Axisymmetric (cylindrical) materials are included in Tensor Mechanics for revolved geometries and assume symmetrical loading. These 'strain calculator' materials compute the strain within the appropriate coordinate system and rely on specialized AxisymmetricRZ kernels to handle the stress divergence. This material supplies material properties with all derivatives required to form an exact Jacobian.

The axis of symmetry must lie along the -axis in a or cylindrical coordinate system. This symmetry orientation is required for the calculation of the residual ADStressDivergenceRZTensors for the residual equation and the germane discussion.

The `AxisymmetricRZ`

material is appropriate for a 2D simulation and assumes symmetry revolved about the z-axis. A 2D formulation of an appropriate simulation problem can reduce the simulation run time while preserving key physics. Axisymmetric simulations are appropriate to problems in which a solid is generated by revolving a planar area about an axis in the same plane.

`RZ`

Coordinate TypeThe coordinate type in the `[Problem]`

block of the input file must be set to `coord_type = RZ`

.

## Axisymmetric Strain Formulation

The axisymmetric model employs the cylindrical coordinates, , , and , where the planar cross section formed by the and axes is rotated about the axial axis, along the length of the cylinder, in the direction. The cylindrical coordinate system strain tensor for axisymmetric problems has the form

(1)

where the value of the strain depends on the displacement and position in the radial direction

(2)

Although axisymmetric problems solve for 3D stress and strain fields, the problem is mathematically 2D. Using an appropriate set of geometry and boundary conditions, these types of problems have strain and stress fields which are not functions of the out of plane coordinate variable. In the cylindrical coordinate axisymmetric system, the values of stress and strain in the direction do not depend on the coordinate.

The axisymmetric system changes the order of the displacement vector from , usually seen in textbooks, to . Take care to follow this convention in your input files and when adding eigenstrains or extra stresses.