Note: The contact interface "sliding-tension-compression" becomes available starting with FEBio 1.5.2.

FEBio is a 3D finite element modeler which, as of the writing of this tutorial, does not have 2D axisymmetric elements. This tutorial shows how to simulate an axisymmetric analysis using only one sliver of elements along the circumferential direction.

For illustration, consider a cylindrical elastic solid subjected to a uniform compressive pressure on the top face and a fixed bottom face. This analysis may be performed on the full geometry:

DiskFull.jpg

More commonly, using the x-z and y-z coordinate planes as symmetry planes, the analysis may be performed on a quarter geometry (DiskUniformPressureQuarter.feb):

DiskQuarter.jpg

However, significant computational efficiency would be gained by performing the analysis on a single sliver or wedge portion of the axisymmetric problem (DiskUniformPressureSliver.feb):

DiskSliver.jpg

To perform the latter analysis, the cross-sections on either side of the wedge need to be defined as planes of symmetry.

- The face lying in the x-z plane may be constrained as usual (fixed along y).
- If the geometry includes an edge on the z-axis (as in this example), fix the x and y displacements for that edge.
- To constrain the face lying at an angle to the x-z plane, create a planar surface in the x-z plane and rotate it about the z axis by an angle equal to the wedge angle. Define a rigid body material and attach it to this symmetry plane, then fix all six of its degrees of freedom.
- Define a contact interface of type "sliding-tension-compression" between the symmetry plane and the mating wedge cross-section (single pass, slave surface on the wedge, master surface on the rigid plane, auto-penalty on, penalty=1e4) and make sure to turn on the tension flag (to allow this sliding interface to sustain tension).
- Apply all other relevant boundary conditions on the wedge and run the analysis.

Check the attached file DiskUniformPressureSliver.feb for more details. Even though a contact analysis needs to be performed on the rotated symmetry plane, the analysis runs much faster than the quarter-symmetry model.

Notes:

- Make sure that the outward normal to the symmetry plane faces opposite to the outward normal of the mating wedge cross-section.
- In principle, the smaller the wedge angle, the greater the fidelity of the model to true axisymmetry. As the wedge angle is decreased, consider increasing the contact penalty to ensure accurate enforcement of the symmetry requirement.