22.1.6 Axisymmetric solid element library

**Products: **ABAQUS/Standard ABAQUS/Explicit ABAQUS/CAE

Coordinate 1 is , coordinate 2 is . At the *r*-direction corresponds to the global *x*-direction and the *z*-direction corresponds to the global *y*-direction. This is important when data must be given in global directions. Coordinate 1 must be greater than or equal to zero.

Degree of freedom 1 is , degree of freedom 2 is . Generalized axisymmetric elements with twist have an additional degree of freedom, 5, corresponding to the twist angle (in radians).

ABAQUS does not automatically apply any boundary conditions to nodes located along the symmetry axis. You must apply radial or symmetry boundary conditions on these nodes if desired.

In certain situations in ABAQUS/Standard it may become necessary to apply radial boundary conditions on nodes that are located on the symmetry axis to obtain convergence in nonlinear problems. Therefore, the application of radial boundary conditions on nodes on the symmetry axis is recommended for nonlinear problems.

Point loads and moments, concentrated (nodal) fluxes, electrical currents, and seepage should be given as the value integrated around the circumference (that is, the total value on the ring).

Stress/displacement elements without twist

CAX3 | 3-node linear |

CAX3H^{(S)} | 3-node linear, hybrid with constant pressure |

CAX4^{(S)} | 4-node bilinear |

CAX4H^{(S)} | 4-node bilinear, hybrid with constant pressure |

CAX4I^{(S)} | 4-node bilinear, incompatible modes |

CAX4IH^{(S)} | 4-node bilinear, incompatible modes, hybrid with linear pressure |

CAX4R | 4-node bilinear, reduced integration with hourglass control |

CAX4RH^{(S)} | 4-node bilinear, reduced integration with hourglass control, hybrid with constant pressure |

CAX6^{(S)} | 6-node quadratic |

CAX6H^{(S)} | 6-node quadratic, hybrid with linear pressure |

CAX6M | 6-node modified, with hourglass control |

CAX6MH^{(S)} | 6-node modified, with hourglass control, hybrid with linear pressure |

CAX8^{(S)} | 8-node biquadratic |

CAX8H^{(S)} | 8-node biquadratic, hybrid with linear pressure |

CAX8R^{(S)} | 8-node biquadratic, reduced integration |

CAX8RH^{(S)} | 8-node biquadratic, reduced integration, hybrid with linear pressure |

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

Element types CAX4I and CAX4IH have five additional variables relating to the incompatible modes.

Element types CAX6M and CAX6MH have two additional displacement variables.

Stress/displacement elements with twist

CGAX3^{(S)} | 3-node linear |

CGAX3H^{(S)} | 3-node linear, hybrid with constant pressure |

CGAX4^{(S)} | 4-node bilinear |

CGAX4H^{(S)} | 4-node bilinear, hybrid with constant pressure |

CGAX4R^{(S)} | 4-node bilinear, reduced integration with hourglass control |

CGAX4RH^{(S)} | 4-node bilinear, reduced integration with hourglass control, hybrid with constant pressure |

CGAX6^{(S)} | 6-node quadratic |

CGAX6H^{(S)} | 6-node quadratic, hybrid with linear pressure |

CGAX6M^{(S)} | 6-node modified, with hourglass control |

CGAX6MH^{(S)} | 6-node modified, with hourglass control, hybrid with linear pressure |

CGAX8^{(S)} | 8-node biquadratic |

CGAX8H^{(S)} | 8-node biquadratic, hybrid with linear pressure |

CGAX8R^{(S)} | 8-node biquadratic, reduced integration |

CGAX8RH^{(S)} | 8-node biquadratic, reduced integration, hybrid with linear pressure |

Diffusive heat transfer or mass diffusion elements

DCAX3^{(S)} | 3-node linear |

DCAX4^{(S)} | 4-node linear |

DCAX6^{(S)} | 6-node quadratic |

DCAX8^{(S)} | 8-node quadratic |

Forced convection/diffusion elements

DCCAX2^{(S)} | 2-node |

DCCAX2D^{(S)} | 2-node with dispersion control |

DCCAX4^{(S)} | 4-node |

DCCAX4D^{(S)} | 4-node with dispersion control |

Coupled thermal-electrical elements

DCAX3E^{(S)} | 3-node linear |

DCAX4E^{(S)} | 4-node linear |

DCAX6E^{(S)} | 6-node quadratic |

DCAX8E^{(S)} | 8-node quadratic |

Coupled temperature-displacement elements without twist

CAX3T^{(E)} | 3-node linear displacement and temperature |

CAX4T^{(S)} | 4-node bilinear displacement and temperature |

CAX4HT^{(S)} | 4-node bilinear displacement and temperature, hybrid with constant pressure |

CAX4RT | 4-node bilinear displacement and temperature, reduced integration with hourglass control |

CAX4RHT^{(S)} | 4-node bilinear displacement and temperature, reduced integration with hourglass control, hybrid with constant pressure |

CAX6MT | 6-node modified displacement and temperature, with hourglass control |

CAX6MHT^{(S)} | 6-node modified displacement and temperature, with hourglass control, hybrid with linear pressure |

CAX8T^{(S)} | 8-node biquadratic displacement, bilinear temperature |

CAX8HT^{(S)} | 8-node biquadratic displacement, bilinear temperature, hybrid with linear pressure |

CAX8RT^{(S)} | 8-node biquadratic displacement, bilinear temperature, reduced integration |

CAX8RHT^{(S)} | 8-node biquadratic displacement, bilinear temperature, reduced integration, hybrid with linear pressure |

Coupled temperature-displacement elements with twist

CGAX3T^{(S)} | 3-node linear displacement and temperature |

CGAX3HT^{(S)} | 3-node linear displacement and temperature, hybrid with constant pressure |

CGAX4T^{(S)} | 4-node bilinear displacement and temperature |

CGAX4HT^{(S)} | 4-node bilinear displacement and temperature, hybrid with constant pressure |

CGAX4RT^{(S)} | 4-node bilinear displacement and temperature, reduced integration with hourglass control |

CGAX4RHT^{(S)} | 4-node bilinear displacement and temperature, reduced integration with hourglass control, hybrid with constant pressure |

CGAX6MT^{(S)} | 6-node modified displacement and temperature, with hourglass control |

CGAX6MHT^{(S)} | 6-node modified displacement and temperature, with hourglass control, hybrid with constant pressure |

CGAX8T^{(S)} | 8-node biquadratic displacement, bilinear temperature |

CGAX8HT^{(S)} | 8-node biquadratic displacement, bilinear temperature, hybrid with linear pressure |

CGAX8RT^{(S)} | 8-node biquadratic displacement, bilinear temperature, reduced integration |

CGAX8RHT^{(S)} | 8-node biquadratic displacement, bilinear temperature, reduced integration, hybrid with linear pressure |

1, 2, 5, 11 at corner nodes

1, 2, 5 at midside nodes of second-order elements

1, 2, 5, 11 at midside nodes of the modified displacement and temperature elements

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

Element types CGAX6MT and CGAX6MHT have two additional displacement variables and one additional temperature variable.

Pore pressure elements

CAX4P^{(S)} | 4-node bilinear displacement and pore pressure |

CAX4PH^{(S)} | 4-node bilinear displacement and pore pressure, hybrid with constant pressure |

CAX4RP^{(S)} | 4-node bilinear displacement and pore pressure, reduced integration with hourglass control |

CAX4RPH^{(S)} | 4-node bilinear displacement and temperature, reduced integration with hourglass control, hybrid with constant pressure |

CAX6MP^{(S)} | 6-node modified displacement and pore pressure, with hourglass control |

CAX6MPH^{(S)} | 6-node modified displacement and pore pressure, with hourglass control, hybrid with linear pressure |

CAX8P^{(S)} | 8-node biquadratic displacement, bilinear pore pressure |

CAX8PH^{(S)} | 8-node biquadratic displacement, bilinear pore pressure, hybrid with linear pressure |

CAX8RP^{(S)} | 8-node biquadratic displacement, bilinear pore pressure, reduced integration |

CAX8RPH^{(S)} | 8-node biquadratic displacement, bilinear pore pressure, reduced integration, hybrid with linear pressure |

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 CAX6MP and CAX6MPH have two additional displacement variables and one additional pore pressure variable.

For element types DCCAX2 and DCCAX2D, you must specify the channel thickness of the element in the (*r*–*z*) plane. The default is unit thickness if no thickness is given.

For all other elements, you do not need to specify the thickness.

Input File Usage: | *SOLID SECTION |

ABAQUS/CAE Usage: | Property module: |

Distributed loads

Distributed loads are available for all elements with displacement degrees of freedom. They are specified as described in “Distributed loads,” Section 27.4.3. Distributed load magnitudes are per unit area or per unit volume. They do not need to be multiplied by .

**Load ID (*DLOAD):** BR**ABAQUS/CAE Load/Interaction:** **Body force****Units:** FL^{–3}**Description: **Body force in radial direction.

**Load ID (*DLOAD):** BZ**ABAQUS/CAE Load/Interaction:** **Body force****Units:** FL^{–3}**Description: **Body force in axial direction.

**Load ID (*DLOAD):** BRNU**ABAQUS/CAE Load/Interaction:** **Body force****Units:** FL^{–3}**Description: **Nonuniform body force in radial direction with magnitude supplied via user subroutine `DLOAD` in ABAQUS/Standard and `VDLOAD` in ABAQUS/Explicit.

**Load ID (*DLOAD):** BZNU**ABAQUS/CAE Load/Interaction:** **Body force****Units:** FL^{–3}**Description: **Nonuniform body force in axial direction with magnitude supplied via user subroutine `DLOAD` in ABAQUS/Standard and `VDLOAD` in ABAQUS/Explicit.

**Load ID (*DLOAD):** CENT^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** FL^{–4}M^{–3}T^{–2}**Description: **Centrifugal load (magnitude input as , where is the mass density per unit volume, is the angular velocity). Not available for pore pressure elements.

**Load ID (*DLOAD):** CENTRIF^{(S)}**ABAQUS/CAE Load/Interaction:** **Rotational body force****Units:** T^{–2}**Description: **Centrifugal load (magnitude is input as , where is the angular velocity).

**Load ID (*DLOAD):** GRAV**ABAQUS/CAE Load/Interaction:** **Gravity****Units:** LT^{–2}**Description: **Gravity loading in a specified direction (magnitude is input as acceleration).

**Load ID (*DLOAD):** HP*n*^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** FL^{–2}**Description: **Hydrostatic pressure on face *n*, linear in global *Z*.

**Load ID (*DLOAD):** P*n***ABAQUS/CAE Load/Interaction:** **Pressure****Units:** FL^{–2}**Description: **Pressure on face *n*.

**Load ID (*DLOAD):** P*n*NU**ABAQUS/CAE Load/Interaction:** Not supported**Units:** FL^{–2}**Description: **Nonuniform pressure on face *n* with magnitude supplied via user subroutine `DLOAD` in ABAQUS/Standard and `VDLOAD` in ABAQUS/Explicit.

**Load ID (*DLOAD):** SBF^{(E)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** FL^{–5}T^{2}**Description: **Stagnation body force in radial and axial directions.

**Load ID (*DLOAD):** SP*n*^{(E)}**ABAQUS/CAE Load/Interaction:** **Pressure****Units:** FL^{–4}T^{2}**Description: **Stagnation pressure on face *n*.

**Load ID (*DLOAD):** TRSHR*n***ABAQUS/CAE Load/Interaction:** Not supported**Units:** FL^{–2}**Description: **Shear traction on face *n*.

**Load ID (*DLOAD):** TRSHR*n*NU^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** FL^{–2}**Description: **Nonuniform shear traction on face *n* with magnitude and direction supplied via user subroutine `UTRACLOAD`.

**Load ID (*DLOAD):** TRVEC*n***ABAQUS/CAE Load/Interaction:** Not supported**Units:** FL^{–2}**Description: **General traction on face *n*.

**Load ID (*DLOAD):** TRVEC*n*NU^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** FL^{–2}**Description: **Nonuniform general traction on face *n* with magnitude and direction supplied via user subroutine `UTRACLOAD`.

**Load ID (*DLOAD):** VBF^{(E)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** FL^{–4}T**Description: **Viscous body force in radial and axial directions.

**Load ID (*DLOAD):** VP*n*^{(E)}**ABAQUS/CAE Load/Interaction:** **Pressure****Units:** FL^{–3}T**Description: **Viscous pressure on face *n*, applying a pressure proportional to the velocity normal to the face and opposing the motion.

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.

**Load ID (*FOUNDATION):** F*n*^{(S)}**ABAQUS/CAE Load/Interaction:** **Elastic foundation****Units:** FL^{–3}**Description: **Elastic foundation on face *n*. For CGAX elements the elastic foundations are applied to degrees of freedom and only.

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 27.4.4. Distributed heat flux magnitudes are per unit area or per unit volume. They do not need to be multiplied by .

**Load ID (*DFLUX):** BF**ABAQUS/CAE Load/Interaction:** **Body heat flux****Units:** JL^{–3}T^{–1}**Description: **Heat body flux per unit volume.

**Load ID (*DFLUX):** BFNU^{(S)}**ABAQUS/CAE Load/Interaction:** **Body heat flux****Units:** JL^{–3}T^{–1}**Description: **Nonuniform heat body flux per unit volume with magnitude supplied via user subroutine `DFLUX`.

**Load ID (*DFLUX):** S*n***ABAQUS/CAE Load/Interaction:** Not supported**Units:** JL^{–2}T^{–1}**Description: **Heat surface flux per unit area into face *n*.

**Load ID (*DFLUX):** S*n*NU^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** JL^{–2}T^{–1}**Description: **Nonuniform heat surface flux per unit area into face *n* with magnitude supplied via user subroutine `DFLUX`.

Film conditions

Film conditions are available for all elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 27.4.4.

**Load ID (*FILM):** F*n***ABAQUS/CAE Load/Interaction:** **Surface film condition****Units:** JL^{–2}T^{–1}^{–1}**Description: **Film coefficient and sink temperature (units of ) provided on face *n*.

**Load ID (*FILM):** F*n*NU^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** JL^{–2}T^{–1}^{–1}**Description: **Nonuniform film coefficient and sink temperature (units of ) provided on face *n* with magnitude supplied via user subroutine `FILM`.

Radiation types

Radiation conditions are available for all elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 27.4.4.

**Load ID (*RADIATE):** R*n***ABAQUS/CAE Load/Interaction:** Not supported**Units:** Dimensionless**Description: **Emissivity and sink temperature provided for face *n*.

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 27.4.6. Distributed flow magnitudes are per unit area or per unit volume. They do not need to be multiplied by .

**Load ID (*FLOW/ *DFLOW):** Q*n*^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** F^{–1}L^{3}T^{–1}**Description: **Seepage (outward normal flow) proportional to the difference between surface pore pressure and a reference sink pore pressure on face *n* (units of FL^{–2}).

**Load ID (*FLOW/ *DFLOW):** Q*n*D^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** F^{–1}L^{3}T^{–1}**Description: **Drainage-only seepage (outward normal flow) proportional to the surface pore pressure on face *n* only when that pressure is positive.

**Load ID (*FLOW/ *DFLOW):** Q*n*NU^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** F^{–1}L^{3}T^{–1}**Description: **Nonuniform seepage (outward normal flow) proportional to the difference between surface pore pressure and a reference sink pore pressure on face *n* (units of FL^{–2}) with magnitude supplied via user subroutine `FLOW`.

**Load ID (*FLOW/ *DFLOW):** S*n*^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** LT^{–1}**Description: **Prescribed pore fluid effective velocity (outward from the face) on face *n*.

**Load ID (*FLOW/ *DFLOW):** S*n*NU^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** LT^{–1}**Description: **Nonuniform prescribed pore fluid effective velocity (outward from the face) on face *n* with magnitude supplied via user subroutine `DFLOW`.

Distributed impedances

Distributed impedances are available for all elements with acoustic pressure degrees of freedom. They are specified as described in “Acoustic loads,” Section 27.4.5.

**Load ID (*IMPEDANCE):** I*n***ABAQUS/CAE Load/Interaction:** Not supported**Units:** None**Description: **Name of the impedance property that defines the impedance on face *n*.

Electric fluxes

Electric fluxes are available for piezoelectric elements. They are specified as described in “Piezoelectric analysis,” Section 6.6.3.

**Load ID (*DECHARGE):** EBF^{(S)}**ABAQUS/CAE Load/Interaction:** **Body charge****Units:** CL^{–3}**Description: **Body flux per unit volume.

**Load ID (*DECHARGE):** ES*n*^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** CL^{–2}**Description: **Prescribed surface charge on face *n*.

Distributed electric current densities

Distributed electric current densities are available for coupled thermal-electrical elements. They are specified as described in “Coupled thermal-electrical analysis,” Section 6.6.2.

**Load ID (*DECURRENT):** CBF^{(S)}**ABAQUS/CAE Load/Interaction:** **Body current****Units:** CL^{–3}T^{–1}**Description: **Volumetric current source density.

**Load ID (*DECURRENT):** CS*n*^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** CL^{–2}T^{–1}**Description: **Current density on face *n*.

Distributed concentration fluxes

Distributed concentration fluxes are available for mass diffusion elements. They are specified as described in “Mass diffusion analysis,” Section 6.8.1.

**Load ID (*DFLUX):** BF^{(S)}**ABAQUS/CAE Load/Interaction:** **Body concentration flux****Units:** PT^{–1}**Description: **Concentration body flux per unit volume.

**Load ID (*DFLUX):** BFNU^{(S)}**ABAQUS/CAE Load/Interaction:** **Body concentration flux****Units:** PT^{–1}**Description: **Nonuniform concentration body flux per unit volume with magnitude supplied via user subroutine `DFLUX`.

**Load ID (*DFLUX):** S*n*^{(S)}**ABAQUS/CAE Load/Interaction:** **Surface concentration flux****Units:** PLT^{–1}**Description: **Concentration surface flux per unit area into face *n*.

**Load ID (*DFLUX):** S*n*NU^{(S)}**ABAQUS/CAE Load/Interaction:** **Surface concentration flux****Units:** PLT^{–1}**Description: **Nonuniform concentration surface flux per unit area into face *n* with magnitude supplied via user subroutine `DFLUX`.

Distributed loads

Surface-based distributed loads are available for all elements with displacement degrees of freedom. They are specified as described in “Distributed loads,” Section 27.4.3. Distributed load magnitudes are per unit area or per unit volume. They do not need to be multiplied by .

**Load ID (*DSLOAD):** HP^{(S)}**ABAQUS/CAE Load/Interaction:** **Pressure****Units:** FL^{–2}**Description: **Hydrostatic pressure on the element surface, linear in global *Z*.

**Load ID (*DSLOAD):** P**ABAQUS/CAE Load/Interaction:** **Pressure****Units:** FL^{–2}**Description: **Pressure on the element surface.

**Load ID (*DSLOAD):** PNU**ABAQUS/CAE Load/Interaction:** **Pressure****Units:** FL^{–2}**Description: **Nonuniform pressure on the element surface with magnitude supplied via user subroutine `DLOAD` in ABAQUS/Standard and `VDLOAD` in ABAQUS/Explicit.

**Load ID (*DSLOAD):** SP^{(E)}**ABAQUS/CAE Load/Interaction:** **Pressure****Units:** FL^{–4}T^{2}**Description: **Stagnation pressure on the element surface.

**Load ID (*DSLOAD):** TRSHR**ABAQUS/CAE Load/Interaction:** **Surface traction****Units:** FL^{–2}**Description: **Shear traction on the element surface.

**Load ID (*DSLOAD):** TRSHRNU^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** FL^{–2}**Description: **Nonuniform shear traction on the element surface with magnitude and direction supplied via user subroutine `UTRACLOAD`.

**Load ID (*DSLOAD):** TRVEC**ABAQUS/CAE Load/Interaction:** **Surface traction****Units:** FL^{–2}**Description: **General traction on the element surface.

**Load ID (*DSLOAD):** TRVECNU^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** FL^{–2}**Description: **Nonuniform general traction on the element surface with magnitude and direction supplied via user subroutine `UTRACLOAD`.

**Load ID (*DSLOAD):** VP^{(E)}**ABAQUS/CAE Load/Interaction:** **Pressure****Units:** FL^{–3}T**Description: **Viscous pressure applied on the element surface. The viscous pressure is proportional to the velocity normal to the face and opposing the motion.

Distributed heat fluxes

Surface-based heat fluxes are available for all elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 27.4.4. Distributed heat flux magnitudes are per unit area or per unit volume. They do not need to be multiplied by .

**Load ID (*DSFLUX):** S**ABAQUS/CAE Load/Interaction:** **Surface heat flux****Units:** JL^{–2}T^{–1}**Description: **Heat surface flux per unit area into the element surface.

**Load ID (*DSFLUX):** SNU^{(S)}**ABAQUS/CAE Load/Interaction:** **Surface heat flux****Units:** JL^{–2}T^{–1}**Description: **Nonuniform heat surface flux per unit area into the element surface with magnitude supplied via user subroutine `DFLUX`.

Film conditions

Surface-based film conditions are available for all elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 27.4.4.

**Load ID (*SFILM):** F**ABAQUS/CAE Load/Interaction:** **Surface film condition****Units:** JL^{–2}T^{–1}^{–1}**Description: **Film coefficient and sink temperature (units of ) provided on the element surface.

**Load ID (*SFILM):** FNU^{(S)}**ABAQUS/CAE Load/Interaction:** **Surface film condition****Units:** JL^{–2}T^{–1}^{–1}**Description: **Nonuniform film coefficient and sink temperature (units of ) provided on the element surface with magnitude supplied via user subroutine `FILM`.

Radiation types

Surface-based radiation conditions are available for all elements with temperature degrees of freedom. They are specified as described in “Thermal loads,” Section 27.4.4.

**Load ID (*SRADIATE):** R**ABAQUS/CAE Load/Interaction:** **Surface radiation to ambient****Units:** Dimensionless**Description: **Emissivity and sink temperature provided for the element surface.

Distributed flows

Surface-based distributed flows are available for all elements with pore pressure degrees of freedom. They are specified as described in “Pore fluid flow,” Section 27.4.6. Distributed flow magnitudes are per unit area or per unit volume. They do not need to be multiplied by .

**Load ID (*SFLOW/ *DSFLOW):** Q^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** F^{–1}L^{3}T^{–1}**Description: **Seepage (outward normal flow) proportional to the difference between surface pore pressure and a reference sink pore pressure on the element surface (units of FL^{–2}).

**Load ID (*SFLOW/ *DSFLOW):** QD^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** F^{–1}L^{3}T^{–1}**Description: **Drainage-only seepage (outward normal flow) proportional to the surface pore pressure on the element surface only when that pressure is positive.

**Load ID (*SFLOW/ *DSFLOW):** QNU^{(S)}**ABAQUS/CAE Load/Interaction:** Not supported**Units:** F^{–1}L^{3}T^{–1}**Description: **Nonuniform seepage (outward normal flow) proportional to the difference between surface pore pressure and a reference sink pore pressure on the element surface (units of FL^{–2}) with magnitude supplied via user subroutine `FLOW`.

**Load ID (*SFLOW/ *DSFLOW):** S^{(S)}**ABAQUS/CAE Load/Interaction:** **Surface pore fluid****Units:** LT^{–1}**Description: **Prescribed pore fluid effective velocity outward from the element surface.

**Load ID (*SFLOW/ *DSFLOW):** SNU^{(S)}**ABAQUS/CAE Load/Interaction:** **Surface pore fluid****Units:** LT^{–1}**Description: **Nonuniform prescribed pore fluid effective velocity outward from the element surface with magnitude supplied via user subroutine `DFLOW`.

Distributed impedances

Surface-based impedances are available for all elements with acoustic pressure degrees of freedom. They are specified as described in “Acoustic loads,” Section 27.4.5.

Incident wave loading

Surface-based incident wave loads are available for all elements with displacement degrees of freedom or acoustic pressure degrees of freedom. They are specified as described in “Acoustic loads,” Section 27.4.5. If the incident wave field includes a reflection off a plane outside the boundaries of the mesh, this effect can be included.

Electric fluxes

Surface-based electric fluxes are available for piezoelectric elements. They are specified as described in “Piezoelectric analysis,” Section 6.6.3.

**Load ID (*DSECHARGE):** ES^{(S)}**ABAQUS/CAE Load/Interaction:** **Surface charge****Units:** CL^{–2}**Description: **Prescribed surface charge on the element surface.

Distributed electric current densities

Surface-based electric current densities are available for coupled thermal-electrical elements. They are specified as described in “Coupled thermal-electrical analysis,” Section 6.6.2.

**Load ID (*DSECURRENT):** CS^{(S)}**ABAQUS/CAE Load/Interaction:** **Surface current****Units:** CL^{–2}T^{–1}**Description: **Current density on the element surface.

Output is in global directions unless a local coordinate system is assigned to the element through either the section definition (“Orientations,” Section 2.2.5) or an element property assignment (“Assigning element properties on an element-by-element basis,” Section 21.1.5), 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 Manual, for details. For regular axisymmetric elements, the local orientation must be in the –*z* plane with being a principal direction. For generalized axisymmetric elements with twist, the local orientation can be arbitrary.

Stress, strain, and other tensor components

Stress and other tensors (including strain tensors) are available for elements with displacement degrees of freedom. All tensors have the same components. For example, the stress components are as follows:

S11 | Stress in the radial direction or in the local 1-direction. |

S22 | Stress in the axial direction or in the local 2-direction. |

S33 | Hoop direct stress. |

S12 | Shear stress. |

S11 | Stress in the radial direction or in the local 1-direction. |

S22 | Stress in the axial direction or in the local 2-direction. |

S33 | Stress in the circumferential direction or in the local 3-direction. |

S12 | Shear stress. |

S13 | Shear stress. |

S23 | Shear stress. |

Heat flux components

Available for elements with temperature degrees of freedom.

HFL1 | Heat flux in the radial direction or in the local 1-direction. |

HFL2 | Heat flux in the axial direction or in the local 2-direction. |

Pore fluid velocity components

Available for elements with pore pressure degrees of freedom, except for acoustic elements.

FLVEL1 | Pore fluid effective velocity in the radial direction or in the local 1-direction. |

FLVEL2 | Pore fluid effective velocity in the axial direction or in the local 2-direction. |

Mass concentration flux components

Available for elements with normalized concentration degrees of freedom.

MFL1 | Concentration flux in the radial direction or in the local 1-direction. |

MFL2 | Concentration flux in the axial direction or in the local 2-direction. |

Electrical potential gradient

Available for elements with electrical potential degrees of freedom.

EPG1 | Electrical potential gradient in the 1-direction. |

EPG2 | Electrical potential gradient in the 2-direction. |

For heat transfer applications a different integration scheme is used for triangular elements, as described in “Triangular, tetrahedral, and wedge elements,” Section 3.2.6 of the ABAQUS Theory Manual.