><td>Surface film condition</td><td> $JL^{-2}T^{-1}\theta^{-1}$ </td><td>Film coefficient and sink temperature (units of  $\theta$ ) provided on face n.</td></tr><tr><td>FnNU(S)</td><td>Not supported</td><td> $JL^{-2}T^{-1}\theta^{-1}$ </td><td>Nonuniform film coefficient and sink temperature (units of  $\theta$ ) provided on face n with magnitude supplied via user subroutine FILM.</td></tr></table>

# Radiation types

Radiation conditions are available for all elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 34.4.4.

<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>

# Distributed flows

Distributed flows are available for all elements with pore pressure degrees of freedom. They are specified as described in “Pore fluid flow,” Section 34.4.7.

<table><tr><td>Load ID(*FLOW)</td><td>Abaqus/CAELoad/Interaction</td><td>Units</td><td>Description</td></tr><tr><td> $Qn^{(S)}$ </td><td>Not supported</td><td> $F^{-1}L^{3}T^{-1}$ </td><td>Seepage coefficient and reference sink pore pressure (units of  $FL^{-2}$ ) provided on face n.</td></tr></table>
